Visualize simultaneously position and momentum

[Rade]

Well, I know I must tread very lightly with this topic...so....let me start with my reference. I wish to "discuss" here the comment on page 146 in David Bohm, Quantum Theory, 1951, Dover. Here is the statement:

 

..We cannot visualize simultaneously a particle having definite momentum and position....because such particles do not exist...

This is a true statement if quantum theory is true, at least as understood by Dr. Bohm, a quantum physicist. Since the statement was made in a physics textbook, I post it here, but I would understand if the thread is moved to philosophy. I also note that this comment of Bohm was made well before the personal computer screen that we now use to "visualize" particles.

 

OK, here is my response to Bohm.....

 

Let us claim as true that we can visualize a particle on a computer screen that looks like this particle, :). Then, suppose an x,y,z configuration space in which :) is associated, with the z axis moving into the screen, and x and y the typical two dimension axis.

 

I will now make the claim that :) exists, this I must do to reply to Bohm since he uses the word "exist" in his statement. I will argue that Bohm would agree with me. The :) exists because his statement implies that logically we must have the ability to visualize a particle first for momentum then for position, that is, it must be true that Bohm finds it possible for such a particle to exist, since he makes a claim about "existence of particles". That is, Bohm is not claiming that no particles exist, only that none exist that we can visualize simultaneously having momentum and position.

 

Next I will claim that :) can be visualized for some x, y position on the computer screen in front of you, in fact, it is exactly where you now see it, :), and in the past it was at x-y position as seen, and in the future it will be as visualized below on the screen.

 

I follow with a true claim that :) can have a momentum that you could visualize if it was moving, and one such movement is along the z axis, into the screen.

 

Now, I am sure that many of you have seen powerpoint presentations where some object such as :) is made to disappear, sometimes slowly, sometime very quick. I will claim that this type of momentum is something that can be visualized, and logically that one direction such momentum can take is along the z axis direction, into the computer screen. Not sure about anyone else, but I have seen this action often, and if I understood how to, I would make this :) specific particle have such momentum if you clicked on it with your mouse. Thus I claim that I can visualize the :) particle to have momentum in such a way that it very, very slowly disappears from view along the z axis into the screen.

 

Now, according to the above comment of Bohm, quantum theory predicts that I cannot "visualize" simultaneously :) having definite momentum and position....

 

....however, clearly I can so visualize such an action, that is, when I visualize the :) either slowly or quickly moving away from view (with definite momentum that I can visualize) along the z axis into the computer screen, simultaneously while the momentum is in action, I also can visualize a definite x-y screen position for :) along the x-y axis.

 

Now, a very important observation...Bohm does not make any claim at all that I "measure" either momentum or position...only that I "visualize" such.

 

So, what can this mean ? Does it mean that the :) is not a particle to which the quantum theory can be applied ? If yes, OK, then I better understand the limits of quantum theory in a way that I can visualize. But, if you answer no, that is, if you answer that the :) is a particle to which quantum theory applies, then have I found an error in the logic of the statement of Bohm (very unlikely) or is there an error in my argument presented (much higher probability I agree).

 

In short, I argue above that I can in fact "visualize" simultaneously a particle such as :) having definitive momentum and position. Thus, I argue that I can "visualize" what quantum theory informs I cannot (at least as presented by David Bohm, a quantum physicist). I look for someone to falsify the logic of my thinking.

[lawcat]

I think what is meant by that statement is: something can not be static and dynamic at the same time. Something can not be stationary and move, from our point of view, unless we consider two different frames. In your example, if you focus on exact point in space, you have no frame of reference for the momentum. If you focus on momentum, the motion, you only see differential change of position which is speed or velocity, but not the exact position.

[JMJones0424]

Rade, if you must tread lightly, then I must levitate.

 

I don't know the context in which the quote was made, but it seems to me that it is just a sloppy way of describing the uncertainty principle. We can not visualize a particle with both definite momentum and position, because to be definite in one, we alter the other.

 

Where your logic seems to fail in my eyes is that you define your particle :) to be the same type of entity as described in the quote as a particle, and then proceed to describe properties of :) that prove that it can not be the same type of entity defined as a particle in the quote.

 

I can visualize a unicorn, but unicorns don't exist. This is an example of why I think the quote is sloppy.

[Rade]

Thank you Lawcat and JM.. for the replies. On page 206 Bohm makes the following comment concerning any two operators, such as one to visualize momentum for :) in my above example (let us call it A), and a second to visualize position (call it :):

 

..whenever A and B do not commute, they cannot be measured simultaneously with perfect accuracy. If A and B do commute, however, then it can proved that it is possible to measure them simultaneously

So, I think it possible that the two visual operators in my example (one for momentum and one for position) do commute--that the human mind does not place one visual action prior to the other.

[JMJones0424]

Once again, I do not have the text in front of me, but what leads you to believe in any way that David Bohm is making claims about the order or simultaneity of visual actions in the human mind? Again it appears he is speaking of properties of particles, while you are speaking of properties of imagination. His fault appears to be in stating that one can not imagine something that does not exist, but even this I am unsure of, as i have not seen the entire quote, much less the context that the quote was taken from.

[Rade]

Thank you JM....but, Bohm is talking about the human mind..imagination. So he says prior..on page 145...

..to picture the actual process of motion taking place in a simultaneous manner, we must imagine an object that is covering some space during an interval of time....in other words, we cannot think of the position of an object and its velocity simultaneously

Bohm is talking about the human process of visualization and thinking, this is the context of his statement. Now, I have no idea if anywhere in this book he makes a claim that one cannot imagine something that does not exist. I am just making an observation about a comment Bohm made that I do not believe is a true statement, at least not for how I visualize particles (or think about objects) on a computer screen.

[JMJones0424]

Well, in that case, I'm not sure how much stock I would put into the musics of a quantum physicist on the human mind written in a book titled Quantum Theory in 1951.

 

However, once again, just because you can imagine or visualize a point or a :) or a volkswagon to have both simultaneously definite position and motion, and call that object a particle, does not make it a particle in the quantum mechanical sense.