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Author Topic: Uncertainty in motion and location really a quantum effect?  (Read 3028 times)

Offline McKay

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Is it really a mysterious quantum effect that does not reconcile with what we are used to in our macroscopical lives? Or is it just a basic measurement property for any sized object?
I mean - if I take a photo of something moving fast relative to my camera shutter speed, there is going to be motion blur. Now, knowing the shutter speed (the exposure time of the image), I could calculate the speed of the moving object, but can you point a precise location of the object in the image.. ? It is blurred, there is some uncertainty.
That is, in fact, THE way to measure speed - fix the location at t0 and, later, at t1, then read the distance traveled in given amount of time.
If we just look at the object at t0 or t1 alone, we dont know how fast it is moving, but we know where it is in each moment of time..
We NEED that motion blur, that uncertainty to tell speed. I dont see anything quantum about this "uncertainty principle".
Can anyone explain?


 

Offline chiralSPO

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With an extremely fast shutter speed and very fine frequency (of light) resolution you could take a picture of an object (showing where it is) and its velocity relative to you (looking at the Doppler shift of the lift returned to you) without detecting any blur. This is THE way traffic police measure speed (they look at Doppler shift of microwaves/radio waves, but it's the same idea).

The uncertainty principle arises from the fact that there is no way to "observe" something without interacting with it. And that interaction necessarily changes the trajectory/position/energy etc. of whatever is being observed.

I will take this opportunity to address a common misconception about observation. Observation and interaction are exactly the same thing. There is no requirement for a human or consciousness or anything of that nature for observation--just interaction of the particle/wave of interest with another particle, wave field etc. For instance, the uncertainty principle become very important with very, very short laser pulses (duration/frequency uncertainty arises the same way as the position/momentum uncertainty). The shorter the laser pulse, the more uncertainty there is in the frequency (color) of light coming out, so much so that pulses on the order of femtoseconds can be thought of as "white light." In this way a "red" laser with not enough energy to excite an electron in a molecule (say it requires "green" light) can have a nonzero chance of causing that excitation if the photon only has a very, very short time in which it could interact with the molecule. No human observation is required here, it is the molecule that "observes" the light by interacting with it.

For macroscopic objects there is no apparent paradox because the degree of uncertainty is typically several orders of magnitude less than the size and speed of the object itself.
 

Offline dlorde

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It's worth noting that the 'Observer Effect' described above by chiralSPO is not the same as quantum uncertainty (Heisenberg Uncertainty Principle). There is an inherent uncertainty in the precision with which complementary variables (e.g. position & momentum) can be known, regardless of external influence from observation, due to the wave-like nature of quantum objects. This is the same quantum uncertainty that gives rise to zero point energy, the lowest energy a quantum system can have (it's 'ground state'), which is not zero, so no quantum object can be completely motionless.
« Last Edit: 25/04/2014 17:49:28 by dlorde »
 

Offline JP

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There is an inherent uncertainty in the precision with which complementary variables (e.g. position & momentum) can be known, regardless of external influence from observation, due to the wave-like nature of quantum objects.

This is also true of waves in general.  Uncertainty relations are inherent to waves and were known far before quantum mechanics came about.  If you try to construct a wave with a very narrow spread of some variable (for example, pass a laser beam through a pinhole to make it very narrow in space), the wave will spread out automatically in another variable (in this case, it will diffract and spread out in a wide range directions after passing through that slit).  This behavior is due to wave mechanics and can be observed anywhere you have waves: water, sound, light, etc.

Quantum mechanics is unique in that a single particle is ALSO described by a wave.  The fact that a quantum wave spreads out if you try to precisely localize its position means that that particle has very poorly determined momentum if you measure its position precisely.
 

Offline McKay

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With an extremely fast shutter speed and very fine frequency (of light) resolution you could take a picture of an object (showing where it is) and its velocity relative to you (looking at the Doppler shift of the lift returned to you) without detecting any blur. This is THE way traffic police measure speed (they look at Doppler shift of microwaves/radio waves, but it's the same idea).

The uncertainty principle arises from the fact that there is no way to "observe" something without interacting with it. And that interaction necessarily changes the trajectory/position/energy etc. of whatever is being observed.

I will take this opportunity to address a common misconception about observation. Observation and interaction are exactly the same thing. There is no requirement for a human or consciousness or anything of that nature for observation--just interaction of the particle/wave of interest with another particle, wave field etc. For instance, the uncertainty principle become very important with very, very short laser pulses (duration/frequency uncertainty arises the same way as the position/momentum uncertainty). The shorter the laser pulse, the more uncertainty there is in the frequency (color) of light coming out, so much so that pulses on the order of femtoseconds can be thought of as "white light." In this way a "red" laser with not enough energy to excite an electron in a molecule (say it requires "green" light) can have a nonzero chance of causing that excitation if the photon only has a very, very short time in which it could interact with the molecule. No human observation is required here, it is the molecule that "observes" the light by interacting with it.

For macroscopic objects there is no apparent paradox because the degree of uncertainty is typically several orders of magnitude less than the size and speed of the object itself.

Well, the Doppler shift would tell you how fast the object WAS moving when the picture was snapped, no? Since it takes time for the shifted photon to get  back. Actually, all the light that makes it possible to see the object itself is from the past.
So we know from the picture where the object was, how fast it was moving, but can only guess where it is at the time of the photo snap. We could calculate its location from its now known speed and trajectory, but perhaps the object accelerated in one direction or another, the measurement changed its speed and trajectory? Isn't there an uncertainty? Small one, yes, since photons do not push macroscopic objects much, but still.


The reflected EM radiation using Doppler shift analysis shows the speed at which the object is moving after the emission/ reflection of the measuring photon or before the emission?


Duration of a laser pulse only makes sense if there is more than one photon in the pulse, otherwise the length of the pulse would be exactly the wavelength of the photon?

In a physics lab I once saw a laser that produced very high intensity laser pulses to excite the atoms of a fluorescent material with the cache that the frequency of the laser was lower than the required frequency for excitement - what happened was two photons managed to hit an electron in such a short time interval (at "the same time"), that they ware able to excite the electron with their combined energy..

 
 

Offline McKay

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Measurment of a photon takes time, doesnt it?  Neasuring a photon is measuring how the EM field changes with time.
Does that mean when looking at the dopler shifted photon we are stil looking at a tine t0 and t1 abd deducing the frequency from that time interval? And from that interval, ultimetly, the speed of the object?
 

Offline JP

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Measurment of a photon takes time, doesnt it?  Neasuring a photon is measuring how the EM field changes with time.
Does that mean when looking at the dopler shifted photon we are stil looking at a tine t0 and t1 abd deducing the frequency from that time interval? And from that interval, ultimetly, the speed of the object?

That's basically a statement of the energy-time uncertainty relationship for classical light.  If you take an arbitrarily short time interval, you can't be sure of the frequency of the light (you would want to see the sinusoidal oscillations to determine its frequency).  If you take long time interval, you can be sure of the frequency.  So either you have good time resolution and poor frequency resolution or poor time resolution but good frequency resolution.  And that's purely classical--it holds for example in signal analysis when you're dealing with continuous waves, not particles.
 

Offline JP

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The best way I've found to get the uncertainty relationship is to understand 2 key concepts.

1) Diffraction--if I send a nice clean plane wave through a tiny slit, it will spread out.  This is a key property of waves (see the images here) http://en.wikipedia.org/wiki/Diffraction#Single-slit_diffraction

2) Particles in quantum mechanics are measured as point particles, but in between measurements, they behave like waves (in that the waves represent the probability of measuring them at points).  In fact, the best we can do to predict the results of future measurements is to compute the probabilities by modeling these probability waves.  (There are other interpretations of the mathematics, but they all predict the same results).

Putting these together, you can imagine a setup that takes a single particle (or a stream of particles) all going in one direction.  Their waves all move together in one direction.  We try to figure out where a particle is in time by passing it through a narrow slit.  Any particle coming out the other side had a very precise location (within that slit).  But if we now ask which way the particle is moving, we can't say for sure--the wave coming out of the slit has diffracted and is going in a range of directions.  Because this wave tells us the probability of finding a particle, we have to say we're uncertain about the direction (velocity/momentum) in which the particle has traveled. 

The slit is just one example of a measurement process--you can have other measurement processes that try to localize the particle within space, but they all amount to the same thing.  If we have some window in space and we know the particle was there, the same calculation as diffraction says that we can only know direction of the particle (velocity/momentum) to within some particular range.
 

Offline chiralSPO

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It's worth noting that the 'Observer Effect' described above by chiralSPO is not the same as quantum uncertainty (Heisenberg Uncertainty Principle). There is an inherent uncertainty in the precision with which complementary variables (e.g. position & momentum) can be known, regardless of external influence from observation, due to the wave-like nature of quantum objects. This is the same quantum uncertainty that gives rise to zero point energy, the lowest energy a quantum system can have (it's 'ground state'), which is not zero, so no quantum object can be completely motionless.

As I understand it there is little difference between the inherent Uncertainty and the observer effect. There are some observer effects that can be avoided, and the inherent uncertainty is the limit of least interference with that which is being measured.

Essentially any value that one would care to know can be calculated from the wave equation and the operator associated with the value that one wants to know. One can do the math on a hypothetical system with no actual observation taking place (and nothing to be observed), and still arrive at the same conclusion about uncertainty, but I would argue that applying the momentum operator or the position operator, or whichever operator one wishes is equivalent to making that observation. A wave doesn't have an "actual, exact" position or momentum, these are only properties that arise through the interaction of the wave with something else.
 

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