Measurement disturbs the system.

[jewbinson]

"Measurement disturbs the system."

Okay so I explained the uncertainty principle to my non-scientist friend, and he came up with a basic thought experiment.

I know there is something wrong with it, so I read paragraph 8 from here: http://www.oberlin.edu/physics/dstyer/TeachQM/misconnzz.pdf

However, can someone clarify what the underlying idea of the uncertainty principle, if it is not the fact that "measurement disturbs the system".

"In more detail, this misconception holds that each particle really does have denite values for both position and momentum, but these denite values cannot be determined because measurement of, say, a particle's position alters the value of its momentum."

Is it true that a particle in QM has definite position and/or momentum at a particular time T?
If so, what IS wrong with the above quotation?

I might post the thought experiment if I don't fully understand replies and still need help understanding why the thought experiment doesn't work IRL.

Thanks

 

[xts]

Is it true that a particle in QM has definite position and/or momentum at a particular time T?
If so, what IS wrong with the above quotation?

No, that is not true (thus the quotation is perfectly ok). It makes no sense to speak about particle position and momentum at the same time (with respect to precision - of course it makes sense to say that your car stays still while parked on your driveway). Assumtion that the particle has both those values defined (not known, just defined) leads to paradoxes and conclusions contradicting the observations.

I might post the thought experiment if I don't fully understand replies

Do it!

 

[nonequilibrium]

Hello.

Assumtion that the particle has both those values defined (not known, just defined) leads to paradoxes and conclusions contradicting the observations.

Can you go into more detail?

 

[jewbinson]

Wait, I thought electrons (for example) DO have a definite position and momentum at a particular time T.

Let's concentrate on just one of these for the moment. I thought that position simply cannot be determined. So for example you have your cloud of probability for the position of a particle because you are forbidden to determine precisely where it is without measuring it, but at each moment it DOES have a position, it isn't just a cloud of probability. Is this still wrong?? Now I think about it this doesn't make much sense, but I am confused / unsure about things.Now I don't know how electrons and photons interact, but let's say they "stick" to electrons and when you look at electrons, the photons are "released" from the electrons. I don't know how else they detect electrons...

[PLAIN]http://img685.imageshack.us/img685/5434/diagram1k.jpg

In the diagram above, we pretend we are in a dark room and the only thing is an electron and two photons and no external interference. The electron starts with a definite momentum and velocity (it comes from the bottom left and moves up and right). There are two photons "sticking" to the electron. Now our "eye" - which is not really our eye, but represents our measuring devices - can measure the mass-energy of the incident photon, as well as it's momentum and direction.

Now the "electron and remaining photon" is a free particle not under the influence of gravity (assumed), and so travels in a straight line at a constant speed (Newton's 1st Law).

Soon after, we look at the electron again and the second photon falls into our eye. We take the same measurements as before and we then can determine precisely where the electron was when we first measured it, and precisely where it is now.

Edit: I just realized we cannot measure the time taken for the first photon to reach our eye because that would mean we would know the position of the electron to begin with. So maybe we need to do this with 3 photons for it to work.

 

[xts]

@Mr.Vodka
Sure. The most common explanation is double slit experiment, which cannot be simply explained under assumption that paths of particles have any meaning.
Of course, you may go into weirdness of Many Words or Bohmian pilot waves, but it is up to your methaphysical taste if those constructs are more appealing than resignation from definite position when it is not measured.

 

[xts]

@Jewbinson - you may measure positions of your electron multiple times, every time getting some value (within some assumed accuracy). But those points won't form a straight line. More precisely you measure position - more curved the "trajectory" will be. So if you just measured the position, you may not predict next position - thus it makes no sense to say what is a direction of electron path. Direction is simply related to momentum - it is a line parallel to momentum vector.

 

[jewbinson]

If we have 3 photons instead of 2 we can solve the system and we will know the position and momentum of the electron at each of the 3 different times

 

[xts]

No.
You could know positions at 3 different times. You may repeat that 1000 times. But those 3 (or 1000) points do not form a straight, uniform line. Knowing 999 first points, you may not predict where will the 1000th one be.

 

[nonequilibrium]

Sure. The most common explanation is double slit experiment, which cannot be simply explained under assumption that paths of particles have any meaning.
Of course, you may go into weirdness of Many Words or Bohmian pilot waves, but it is up to your methaphysical taste if those constructs are more appealing than resignation from definite position when it is not measured.

I don't want to advocate any specific interpretation, but I do like to be exact, so would you agree if I were to rephrase your quote

Assumtion that the particle has both those values defined (not known, just defined) leads to paradoxes and conclusions contradicting the observations.

to

Assumtion that the particle has both those values defined (not known, just defined) and moves according to the laws of Newton leads to paradoxes and conclusions contradicting the observations.

?

 

[jewbinson]

No.
You could know positions at 3 different times. You may repeat that 1000 times. But those 3 (or 1000) points do not form a straight, uniform line. Knowing 999 first points, you may not predict where will the 1000th one be.

So in outer space with no external force a free particle does not move in a straight line? Because that is an assumption of the experiment which I mentioned.

 

[nonequilibrium]

So in outer space with no external force a free particle does not move in a straight line? Because that is an assumption of the experiment which I mentioned.

I think questions like this are hard (impossible?) to answer, cause it uses concepts that simply are not part of the quantum formalism (but are part of some interpretations; as such answers exist, but are dependent on the interpretation)

Frustrating, I know.

 

[jewbinson]

So what is the quantum mechanical equation for an electron moving through empty space - is THIS is SE for a free particle? Because if so, things are starting to click in my brain...

 

[nonequilibrium]

is THIS is SE for a free particle

Can you rephrase? I don't understand.

If you're asking if it's given by the Schrödinger equation: then the answer is yes.

 

[jewbinson]

typo...i meant "is this the SE for a free particle?"

Okay, so basically Quantum Mechanics describes the cloud of probability of different particles and the consequences. Other things like whether or not a particle has definite position and other observables is open to interpretation. Correct?

 

[nonequilibrium]

Indeed, for me it goes even further: I'd say even the meaning given to a number on a position measuring apparatus is open to interpretation. After all, what does "the position of a particle" mean if you don't have a particle?

For as far as I can see, the only use the word "particle" seems to have in the quantum formalism is to determine on how many variables your wave function depends...

 

[jewbinson]

Well the point is that we are dealing with a system based on "clouds", or as most people would say, "probabilities". The point is that the main object in our system is not a dot, but a cloud itself, or not necessarily a cloud, but something that can be interpreted as a cloud...

 

[StevieTNZ]

No.
You could know positions at 3 different times. You may repeat that 1000 times. But those 3 (or 1000) points do not form a straight, uniform line. Knowing 999 first points, you may not predict where will the 1000th one be.

Does the particle travel between two certain points (i.e. the position found at time1, and the position found at time2), or is more like the particle was found there at time1, then it jumps to the new position at time2 without going inbetween?

 

[xts]

Assumtion that the particle has both those values defined (not known, just defined) and moves according to the laws of Newton leads to paradoxes and conclusions contradicting the observations.

The assumption about mere existence of "path" leads to paradoxes. Take double slit experiment performed with single electrons (photons, whatever else) at a time. If you insist that electrons have defined paths, you could divide (just in set theory sense, you don't need to tag individual events to which class they belong) events into two classes: those going through left slit and those going through right one. The pattern created by all events should be a sum of patterns made by L and R classes. We know what pattern is created if only one slit is open. Experimental pattern is different than sum of patterns with one slit open. So - if you want to say that "electron passed left slit" you must accept that behaviour of the "electron traveling through left slit" is magically affected at a distance by opening or closing the right slit.

So in outer space with no external force a free particle does not move in a straight line? Because that is an assumption of the experiment which I mentioned.

As above - it makes no sense to use the term "path" regarding the particle. The particle may be observed at some point (rather some area), but between observations "path" makes little sense.
You may also create lots of experiments in which the straight line between source and detector is blocked, but particles are still observed.

Does the particle travel between two certain points (i.e. the position found at time1, and the position found at time2), or is more like the particle was found there at time1, then it jumps to the new position at time2 without going inbetween?

If any I would rather prefer the second view. Personally, I like most Zeilinger's approach: we use the word "particle" only regarding the very moment of detection or emission. In between we should speak about evolution of the wavefunction, but not about particle.

 

[Ken G]

So - if you want to say that "electron passed left slit" you must accept that behaviour of the "electron traveling through left slit" is magically affected at a distance by opening or closing the right slit.

Yet this is just what Bohmian mechanics asserts. Remember, we can generalize Arthur C. Clarke's "any sufficiently advanced technology is indistinguishable from magic" to "any physical effect we don't understand is indistinguishable from magic." I believe Bohm showed that quantum mechanics does admit the interpretation that a particle does always have a definite position and momentum, but it requires adding another layer to the theory, it requires a "pilot wave" to shepherd the various possible trajectories into acting as though they were indeterminate about those quantities if one can't see what the pilot wave is doing. Of course, a more standard interpretation of the situation is that if you can get rid of the pilot wave by invoking indeterminacy, and the pilot wave has no measurable consequences, then this is what you should do, and that's what you are doing. But there is no observation that tells us "the particle does not have a definite but unknown position and momentum at any given time."

As above - it makes no sense to use the term "path" regarding the particle. The particle may be observed at some point (rather some area), but between observations "path" makes little sense.

For the same reason, perhaps we should just say "there is no empirical evidence that it makes any sense to use the term 'path', and little but a kind of classical prejudice motivates its use in quantum mechanics. Of course, some view classical prejudices as a good idea, it really depends on personal preference."

You may also create lots of experiments in which the straight line between source and detector is blocked, but particles are still observed.

Yes, the notion of purely classical trajectories is definitely out the window. But pilot-wave guided trajectories are still possible, we just don't know and might not get to know.

 

[xts]

Of course, we may insist for "existence" of something which is fundamentally impossible to observe. It is a matter of taste, and metaphysical and religious formation.
I (like Carl Sagan) keep an invisible dragon in my garrage.

Bohmian mechanics preserves classic-like image of the particle of well defined parameters at the terrible expense of introduction of non-measurable 'real' entities, acting non-locally and backward in time, while still having problems to interprete some phenomena. It is a matter of taste if the 'reality' of particle between interactions is worth of such price. My Occamian nature definitely dislikes Bohm...

perhaps we should just say "there is no empirical evidence that it makes any sense to use the term 'path' [...]

Fully agreed!
My positivistic nature tells me that in science we should not speak about existence of anything which is not backed by empirical evidence...

 

[Ken G]

Bohmian mechanics preserves classic-like image of the particle of well defined parameters at the terrible expense of introduction of non-measurable 'real' entities, acting non-locally and backward in time, while still having problems to interprete some phenomena. It is a matter of taste if the 'reality' of particle between interactions is worth of such price. My Occamian nature definitely dislikes Bohm...

Mine too, I merely recognize he achieved something important in showing why we can't really say we know there is indeterminacy in the "actual reality." To me, all these differing interpretations are just a kind of caution to us that we're still pretty far from knowing the reality, if indeed it even makes sense to make that our goal.

Fully agreed!
My positivistic nature tells me that in science we should not speak about existence of anything which is not backed by empirical evidence...

It does seem to be the only way to remove opinion from the issue. But maybe that is itself only an opinion-- rationalists are quite rightly quick to point out that we have no empirical evidence that the only things that exist are what we have empirical evidence of! In other words, to be completely consistent, must the empiricist replace the last seven words of your statement with "except the observations themselves"?

 

[xts]

I am far from advocating Mach's extreme positivism ;) We just should keep common sense and be practical. It is convenient to speak, e.g. about electric field as about something real and it rarely may lead to paradoxes. We should just remember that 'electric field' is not something 'fundamentally real', but rather our mathemetical construct, resulting from Coulomb's experiments.
As we go into troubles with it, we don't cry being forced to throw it out, and switch to other view (exchange of virtual photons) to describe electric interactions.
Here we are in the same situation - our well established intuitions about reality of paths may be quite useful not only in common life, but also regarding particles. The 10 MeV electron in a tracking chamber has well defined path. But we shouldn't use that word when it leads into paradoxes, by bringing in all the baggage associated with 'existence'.

 

[StevieTNZ]

What happens if we measure a particle's momentum? Would that indicate a path the particle is traveling on? (I guess we'd need to add forces/interactions into the equation)

 

[xts]

If you measure the momentum, you may find the direction the particle comes from, but to measure it accurately, the aperture of your tool must be large - thus you don't know its path, as it could be shifted to left or right by significant displacement

That's a classical version of Wheelers experiment: in double slit, you may find accurate positions where particles hit the screen - or - you may use a telescope installed at the screen plane to see if the particle comes from left or rather right slit. But in order to measure the direction precisely enough, the aperture of your telescope must be bigger than distance between fringes.