Uncertain about Heisenberg's Principle

Factual Questions
1

IANA physicist. I didn’t even have a high school physics course, so please be gentle with me.

As I understand it, H. principle is that you can either know exactly where an object is, or how fast it’s going, but not both at the same time. Am I right so far?

But, if I were to pinpoint an object’s exact location, and then determine its velocity and direction (assuming everything remains constant) I would be able to determine the precise instant the object reaches a predetermined point. This is how scientists got Voyager to fly by Jupiter, Saturn, Uranus and Neptune, right? (Or, on a more earthly level, knowing when to open a parachute when free-falling).

So, how is it theoreticaly impossible but practical in the real universe?

2

Because the photons required to actually detect an object the size of Jupiter affect it in the smallest way possible, while they affect subatomic particles (which is ALL that HUP pertains to) in much more profound ways, because their sizes are much closer together. It’s the difference between throwing a baseball at the Earth and throwing it at a softball.

3

To make JayJay’s point even clearer, think of taking a picture of a basketball by means of throwing other basketballs at it. The more direct the hit, the more accurate your will be about about its position, but, as you just knocked it away from its path, you know very little about the speed or direction it was moving in. However, if you barely glance one basketball with the other, you’ll have a better read on the target’s speed/direction, but you’ll know far less about its exact position.

4

For Heisenberg’s uncertainty principle to be relevant, you need to be working with atomic or subatomic precision. When you’re measuring an object like Voyager, it isn’t really sensible to talk about position or velocity at that scale, as the 10^25 or so atoms in it are all bouncing around with different exact positions and completely different velocities (since it’s not at absolute zero).

Measuring to pin point accuracy is incredibly sloppy for this purpose, you need to get (IIRC) about a million times more accurate before you’re certain enough of the location to worry about the HUP. And people measuring Voyager’s position don’t actually measure it to anywhere near pinpoint accuracy, the most precise that I know of is meter precision while it’s around Saturn. Which is really impressive, but around a dozen orders of magnitude (ten to the twelfth power) too large for HUP to be noticeable. Same thing with knowing when to open a parachute or similar macroscopic tasks, skydivers don’t use position measurements that are better than meters under normal circumstances.

5

There’s a simple-minded explanation that you might have learned in your high-school physics class, which is substantially what several posters above have written. It’s also wrong. This explanation suggests that you need to bounce photons off a particle to observe it, and if the observed particle is really small, then bouncing photons off of it will knock it around and mess up whatever you were measuring.

The implication is that a particle, like an electron, actually has an exact position and velocity at every point in time, but that you just can’t measure them both.

That isn’t what Heisenberg’s Uncertainty Principle is all about. HUP states that such a particle really truly doesn’t have both a precise position and a precise location all at once. The more precisely you measure one, the less precisely the other measure even exists at all.

Yeah, that’s weird. Quantum physics is weird. Get used to it.

Here is a better explanation:

6

I’m not a physicist either, but here’s the explanation I got. You can measure it over time, or at a single instant. Measuring over time gives you it’s direction and velocity, but is very vague about it’s final position. An instaneous measurement will tell you precisely where it is, but nothing about it’s direction or velocity. The ‘measurement over time’ isn’t a video, it’s not a series of measurements. It’s more like a single photograph with a really long exposure time.

As I said, that’s probably wrong. However, we can now test the adage ‘the fastest way to get a question answered on the internet is to post a wrong answer’.

7

This is something that you are going to find with any wave function. It has nothing to do with photons bouncing off of a “particle”, partly because there isn’t a “particle” there in the first place. QM is not intuitive and you make a lot of mistakes by projecting the macro world onto the micro (like assuming an electron is a “particle”). Suffice it to say that anything that is governed by a wave function is going to have variables like this that are impossible to determine precisely. The more accurately you know the position, the more uncertain you are about the velocity and vice versa.

8

What is the difference between saying the position and momentum cannot both be measured exactly, and saying that the precise momentum and position simply don’t exist? I contend that those ideas are the same thing.

Like this quote from another context: “the invisible and the nonexistent look very much alike.”

9

just to return to the “real world” examples we are familiar with:

a spaceprobe or a skydiver are VERY large compared with subatomic particles (and more importantly, Planck’s constant). If you could somehow measure position and velocity of these things to within a micron in space and micron/sec (that is, to a size smaller than a red blood cell, which is about 8 microns), you still would be quite far from the theoretical limits imposed by Heisenberg’s Uncertainty principle.

10

Oh, please, that’s like saying that, if no one sees it, the tree doesn’t fall.

11

I recently read David Lindley’s Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science. It’s completely non-technical but approaches the questions involved in quantum matters, including uncertainty, the way that the physicists involved had to overcome them. In doing so, he gives a much more nuanced view of what uncertainty really means than most accounts. It’s a much larger and more complex subject that just position and momentum. The subject of what a measurement is and the role it plays in modern physics is, an almost philosophical issue that haunted the thinking of Bohr and others, is the deep answer to the question. He does a better job of framing the issue, if not answering it, than most popular writers.

12

First off let’s look at the equation in question:

σ[sub]x[/sub]σ[sub]p[/sub] >= ħ/2

so the standard deviation in position multiplied by the standard deviation of the momentum must be bigger than ħ/2 (~5x10[sup]-35[/sup])

So if σ[sub]x[/sub] tends to 0 what happens to σ[sub]p[/sub]? It has to go through the roof.

13

OK, it’s clearly impossible for me to grasp the physics of this because I’m not grounded in the metaphysics behind matter and energy (and measurement, for that matter.) Can anyone recommend a book that’s set at a very, very basic level to get me started?

And please don’t recommend Hawking’s A Brief History of History of Time. I was completely lost before I got to Chapter 3.

14

Well, through the roof of a mouse’s dollhouse.

15

To answer your original question: it’s all about the scale. If you think about atoms as people, this becomes very intuitive. We can predict how a large group of people would move through a space; predicting the path you, Kunilou, would take through that space is impossible. In a large group some people will drift left; some right, others straight down the middle; some will veer back and forth, ducking around people to get through faster; others will meander about, pausing to chat or take in the sights; however, those variations balance each other out, and the path of the entire group can be predicted (and will even be worn into the ground if this is ‘many over time’ group (as opposed to a mob moving through all at once)).

Try this: Uncertainty principle - Simple English Wikipedia, the free encyclopedia . Also, append “for dummies” to any topic when searching for more novice-friendly results.

Finally, I’ll paraphrase a prior poster: if quantum mechanics doesn’t hurt your brain, you’re not understanding it.

16

The physical predictions/implications of the HUP are best understood in terms of taking a bunch of particles that have been prepared so they are in “identical” (quantum) states and then measuring the position of some and the momentum of others. You should expect to see the uncertainty relationship as a statistical relationship in the results of those measurements. As each particle is assumed to be in an identical state the HUP can be seen as distinct from the observer effect whereby taking one measurement influences the results of feature measurements.

17

Let me try a really simple phrasing: The level of uncertainty in measuring position and velocity for the HUP is much, much smaller than the amount of uncertainty used in measurements outside of scientific experiments measuring very small things. Localizing position to a pinpoint is still around a million times too large for the HUP to even be a plausible concern. And it’s not possible for an every day object to have a position measured that narrowly, because when you start to look closely enough to see that they’re made of molecules, you see that what looked like a solid object is actually a bunch of molecules bouncing around rapidly.

18

Psst. Post #11.

19

The uncertainty principle says the more you know about the position of something, the less you know about its momentum, and vice versa. This is true for everything from subatomic particles to aircraft carriers. This uncertainty can be significant for really small stuff like electrons and neutrinos. However, the amount of uncertainty for large, macro scale objects is tiny compared to the size of the object—so small that it’s insignificant for any practical problems (such as getting a space probe to fly past a set of planets, or knowing when to open a parachute). At that level, the uncertainty is probably even unmeasurable.

20

A better name, to some extent at least, is Heisenberg’s indeterminacy principle, because otherwise people confuse it with the uncertainties of measurement.

And I know people have already touched upon this, but I think the OP would benefit from examining the assumptions in their statements, such as in:

“determine the precise instant the object reaches a predetermined point”

And see what that leads to.

What do you mean by precise? If it’s a non-quantum mechanic indivisible instant, that cannot be achieved in practice. You always have a timing device with some level of uncertainty. We can currently make that uncertainty mindbogglingly small, but there’s always an end to the significant figures on the read out. If you’re measuring in nanoseconds, you could be more precise by measuring in picoseconds and so on.

And the same applies to “point”.

Now roughly speaking, the indeterminacy principle says that if I measure the position of, let’s say a baseball, with an accuracy of one micrometer, a small fraction of the diameter of a human hair, there is a fundamental limit to how accurately I can measure its momentum. So even if the baseball is just sitting on my experiment table, obviously not moving, there’s a range of possible speeds it could have.

So what is that range of momentums the baseball could have? It’s ridiculously small. We’re talking 0.0000000000and-then-more-zeros-lifetime-of-the-universe-to-move-an-inch type momentums.

But if you move to the level of atoms and subatomic particles, it starts to matter, and it becomes clear that it’s not just that we can’t measure these things, it’s that “particles” don’t actually have positions and momentums that are “precise”. Their fundamental natures are those of fuzzy wavepackets with all the weirdness that implies.