there are no other variables of which we are ignorant. There is nothing in quantum theory that tells us how an indivisible photon particle navigates its way past the two slits. This doesnât necessarily mean that weâre missing something; that the theory is somehow incomplete. What it does mean is that the particle picture is not relevant here and we canât use it to understand whatâs going on. We use the wave picture instead and revert to the particle picture only when the wavefunction collapses and the photon is detected.
Figure 1 We can observe quantum particles as they pass, one at a time, through a two-slit apparatus by recording where they strike a piece of photographic film. Each white dot indicates that âa quantum particle struck hereâ. Photographs (a)â(e) show the resulting images when, respectively, 10, 100, 3,000, 20,000 and 70,000 particles have been detected. The interference pattern becomes more and more visible as the number of particles increases. From A. Tonomura et al., American Journal of Physics, 57 (1989) , pp. 117â20.
âWe have to remember that what we observe is not nature in itself but nature exposed to our method of questioning,â Heisenberg said.
This notion of the collapse of the wavefunction doesnât completely break the connection between cause and effect, but it does weaken it considerably. In the quantum domain if I do this, then that will happen with a certain probability. No certainty. Some doubt. Quantum events like the detection of a photon appear to be left entirely to chance.
Einstein didnât like it at all:
Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that He does not play dice. 8
The collapse of the wavefunction continues to plague the current authorized version of reality.
The uncertainty principle
According to Newtonâs mechanics, although I might not have the means at my disposal, I can have some confidence that I can measure with arbitrary precision the position and momentum of an object moving through space.
Imagine we fire a cannonball. The cannonball shoots out of the cannon with a certain speed and traces a parabolic path through the air before hitting the ground. It moves through space, passing instantaneously through a series of positions with specific speeds. Although here again I would need to figure out all the different variables at play (wind speed, the precise pull of earthâs gravity), there is nothing in principle preventing me from finding out what these are. After some computation, I produce a map of position and speed throughout the cannonballâs trajectory.
If I know the mass of the cannonball (which I can measure separately), I can calculate the momentum at each point in the trajectory, by multiplying together mass and speed at that point.
Once again, however, in quantum mechanics things are rather different. Quantum particles are also waves. Suppose we were somehow able to localize a quantum wave particle in a specific region of space so that we could measure its position with arbitrary precision. In the wave description, this is in principle possible by combining a large number of wave forms of different frequencies in a superposition (called a âwavepacketâ), such that they add up to produce a resultant wave which is large in one location in space and small everywhere else. Great. This gives us the position.
What about the momentum? Thatâs a bit of a problem. We localized the wave by combining lots of waves with different frequencies. This means that we have a spread of frequencies in the superposition and hence a spread of wavelengths. 9 According to French physicist Louis de Broglie, the wavelength of a quantum wave is inversely proportional to the quantum particleâs momentum. 10 The spread of
Figure 1 We can observe quantum particles as they pass, one at a time, through a two-slit apparatus by recording where they strike a piece of photographic film. Each white dot indicates that âa quantum particle struck hereâ. Photographs (a)â(e) show the resulting images when, respectively, 10, 100, 3,000, 20,000 and 70,000 particles have been detected. The interference pattern becomes more and more visible as the number of particles increases. From A. Tonomura et al., American Journal of Physics, 57 (1989) , pp. 117â20.
âWe have to remember that what we observe is not nature in itself but nature exposed to our method of questioning,â Heisenberg said.
This notion of the collapse of the wavefunction doesnât completely break the connection between cause and effect, but it does weaken it considerably. In the quantum domain if I do this, then that will happen with a certain probability. No certainty. Some doubt. Quantum events like the detection of a photon appear to be left entirely to chance.
Einstein didnât like it at all:
Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that He does not play dice. 8
The collapse of the wavefunction continues to plague the current authorized version of reality.
The uncertainty principle
According to Newtonâs mechanics, although I might not have the means at my disposal, I can have some confidence that I can measure with arbitrary precision the position and momentum of an object moving through space.
Imagine we fire a cannonball. The cannonball shoots out of the cannon with a certain speed and traces a parabolic path through the air before hitting the ground. It moves through space, passing instantaneously through a series of positions with specific speeds. Although here again I would need to figure out all the different variables at play (wind speed, the precise pull of earthâs gravity), there is nothing in principle preventing me from finding out what these are. After some computation, I produce a map of position and speed throughout the cannonballâs trajectory.
If I know the mass of the cannonball (which I can measure separately), I can calculate the momentum at each point in the trajectory, by multiplying together mass and speed at that point.
Once again, however, in quantum mechanics things are rather different. Quantum particles are also waves. Suppose we were somehow able to localize a quantum wave particle in a specific region of space so that we could measure its position with arbitrary precision. In the wave description, this is in principle possible by combining a large number of wave forms of different frequencies in a superposition (called a âwavepacketâ), such that they add up to produce a resultant wave which is large in one location in space and small everywhere else. Great. This gives us the position.
What about the momentum? Thatâs a bit of a problem. We localized the wave by combining lots of waves with different frequencies. This means that we have a spread of frequencies in the superposition and hence a spread of wavelengths. 9 According to French physicist Louis de Broglie, the wavelength of a quantum wave is inversely proportional to the quantum particleâs momentum. 10 The spread of
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