Date: Thu, 24 Oct 96 12:14:13 -0500 (CDT) From: cutter@pkmfgvm4 To: External Network Bboard Subject: Heisenberg Uncertainty Principle In a discussion with a colleague the HUP came up. I agreed that its usual interpretation was based on the rationale that one could not measure something without disturbing it. However, I seem to recall having read somewhere that there was a deeper cause/rationale for HUP, to the effect that HUP would still apply even if one could make accurate simultaneous measurements of complementary properties (like position and momentum). Can someone correct my understanding and/or point me to a source. It's possible I may be confusing the no-measurement-without- disturbance argument with the particle-wave-duality argument, which I would consider to be a deeper conceptual basis. Larry Cutter =================================================================== Date: Thu, 24 Oct 96 17:21:18 -0500 (CDT) From: czar@owgvm3 To: External Network Bboard Subject: Heisenberg Uncertainty Principle Ref: Append at 17:14:13 on 96/10/24 GMT (by CUTTER at PKMFGVM4) The "deep" uncertainty principle asserts that there must at least a minimum amount of spread associated with complementary characteristics. The quantum-mechanical classic is position and velocity. This spread has come to be known as "uncertainty", but this is in a technical sense, not in the sense of uncertainty due to error. The "spread" principle asserts that a particle cannot be both point- like (and thereby have single position) and move with single velocity-- we can't measure position and velocity simultaneously with arbitrary position simply because nature doesn't allow particles to behave in such a way that they have both an exact postion and velocity! There are analogies in the classical, macroscopic world. For example the duration and bandwidth of a signal obey an uncertainty principle; they are measures from complementary domains (time and frequency) and the product of a signal's duration and its bandwidth must be greater than a minimum value that may be established from first princtiples. For example, short pulses have large bandwidth, and narrow bandwidth implies long pulses (fast rise and fall times have lots of high frequency content; if you have energy at low frequencies only, then the thing can't change very quickly). The signal duration defines an aperture that bounds a time interval for when the signal arrives. The bandwith defines an aperture that bounds the range of frequencies at which the signal exists. Note that this has nothing to do with measurement errors; a signal simply doesn't *have* both a sigle, discrete time of arrival and single frequency. In general, the signal is smeared out somewhat in both domains. For example, consider the pathological cases of a delta function and a sine wave. A delta function has zero duration, but infinite bandwidth. A sine wave has zero bandwidth, but infinite duration. Now let's relate this to measurement of time and frequency: the implication is that to measure time of arrival of a signal accurately, on must have a very large frequency aperture. Conversely, to measure the signal frequency accurately, one must have a very large time aperture. The uncertainty principle does not allow us to have simultaneously large time and frequency apertures, and we cannot measure time and frequency simultaneously with arbitrary accuracy. If we wanted to measure the time of arrival of a delta function, the measurement uncertainty would be proportional to the reciprocal of the device's bandwidth. Similarly, if we want to measure the frequency of a sine wave, the frequency accuracy would be proportional to the reciprocal of the observation time. These limitation are are due to practical limitations of our measurement approach, not fundamental limits of nature. It's easy to think from this argument that the uncertainty principle is a limitation on measurement ability. The reality is twofold: first, the measurement limitation arises as consequence of the deeper time-frequency uncertainty principle; but secondly, even setting this measurement limitation aside, uncertainty principle inists that signals simply don't *have* both exact time of arrivals and exact frequencies. Back to quantum physics. Effectively, the position-velocity uncertainty principle fundamentally says that no particle can simultaneously be both point-like and moving with single velocity; instead, the particle must be smeared out in position as well as in velocity, at least to some minimal amount so that the product of its size and velocity spread is larger than some nonzero minimum, with that minimum defined by the unit systems and definitions of "size" and "velocity spread". And secondly, the uncertainty principle says that as a consequence our ability to simultaneously measure position and velocity will be limited by the contradictory need to have small time aperture for position measurement ("where is it *now*") and large time aperture for velocity measurement ("watch it for a while and see where it's going") Steve Czarnecki