# Questions about the Uncertainty Principle **URL:** \ **Category:** Factual Questions\ **Created:** [April 11, 2014, 2:48pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875 "2014-04-11T14:48:39Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [April 11, 2014, 2:48pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/1 "2014-04-11T14:48:39Z")
I was watching a video lecture on quantum mechanics given by Leonard Susskind, wherein he was explaining the uncertainty principle. He pointed out by saying that the momentum of a photon is inversely proportional to its wavelength. For a wavelength on the order of magnitude as an electron, there will be enough momentum to knock it away such that you can’t say anything about it’s current position. He didn’t generalize it, however, such that I could get my head around what happens if the particle is really heavy, say 99% of the Planck Mass. Is it the case there that you know the position of the particle only to within one Planck Length and that if the particle is lighter, your measurement is even more imprecise? Also, once we hit the particle, can we say with arbitrary position where it _was_? Finally, won’t the photon that we struck it with be reflected and checking the wavelength of the reflected photon, can’t we work out the momentum we imparted to the electron? Thanks, Rob ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [April 11, 2014, 3:00pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/2 "2014-04-11T15:00:15Z")
I’m not sure. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [April 11, 2014, 3:08pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/3 "2014-04-11T15:08:42Z")
> [@njtt](#): > > I’m not sure. 😃 But kind of mean as first reply. As is this as second reply. OP: physics people will definitely come along… ---
**Author:** ![bup](https://avatars.discourse-cdn.com/v4/letter/b/6bbea6/32.png) [@bup](https://boards.straightdope.com/u/bup)\ **Post date:** [April 11, 2014, 3:12pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/4 "2014-04-11T15:12:41Z")
[del]I’m pretty sure that anything below a Planck \_\_\_\_ (length, mass, length of time) is meaningless in the quantum model. Therefore, the question cannot be answered by that model. But I am a theoretical physics dilettante. I welcome correction.[/del] From Wikipedia: _Unlike all other Planck base units and most Planck derived units, the Planck mass has a scale more or less conceivable to humans. It is traditionally said to be about the mass of a flea, but more accurately it is about the mass of a flea egg._ So nevermind. I don’t know at all. ---
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [April 11, 2014, 4:44pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/5 "2014-04-11T16:44:04Z")
The Planck Mass, for those that care but don’t already know, is the mass at which an elementary particle will become a black hole. ---
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [April 11, 2014, 4:46pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/6 "2014-04-11T16:46:07Z")
I also thought of another question. According to the U.P., you cannot know both the position and momentum of a particle to arbitrary precision at the same time. IIRC, there are other pairs of properties which are similar in nature. If that is so, what are they? Thanks, Rob ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [April 11, 2014, 6:38pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/7 "2014-04-11T18:38:12Z")
> [@sweeteviljesus](#): > > I also thought of another question. According to the U.P., you cannot know both the position and momentum of a particle to arbitrary precision at the same time. IIRC, there are other pairs of properties which are similar in nature. If that is so, what are they? > > Thanks, > Rob Time and energy are the major other complementary pair. This is what makes virtual particles possible. If the energy exists for a short enough period of time it can create particles that immediately wink out. Virtual particles have all sorts of implications for the way things work, but I’ll let a physicist discuss that. My memory (always a bad cite) tells me there are many other pairs. Ah, here’s the right Wikipedia page: [conjugate variables](http://en.wikipedia.org/wiki/Conjugate_variables). > [@](#): > > Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals of one another,[1][2] or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty in physics called the Heisenberg uncertainty principle relation between them. In mathematical terms, conjugate variables are part of a symplectic basis, and the uncertainty principle corresponds to the symplectic form. > > Examples > > There are many types of conjugate variables, depending on the type of work a certain system is doing (or is being subjected to). Examples of canonically conjugate variables include the following: > > • Time and frequency: the longer a musical note is sustained, the more precisely we know its frequency (but it spans more time). Conversely, a very short musical note becomes just a click, and so one can’t know its frequency very accurately.[citation needed] > • Doppler and range: the more we know about how far away a radar target is, the less we can know about the exact velocity of approach or retreat, and vice versa. In this case, the two dimensional function of doppler and range is known as a radar ambiguity function or radar ambiguity diagram. > • Surface energy: γdA (γ = surface tension ; A = surface area). > • Elastic stretching: FdL (F = elastic force; L length stretched). > > Derivatives of action > > In classical physics, the derivatives of action are conjugate variables to the quantity with respect to which one is differentiating. In quantum mechanics, these same pairs of variables are related by the Heisenberg uncertainty principle. > > • The energy of a particle at a certain event is the negative of the derivative of the action along a trajectory of that particle ending at that event with respect to the time of the event. > • The linear momentum of a particle is the derivative of its action with respect to its position. > • The angular momentum of a particle is the derivative of its action with respect to its orientation (angular position). > • The electric potential (φ, voltage) at an event is the negative of the derivative of the action of the electromagnetic field with respect to the density of (free) electric charge at that event.[citation needed] > • The magnetic potential (A) at an event is the derivative of the action of the electromagnetic field with respect to the density of (free) electric current at that event.[citation needed] > • The electric field (E) at an event is the derivative of the action of the electromagnetic field with respect to the electric polarization density at that event.[citation needed] > • The magnetic induction (B) at an event is the derivative of the action of the electromagnetic field with respect to the magnetization at that event.[citation needed] > • The Newtonian gravitational potential at an event is the negative of the derivative of the action of the Newtonian gravitation field with respect to the mass density at that event.[citation needed] ---
**Author:** ![Itself](https://avatars.discourse-cdn.com/v4/letter/i/d07c76/32.png) [@Itself](https://boards.straightdope.com/u/Itself)\ **Post date:** [April 11, 2014, 6:46pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/8 "2014-04-11T18:46:17Z")
> [@sweeteviljesus](#): > > I also thought of another question. According to the U.P., you cannot know both the position and momentum of a particle to arbitrary precision at the same time. IIRC, there are other pairs of properties which are similar in nature. If that is so, what are they? > > Thanks, > Rob Yes. Without going too far into the math, there are a couple of more general uncertainty relations. One relates time and energy, and is similar to the position-momentum one (but requires a bit more care to derive and use). In addition, there’s a general uncertainty principle for operators that don’t commute (modulo some details I’m not omitting here). For motivation in the simplest case, taking a measurement in quantum mechanics corresponds to forcing the wave-function into an eigenstate of a (for simplicity) finite-dimensional operators. Unless operators commute, eigenstates of one aren’t necessarily eigenstates of the other. ---
**Author:** ![Blue\_Blistering\_Barnacle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/blue_blistering_barnacle/32/3386_2.png) [@Blue\_Blistering\_Barnacle](https://boards.straightdope.com/u/Blue_Blistering_Barnacle)\ **Post date:** [April 11, 2014, 6:48pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/9 "2014-04-11T18:48:31Z")
> [@sweeteviljesus](#): > > I also thought of another question. According to the U.P., you cannot know both the position and momentum of a particle to arbitrary precision at the same time. IIRC, there are other pairs of properties which are similar in nature. If that is so, what are they? > > Thanks, > Rob Time/energy, for one. ---
**Author:** ![Blue\_Blistering\_Barnacle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/blue_blistering_barnacle/32/3386_2.png) [@Blue\_Blistering\_Barnacle](https://boards.straightdope.com/u/Blue_Blistering_Barnacle)\ **Post date:** [April 11, 2014, 7:09pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/10 "2014-04-11T19:09:54Z")
Any two quantities whose units multiply to the units of the Planck constant. Kg x (m/s)\*2 position/momentum and energy/time are most frequently discussed in (simple) articles I am capable of understanding. (I stand ready for correction.) 🙂 ---
**Author:** ![Itself](https://avatars.discourse-cdn.com/v4/letter/i/d07c76/32.png) [@Itself](https://boards.straightdope.com/u/Itself)\ **Post date:** [April 11, 2014, 7:23pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/11 "2014-04-11T19:23:22Z")
> [@Blue\_Blistering\_Barnacle](#): > > Any two quantities whose units multiply to the units of the Planck constant. Not true. Commuting operators have no such bound. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 11, 2014, 7:53pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/12 "2014-04-11T19:53:54Z")
What **Blue Blistering Barnacle** said might be usable as a rule of thumb, but it leaves out a lot. For instance, two different components of angular momentum don’t commute with each other (and hence have an uncertainty relationship), but any single component of angular momentum commutes with the total angular momentum. ---
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [April 11, 2014, 10:06pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/13 "2014-04-11T22:06:25Z")
OK, I think I have enough to go on to learn about conjugate variables. But what about the other questions, namely: As the particle’s mass approaches Planck Mass, does precision of position and momentum measurement uncertainty approach Planck’s constant (or the reduced one, I can’t remember)? Can we say with arbitrary precision where a particle **was** as opposed to is right now? Can we work out from the reflected photon the new momentum of the particle with arbitrary precision? How about any momentum we added to the particle? Thanks, Rob ---
**Author:** ![ThisUsernameIsForbidden](https://avatars.discourse-cdn.com/v4/letter/t/b4bc9f/32.png) [@ThisUsernameIsForbidden](https://boards.straightdope.com/u/ThisUsernameIsForbidden)\ **Post date:** [April 11, 2014, 10:36pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/14 "2014-04-11T22:36:04Z")
Ugh. I need to know more about these particles. Any suggestions for a good read, introductory level. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [April 12, 2014, 1:02am UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/15 "2014-04-12T01:02:48Z")
**Exapno** , thanks for the cite. Now I have to find out what “symplectic” means because that word is killer. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [April 12, 2014, 12:28pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/16 "2014-04-12T12:28:05Z")
> [@sweeteviljesus](#): > > As the particle’s mass approaches Planck Mass, does precision of position and momentum measurement uncertainty approach Planck’s constant (or the reduced one, I can’t remember)? > > Can we say with arbitrary precision where a particle **was** as opposed to is right now? > > Can we work out from the reflected photon the new momentum of the particle with arbitrary precision? How about any momentum we added to the particle? First, you should not attach too much weight to the heuristic ‘Heisenberg’s microscope’-style derivation of the uncertainty relation. (In fact, it’s been a point of contention recently if this ‘measurement-disturbance relation’, as it’s usually called, holds as such, though without going into the details, I think the side arguing that it indeed does hold has some better arguments.) What’s really important is that in the case of canonically conjugate variables, which are ‘translated’ to noncommuting operators in the quantum theory, the mathematics forces an uncertainty relationship on us, the so-called [Robertson-Schrödinger](http://en.wikipedia.org/wiki/Robertson%E2%80%93Schr%C3%B6dinger_relation#Robertson.E2.80.93Schr.C3.B6dinger_uncertainty_relations) relation. That this holds is beyond contention (well, to the extent quantum theory itself is, of course); unfortunately, it doesn’t have a nice visualizable picture behind it. But the picture in the Heisenberg’s microscope thought experiment is actually misleading: it makes it seem as if the particle’s position/momentum is merely influenced by the act of measurement, and that thus, we simply can’t _know_ it exactly, but if we could enact some form of measurement without this disturbance, then we could, in principle, know both a particle’s momentum and position exactly. But this kind of thinking actually leads to contradictions with quantum mechanical predictions, and experiments supporting them; this is encapsulated in the [Kochen-Specker theorem](http://en.wikipedia.org/wiki/Kochen%E2%80%93Specker_theorem), which roughly says that not all observable quantities about a system can simultaneously have a definite value. Additionally, Heisenberg’s microscope can’t explain all the uncertainty relationships between other quantities, such as the components of angular momentum, for instance. So basically, to try and answer your questions, regardless of the mass of the particle, the uncertainty relation holds always, and the product of the uncertainties in our simultaneous knowledge about a particle’s position and momentum will always be bounded by half the reduced Planck’s constant. We can know either the particle’s position or its momentum (at the time the measurement took place) with (in principle) arbitrary exactness, at the cost of being totally ignorant of the value of the conjugate quantity. There’s no way to ‘cheat’ the uncertainty principle: according to the Kochen-Specker theorem (which, as I said, has experimental consequences), simultaneous values for conjugate quantities simply cannot exist, or if they do, their value must depend on the kind of measurement you’re performing. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 12, 2014, 2:01pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/17 "2014-04-12T14:01:15Z")
I would go further than that, even: The various uncertainty relations aren’t just a limit on what we can know; they’re a limit on what actual, true values the properties can have. A particle with a very well-defined momentum simply does not have a well-defined position, regardless of whether or not anyone is attempting to learn that position. If you want to pin down the position, you can, but the cost is that the particle no longer has any particular momentum. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [April 12, 2014, 2:21pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/18 "2014-04-12T14:21:23Z")
Yes, this is to me an even greater mind-fuck. And many a thread, and many a comment by the respected physicists here, has been to correct/widen the understanding of the UP as “merely” a measurement limit. You know, but aren’t they out there … ? Just, you know, being somewhere at some time? … No? … :: mind fucked :: ETA: Wait–serious question: with that sentence using “they,” you fcan get an answer “Yes,” right? Statistical and all that. But it’s the “it” that prompts a real “No”–right? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 12, 2014, 2:32pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/19 "2014-04-12T14:32:58Z")
> [@](#): > > ETA: Wait–serious question: with that sentence using “they,” you fcan get an answer “Yes,” right? Statistical and all that. But it’s the “it” that prompts a real “No”–right? Could you rephrase this? I’m not sure what you’re trying to say. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [April 12, 2014, 2:44pm UTC](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875/20 "2014-04-12T14:44:18Z")
> [@Leo\_Bloom](#): > > Yes, this is to me an even greater mind-fuck. And many a thread, and many a comment by the respected physicists here, has been to correct/widen the understanding of the UP as “merely” a measurement limit. > > ETA: Wait–serious question: with that sentence using “they,” you fcan get an answer “Yes,” right? Statistical and all that. But it’s the “it” that prompts a real “No”–right? > [@Chronos](#): > > Could you rephrase this? I’m not sure what you’re trying to say. I’m sorry. This: Conversation I \*\*Me: \*\*“You know, but [isn’t it] out there … ? Just, you know, being somewhere at some time?” … \*\*You: \*\*No." **Me:** :: _mind fucked_ :: Conversation II \*\*Me: \*\*“You know, but [aren’t they] out there … ? Just, you know, being somewhere at some time?” … \*\*You: \*\*“Yes, but only as an aggregate, as a statistical measurement approaching certainty but never ever so.” **Me:** :: _mind fucked_ :: Are either/any/both of two conversations correct? And if the last, are they correct simultaneously? [Next page](https://boards.straightdope.com/t/questions-about-the-uncertainty-principle/685875.md?page=2)