Why doesn't QM make particles zig-zag as they travel?

[Demystifier]

When the particle no. is not fixed as, in rel. quantum mechanics,what will become of Q(quantum potential)?Will it keep changing depending on the no. of particles?
Or treating the wavefunction as a functional of the field and using the Schrodinger equation,should one write Q--in this case Q would also be a functional of the field.

To include particle creation/destruction, Bohmian mechanics needs to be modified.
There are several ideas how to do that. Most of them, in one way or another, require introduction of fields. In my opinion, the most elegant way to introduce particle creation/destruction, which is the only way to do it without fields, is by string theory. See, e.g., Sec. IV.B of
http://xxx.lanl.gov/abs/hep-th/0702060
In particular, Fig. 1 summarizes various approaches to particle creation/destruction.
For an additional argument that one has to introduce strings in order to make Bohmian mechanics consistent with particle creation/destruction see
http://xxx.lanl.gov/abs/0705.3542

For those who do not want to read these papers, let me briefly explain the main idea. Kinematically, there is no difference between one string and many strings, because many strings can be viewed as one string splitted in many pieces. The process of particle creation is a continuous process of string splitting (it is continuous in spacetime, not in space). Therefore, all you need is a quantum potential for one string. No fields, no separate quantum potentials for states with different numbers of particles/strings.

 

[marlon]

Where is the difference between seeing a car crossing a certain area and seeing an (high energy) electron crossing a bubble chamber?

The difference is in the fundamentally distinct nature between classical physics and QM. Seeing a car allows you to derive an eauqtion of its movement in terms of time or position, ie you can rewrite the equation of the trajectory. In QM, you cannot do this for an electron because of the HUP and because of the fact that you are seeing emitted EM radiation.


marlon

 

[lightarrow]

The difference is in the fundamentally distinct nature between classical physics and QM. Seeing a car allows you to derive an eauqtion of its movement in terms of time or position, ie you can rewrite the equation of the trajectory. In QM, you cannot do this for an electron because of the HUP and because of the fact that you are seeing emitted EM radiation.
marlon

If you remember I talked about high energy electrons. I don't think a 1 TeV electron has "problems" of HUP. About radiation, if the problem is light emitted from the atoms that have interacted with the electron, we use another way: we simply enlighten it. We will see the electron's trajectory as well.

 

[marlon]

If you remember I talked about high energy electrons. I don't think a 1 TeV electron has "problems" of HUP.

Well, i am talking about ANY electron. But that's irrelevant to this discussion.

About radiation, if the problem is light emitted from the atoms that have interacted with the electron, we use another way: we simply enlighten it. We will see the electron's trajectory as well.

"we simply emlighten it", what does that mean ? How does one achieve that experimentally.

I really feel that we are turning in circles here. I have said a thousand times that knowing an electrons orbit or trajectory VIOLATES the uncertainty principle. I would like to ask you how you can unify those two "arguing" concepts ?

Check out how an ordinary cathode ray tube operates : http://en.wikipedia.org/wiki/Cathode_ray_tube
An early version of this device was used in the first electron discovery by Thomson. Now, you tell me, when we use such a device, WHAT DO WE OBSERVE ?


Besides, the light emission process you describe there is not accurate. But, ok, that is not relevant now.

marlon

 

[lightarrow]

Well, i am talking about ANY electron. But that's irrelevant to this discussion.
"we simply emlighten it", what does that mean ? How does one achieve that experimentally.

Compton scattering.

I really feel that we are turning in circles here. I have said a thousand times that knowing an electrons orbit or trajectory VIOLATES the uncertainty principle.

The same for a car. The difference clearly is in the values. Let's say we want to know an electron's trajectory with 0.01 mm precision in its width. Since

\Delta p_x \Delta x & \ge\frac{\hbar}{2}

we have:

\Delta p_x & \ge\frac{\hbar}{2\Delta x} \simeq \ 10^{-34}/ 2*10^{-5} = 5*10^{-30}\ kg\ m\ s^{-1}

which corresponds, for an electron's mass \simeq\ 10^{-30}\ kg to a

\Delta v_x\ge\frac{5*10^{-30}}{10^{-30}}\ = \ 5\ m\ s^{-1}

A 1 TeV electron has a speed v \simeq\ (1 - 10^{-11})\ c\simeq\ c

and so travels 1 m in \frac{1}{300,000,000} s

The corrisponding transversal space is:

\Delta s\simeq\frac{5}{300,000,000}\ <\ 2*10^{-8}\ m

which is negligible with respect to 0.01 mm.

 

[gptejms]

For those who do not want to read these papers, let me briefly explain the main idea. Kinematically, there is no difference between one string and many strings, because many strings can be viewed as one string splitted in many pieces. The process of particle creation is a continuous process of string splitting (it is continuous in spacetime, not in space). Therefore, all you need is a quantum potential for one string. No fields, no separate quantum potentials for states with different numbers of particles/strings.

Tell me of attempts to unify Bohm with QFT--let us not bring the string in the ring!

 

[marlon]

Compton scattering.

How does Compton scattering "enlighten" an electron ?

The same for a car. The difference clearly is in the values. Let's say we want to know an electron's trajectory with 0.01 mm precision in its width. Since

So, according to you there is NO conceptual difference between the fact that you CAN calculate the trajectory of a car but you cannot do the same for an electron. In other words, expressing the car's position as a function of time is the same as the notion of orbitals ?

AGAIN, i ask you : how do you unify both visions ?

The example you gave does not say ANYTHING on the electron's position or trajectory because you are not determining the position of that electron. All you do is use the HUP ( ), which means that you are using statistical concepts ! I find that funny because you use the same principle that actually forbids your "i can locate and visualize an electron"-speculations.

I do not quite understand what you are trying to achieve here by keeping on turning in circles (e.g. start mentioning the compton scattering), but any standard QM textbook will teach you that the QM world (e.g. electron photon) behaves entirely different from "the classical world" (e.g. car EM wave interaction). In other words, classical physics gives you the position equations if you know initial and final state of 1 particle, QM will give you the particle behaviour based upon a large distribution of measurements. There is a fundamental difference, whether you like it or not. QM is probabilistic in nature, contrary to classical physics and it is THIS idea to which your claims are an obvious violation.

marlon

 

[Demystifier]

Tell me of attempts to unify Bohm with QFT--let us not bring the string in the ring!

There are basically 3 approaches:

1. The true ontology is not particles but fields. Then Bohmian interpretation of fields is constructed analogously to that for particles. The quantum potential is a functional of fields, not of particle positions. This is straightforward for bosonic fields, but problematic for fermionic ones.

2. The true ontology is particles, but complete determinism is abandoned. Instead, particle trajectories randomly and suddenly get created/destructed at definite points in spacetime. The probabilities for these random events are governed by standard QFT.

3. Particles are ontological as in 2., but their trajectories never really get created or destructed. Instead, particles have an additional property called effectivity, which may continuously (and deterministically) change from 0 (ineffective "virtual" particle) to 1 (fully effective particle). The effectivity is governed by the Bohmian-evolving field. In this interpretation both field and particle have ontology.

There are also combinations of these, such that bosons are fields while fermions are particles, or that only bosonic fields have a true ontology.

 

[lightarrow]

How does Compton scattering "enlighten" an electron ?

Electromagnetic radiation of the right energy is scattered off the electron.

So, according to you there is NO conceptual difference between the fact that you CAN calculate the trajectory of a car but you cannot do the same for an electron.

But you can do it for an higly energetic electron. I showed it in my last post. You measure the electron's position and time at the two ends of the 1 metre bubble chamber, then you compute it's momentum and you see that you can predict its next position after the same interval of time, for example, with a precision of 2*10^(-8) m in its side displacement.

In other words, expressing the car's position as a function of time is the same as the notion of orbitals ?

An atomic electron has a much lower energy than a 1 TeV electron.

AGAIN, i ask you : how do you unify both visions ?

The example you gave does not say ANYTHING on the electron's position or trajectory because you are not determining the position of that electron. All you do is use the HUP ( ), which means that you are using statistical concepts ! I find that funny because you use the same principle that actually forbids your "i can locate and visualize an electron"-speculations.

I do not quite understand what you are trying to achieve here by keeping on turning in circles (e.g. start mentioning the compton scattering), but any standard QM textbook will teach you that the QM world (e.g. electron photon) behaves entirely different from "the classical world" (e.g. car EM wave interaction). In other words, classical physics gives you the position equations if you know initial and final state of 1 particle, QM will give you the particle behaviour based upon a large distribution of measurements. There is a fundamental difference, whether you like it or not. QM is probabilistic in nature, contrary to classical physics and it is THIS idea to which your claims are an obvious violation.

marlon

My problem is that I don't see a 1 TeV electron exactly as a quantum object, differently from an electron of more common energies. I could be making a big mistake, however.

 

[bg032]

Why doesn't QM make particles zig-zag as they travel?

I think that the problem is that you are thinking about paths between measurements. You have to give up that notion.

I find that the question of vpoko is central, and the answer given by the standard (Copenhagen) formulation of quantum mechanics, also reflected in the answer of nrqed, is unsatisfactory.

Consider the following very simple experiment: a laser source sends photons towards a beam-splitter (an half-silvered mirror at 45° with respect to the beam). The reflected and the transmitted photons are detected by two detectors T and R respectively. Suppose that along the two paths between the beam-splitter and the detectors there are two slits, again T and R, through which the photons go (see attachment). A very intuitive assumption is that, for example, the photons detected by the detector T go through the slit T and not through the slit R. However, the standard formulation of quantum mechanics does not allow us to get such a conclusion.

Since such a assumption is too obvious to be rejected, I propose to add it as a new postulate of quantum mechanics (see my papers http://arxiv.org/abs/0705.2877 and http://arxiv.org/abs/quant-ph/0605162). One finds that it is very simple to put this assumption in a mathematical form, and that it can be considered as a generalization of the Born rule. It also strongly suggests a new formulation of quantum mechanics, in which a quantum system is represented as a "quantum process", which is something like a canonical stochastic process in which the notion of probability is replaced by the weaker notion of typicality.

Both the Bohm interpretation and Feynman's Path Integral formulation are ways of interpreting what happens between observations, but it's critical to remember that observations are the only things we can verify - not what happens between them.

This happens in the usual experiments with microscopic systems, where the macroscopic world is assumed as given, and it does not need to be explained. However, if we apply QM to closed quantum systems like, for instance, the universe itself, it also has to explain the emergence of a macroscopic quasi-classical world. This is the reason for which QM has to define something like trajectories, and the absence of such a definition corresponds to the well-known difficulty of standard QM to explain the emergence of a macroscopic quasi-classical world.

 

[marlon]

Electromagnetic radiation of the right energy is scattered off the electron.

I know that and this is exactly what i mean by "going around in circles". The process you describe does not allow you to visualise an electron like you visualise a car because of the HUP. This ENTIRE discussion is about the fundamental difference between classical and quantummechanical measurements !

I can only refer to what i said before about tat distiction.

But you can do it for an higly energetic electron. I showed it in my last post.

No you did not, you did not give me the trajectory equation so you do not know where this electron will be for e certain time or position. Also, i stress again the fact THAT YOU USED THE HUP to derive that result. This implies that you can NEVER know the exact trajectory as a function of time or position.

You measure the electron's position and time at the two ends of the 1 metre bubble chamber, then you compute it's momentum and you see that you can predict its next position after the same interval of time, for example, with a precision of 2*10^(-8) m in its side displacement.An atomic electron has a much lower energy than a 1 TeV electron.

You are again forgetting the influence of the HUP here. Ok, let me give another example to make my point : The HUP for position and momentum states that we cannot know those two observables with absolute accuracy. Experimentally we can detect the momentum for an electron at position x so that we would know both position and momentum. Now, if you would redo that same measurement (same electron, same initial conditions etc etc) at the same position x, the acquired momentum value has a different magnitude ! Do it a third time and again you will have a different momentum value. Actually, after repeating that same experiment over and over again, you will conclude that at position x, the spread on the momentum is infinite ! THIS IS THE ESSENTIAL DIFFERENCE WITH CLASSICAL PHYSICS !

Since you use the HUP to claim that you can locate an electron, i ask you this : if you repeat the same experiment, you WILL acquire different outcome values so how can you be certain that you have located the electron ?

Now, the only thing you could do is try to diminsh the spread on the position, but then you increase the spread on momentum. You gain some, you lose some but you are NOT able to locate the electron no matter how small the uncertainty is. There will always be an uncertainty and it is this uncertainty that forbids you from saying "hey, i have located the electron".

My problem is that I don't see a 1 TeV electron exactly as a quantum object, differently from an electron of more common energies. I could be making a big mistake, however.

Well, i hope you understand your mistake now. You have not located the electron. You have merely found a region where you have a high probability of where the electron will be if you measure.

marlon

 

[gptejms]

There are basically 3 approaches:

1. The true ontology is not particles but fields.

2. The true ontology is particles, but complete determinism is abandoned. 3.

3. Particles are ontological as in 2., but their trajectories never really get created or destructed. Instead, particles have an additional property called effectivity,

There are also combinations of these, such that bosons are fields while fermions are particles, or that only bosonic fields have a true ontology.

Any references to the three approaches?

 

[Demystifier]

Any references to the three approaches?

Let me give you only one typical example for each approach:
1. http://xxx.lanl.gov/abs/0707.3685
2. http://xxx.lanl.gov/abs/quant-ph/0303156
3. http://xxx.lanl.gov/abs/quant-ph/0208185
I assume that then you will be able to find additional related papers by yourself. (If you will need further hints, let me know.)
After you study it, I would like to see your comments on particular approaches. In particular, which of them do you find the most interesting?

 

[lightarrow]

You are again forgetting the influence of the HUP here. Ok, let me give another example to make my point : The HUP for position and momentum states that we cannot know those two observables with absolute accuracy. Experimentally we can detect the momentum for an electron at position x so that we would know both position and momentum. Now, if you would redo that same measurement (same electron, same initial conditions etc etc) at the same position x, the acquired momentum value has a different magnitude ! Do it a third time and again you will have a different momentum value. Actually, after repeating that same experiment over and over again, you will conclude that at position x, the spread on the momentum is infinite ! THIS IS THE ESSENTIAL DIFFERENCE WITH CLASSICAL PHYSICS !

Yes, you're right. My mistake was in believing I could neglect the random momentum given to the electron from the photon, with respect to the high momentum of an electron of very high energy, but it's not.