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**Anckzxik** · 09-09-2012, 01:00 PM

It is often assumed that Heisenberg's uncertainty principle applies to both the intrinsic uncertainty that a quantum system must possess, as well as to measurements. These results show that this is not the case and demonstrate the degree of precision that can be achieved with weak-measurement techniques.

The way I interpret this is that Heisenberg's uncertainty principle still applies to the intrinsic uncertainty and that the mathematics of quantum mechanics is unaltered by this result.

Werner Heisenberg's uncertainty principle, formulated by the theoretical physicist in 1927, is one of the cornerstones of quantum mechanics. In its most familiar form, it says that it is impossible to measure anything without disturbing it. For instance, any attempt to measure a particle's position must randomly change its speed.

I think a misunderstanding exists as to the way that a quantum system is disturbed by measurement. If one thinks that this disturbance acts like a noise, then one has misunderstood the HUP. Prior to measurement the quantum state is a superposition of the states corresponding to the measured result, and that the measurement simply selects one of those states. In the many-worlds interpretation, the other states of the superposition still exist as alternative classical realities, but this interpretational issue is unimportant to the principle that a state is being randomly selected rather than some randomising noise-like disturbance of the original quantum state.

Each shot only gave us a tiny bit of information about the disturbance, but by repeating the experiment many times we were able to get a very good idea about how much the photon was disturbed

More information can be obtained about a quantum state from multiple measurements of identical states than from a single measurement of that state. I suspect that by "weak measurement", the quantum operator associated with the measurement differs only slightly from the identity operator, and that the eigenstates of the weak measurement are not the same as the eigenstates of the full measurement. This means that the original quantum state is a superposition of different states to that of the full measurement and therefore the HUP is different for these measurements.

09-09-2012, 01:00 PM	#12
Anckzxik Join Date Oct 2005 Posts 408 Senior Member	It is often assumed that Heisenberg's uncertainty principle applies to both the intrinsic uncertainty that a quantum system must possess, as well as to measurements. These results show that this is not the case and demonstrate the degree of precision that can be achieved with weak-measurement techniques. The way I interpret this is that Heisenberg's uncertainty principle still applies to the intrinsic uncertainty and that the mathematics of quantum mechanics is unaltered by this result. Werner Heisenberg's uncertainty principle, formulated by the theoretical physicist in 1927, is one of the cornerstones of quantum mechanics. In its most familiar form, it says that it is impossible to measure anything without disturbing it. For instance, any attempt to measure a particle's position must randomly change its speed. I think a misunderstanding exists as to the way that a quantum system is disturbed by measurement. If one thinks that this disturbance acts like a noise, then one has misunderstood the HUP. Prior to measurement the quantum state is a superposition of the states corresponding to the measured result, and that the measurement simply selects one of those states. In the many-worlds interpretation, the other states of the superposition still exist as alternative classical realities, but this interpretational issue is unimportant to the principle that a state is being randomly selected rather than some randomising noise-like disturbance of the original quantum state. Each shot only gave us a tiny bit of information about the disturbance, but by repeating the experiment many times we were able to get a very good idea about how much the photon was disturbed More information can be obtained about a quantum state from multiple measurements of identical states than from a single measurement of that state. I suspect that by "weak measurement", the quantum operator associated with the measurement differs only slightly from the identity operator, and that the eigenstates of the weak measurement are not the same as the eigenstates of the full measurement. This means that the original quantum state is a superposition of different states to that of the full measurement and therefore the HUP is different for these measurements.
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