The reality of time, Lee Smolin lecture.

[Rodd]

10 minutes ago, George Jones said:

I think that you need to take some care, as you seem to have shouted this from on high without referencing any actual arguments.

I don't agree.  I said IF you believe in QM, than at some small size, the QF dominate.  I don't see the problem with this.  It's like saying if you believe the Earth is round then a ships mast will be visible at the horizon before its hull.  

Rodd

[George Jones]

 

9 minutes ago, Rodd said:

I don't agree.  I said IF you believe in QM, than at some small size, the QF dominate.  I don't see the problem with this.

You still haven't referenced an actual argument.

 

9 minutes ago, Rodd said:

 It's like saying if you believe the Earth is round then a ships mast will be visible at the horizon before its hull.  

This attempt at a simile is completely irrelevant.

[Rodd]

16 minutes ago, George Jones said:

You still haven't referenced an actual argument.

It stands to reason that if quantum fluctuations are small (they are known to be tiny) then at some size, their size will be larger than your size.  I do not see the need for further argument.   This, I would say, is common knowledge in the world of Qm aficionados.  How could it be otherwise?

Rodd

[andrew s]

2 hours ago, Rodd said:

It stands to reason that if quantum fluctuations are small (they are known to be tiny) then at some size, their size will be larger than your size.  I do not see the need for further argument.   This, I would say, is common knowledge in the world of Qm aficionados.  How could it be otherwise?

Rodd

You might like to look at this article by Arnold Neumaier from the Physics Forums https://www.physicsforums.com/insights/physics-virtual-particles/ and the follow on articles.

As an example in it he states 

"Vacuum fluctuations. This is the term associated with the formal fact that the distribution of a smeared electromagnetic field operator in the vacuum state of a free quantum field theory is a Gaussian. (See p. 119 in the book Quantum Field Theory by Itzykson and Zuber 1980.) According to the Born rule, the distribution of a quantum observable gives the probabilities for measuring values for the observable in independent, identical preparations of the system in identical states. Thus the presence of a Gaussian distribution means that the value of the electromagnetic field in the vacuum state is not determined with arbitrary precision but has an inherent uncertainty. No temporal or spatial implications can be deduced. (The distribution itself is independent of time and space.) Thus it is misleading to interpret vacuum fluctuations as fluctuations in the common sense of the word, which is the traditional name for random changes in space and time. The vacuum is isotropic (i.e., uniform) in space and time and does not change at all. The particle number does not fluctuate in the vacuum state; it is exactly zero since the vacuum state is an eigenstate of the number operator and its local projections in space-time, with eigenvalue zero. Thus there is no time or place where the vacuum can contain a particle. In particular, in a vacuum particles are nowhere created or destroyed, not even in the tiniest time interval."

Reference https://www.physicsforums.com/insights/physics-virtual-particles/

This contribution corrects my comment on how accurate a single measurement can be made. The last part in italics demonstrates not all mathematical Physicists agree with you view on quantum fluctuations and I am not alone in my views.

Regards Andrew

[Rodd]

 

3 hours ago, andrew s said:

The last part in italics demonstrates not all mathematical Physicists agree with you view on quantum fluctuations and I am not alone in my views.

At least we are not lonely!  I will read the article.  If it contains formulae, I will not fare so well.  

Rodd

[vlaiv]

13 hours ago, andrew s said:

in a vacuum particles are nowhere created or destroyed, not even in the tiniest time interval.

This is obviously beyond my knowledge and understanding, but what about Casimir Effect?

Maybe author is talking about "true" particles, rather than "virtual" ones? (Again, whole on mass shell, off mass shell thing is something that I don't really understand nor have enough insight into).

[andrew s]

22 minutes ago, vlaiv said:

This is obviously beyond my knowledge and understanding, but what about Casimir Effect?

This could trigger a whole new flare-up of this thread. Virtual particles are often used as an heuristic to explain the Casimir effect and other proposed effects like Hawking radiation. 

The series I linked to discusses these issues at length.

On the Casimir effect this 

 "At the fundamental microscopic level of description, Casimir force is produced by van der Waals forces between microscopic charged constituents of metal plates. "

is from a discussion here www.physicsforums.com/threads/casimir-effect-and-vacuum-energy-and-a-bit-of-relativity.882958/

I use the physicsforums a lot as they only allow discussion of standard science and not personal theories. 

Regards Andrew

PS This may also be of interest https://arxiv.org/pdf/1702.03291.pdf by the author of the above quote.

[vlaiv]

45 minutes ago, andrew s said:

This could trigger a whole new flare-up of this thread. Virtual particles are often used as an heuristic to explain the Casimir effect and other proposed effects like Hawking radiation. 

The series I linked to discusses these issues at length.

On the Casimir effect this 

 "At the fundamental microscopic level of description, Casimir force is produced by van der Waals forces between microscopic charged constituents of metal plates. "

is from a discussion here www.physicsforums.com/threads/casimir-effect-and-vacuum-energy-and-a-bit-of-relativity.882958/

I use the physicsforums a lot as they only allow discussion of standard science and not personal theories. 

Regards Andrew

 

Ok, not trying to derail the thread, but did some "fast research" and topic seems to be still rather controversial (or it just might seem that way to me).

Hrvoje Nikolic in his paper, starts with opening remark:

"At the fundamental microscopic level, Casimir force is best viewed as a manifestation of van der Waals forces."

https://arxiv.org/pdf/1702.03291.pdf

On the other hand, group of researchers from from St. Petersburg University in their paper state:

"We review modern achievements and problems in physics of the van der Waals and Casimir forces which arise due to zero - point and thermal fluctuations of the electromagnetic field between closely spaced material surfaces."

They also state:

"In fact, there are no two different forces, van der Waals and Casimir. The van der Waals force is a subdivision of dispersion forces acting at very short separations up to a few nanometers, where the effect of relativistic retardation is very small and can be neglected. As to the Casimir force, it is a subdivision of dispersion forces which acts at larger separation distances, where the effect of relativistic retardation should be taken into account. It is evident that there is some transition region between the two kinds of dispersion forces."

https://arxiv.org/ftp/arxiv/papers/1507/1507.02393.pdf

(btw, looks like really interesting read).

Anyhow, this was just an observation, not trying to pull discussion in certain direction ...

[andrew s]

3 hours ago, vlaiv said:

Ok, not trying to derail the thread, but did some "fast research" and topic seems to be still rather controversial

Certainly you will find various views on this from practicing Physicists. One problem with google is you can get almost any view possible even from arxiv and it is difficult to know if they were ever published, referenced etc.

This is why I like the discussions on PhysicsForums as you often get both sides of the argument discussed by practicing scientists (e.g. George Jones). Sometimes a consensus is reached sometimes not and often it gets far too technical for me to follow in detail. However, one can get a sense of the discussion and the outcome.

It's hard science but I like it!

I also like SGL for many reasons ?

Regards Andrew

[George Jones]

I think that some of the main quantum field misconceptions about Neumaier has written first make their appearance in the simpler context of the uncertainty principle in standard quantum mechanics. Many quantum mechanics texts and courses give incomplete and/or incorrect presentations of the uncertainty principle. At the undergraduate level, "Introduction to Quantum Mechanics" by David Griffiths, and at the (extreme) graduate level, "Lectures on Quantum Mechanics" by Steven Weinberg, give nice presentations. Two of the main competitors to Griffiths do not give presentations that are as nice.

Arnold Neumaier: "According to the Born rule, the distribution of a quantum observable gives the probabilities for measuring values for the observable in independent, identical preparations of the system in identical states. ...   Thus it is misleading to interpret vacuum fluctuations as fluctuations in the common sense of the word, which is the traditional name for random changes in space and time. The vacuum is isotropic (i.e., uniform) in space and time and does not change at all. The particle number does not fluctuate in the vacuum state; it is exactly zero since the vacuum state is an eigenstate of the number operator and its local projections in space-time, with eigenvalue zero. Thus there is no time or place where the vacuum can contain a particle. In particular, in a vacuum particles are nowhere created or destroyed, not even in the tiniest time interval."

Weinberg: "It should be emphasized that Δx is the spread in values found for the position if we make a large number of highly accurate measurements of position, always starting with the same state with the same wave function ψ, and likewise for Δp. The uncertainties depend on the state, not on the method of measurement." Note that Weinberg did not write "... depend on uncertainty in the state ..."

Consider an uncertainty principle example from the first-year text used at my school: "The speed of an electron is measured to be 5.00×10^3 m/s to an accuracy of 0.000300%. Find the minimum uncertainty in determining the position of this electron." As the Weinberg quote shows, this is rubbish.

For concreteness, I am going to consider the position-momentum uncertainty principle ΔxΔp≥ℏ/2 applied to the (quantum mechanical) harmonic oscillator.

Typical woolly statements about why the lowest (ground state) energy of a quantum oscillator is not zero go something like "According to the uncertainty principle, the quantum oscillator has to jiggle a bit." This evokes the image of an oscillator whose state changes in time, but the ground state of oscillator does not change with time.  More about this below.

Consider a very large number N of identical harmonic oscillators all prepared in the identical states, which I will take to be the lowest energy (eigen)state, i.e, the ground state. Very accurately measure the position for half, N/2, of the systems; Very accurately measure the momentum for the other half, N/2, of the systems. Each of the N measurements is on a different oscillator, i.e., on different but identical copies of the system and state.

Calculate the statistical standard deviation for the the N/2 position measurements; call this Δx. Calculate the statistical standard deviation for the the N/2 momentum measurements; call this Δp. When N is very large,  Δx and Δp will satisfy ΔxΔp≥ℏ/2. This is the uncertainty principle in quantum mechanics.

Note that position and momentum are never measured on the same oscillator copy. Note also that Δx and Δp have nothing to do with an intrinsic limitation on the accuracy with which individual measurement are made. Finally, note that nothing was said bout the time at which the measurements were made. All the measurement could be made at the same time, or they could be made spaced by random time intervals. For very large N, the same statistical distributions of measurement vales will result, so the spread in values is not due to oscillators "jiggling" with time. (Since the ground state is an eigenstate of the Hamiltonian, and the Hamiltonian governs time evolution, each oscillator stays in the ground state until a measurement is made, independent of when in time the measurements are made.)

[andrew s]

Thanks for the above George , could you comment on how this relates to the pattern found in a narrow single slit experiment when identically prepared photons or electrons pass thought it and hit a suitable screen.

I think many will have seen this as a demonstration of the Uncertainty Principle in action.

Thanks in advance.

Regards Andrew 

[George Jones]

5 hours ago, andrew s said:

could you comment on how this relates to the pattern found in a narrow single slit experiment when identically prepared photons or electrons pass thought it and hit a suitable screen.

I think many will have seen this as a demonstration of the Uncertainty Principle in action.

I think that you mean something like

https://www.sheffield.ac.uk/polopoly_fs/1.162375!/file/topic5.pptx

 

I am going to try (might not be successful) to expand on the material in (but using electrons)

https://pubs.acs.org/doi/abs/10.1021/ed082p1210

http://iopscience.iop.org/article/10.1088/0143-0807/32/2/018/meta

and in some notes that I wrote 13 years ago for the double slit set-up.

I am not sure if these are behind paywalls, but a version of the first in pre-journal format is at

http://www.users.csbsju.edu/~frioux/diffraction/N-single-slit.pdf

 

 

[andrew s]

16 hours ago, George Jones said:

When N is very large,  Δx and Δp will satisfy ΔxΔp≥ℏ/2. This is the uncertainty principle in quantum mechanics.

Thanks George.

Trying to link the single slit experiment to you excellent description above would you agree with the following?

In the single slit experiment the passage of the photons/electrons though the slit ( width ~ Δx) prepares the system such that the wave function ψ is characterised by statistical standard deviation Δx in position and so a subsequent measurement of momentum, i.e. the pattern on the screen, gives a standard deviation in momentum Δp such that ΔxΔp≥ℏ/2 when averaged over a large number of trials.

Regards Andrew

[vlaiv]

The simplest way for me to think about ΔxΔp≥ℏ/2 is in terms of Fourier transform and a single wave.

One just needs to observe two extreme cases to get the sense of how it works:

Sine wave - have definite wavelength/frequency but it goes on from - infinity to infinity thus wavelength is very definite, but position is very opposite of it - it can be anywhere from - infinity to infinity.

Other example is delta function - it has very definite position, but its Fourier transform is constant function - contains every frequency out there - so we can say that frequency becomes very indeterminate.

So Heisenberg uncertainty principle stems from nature of wave function of system, and should not be considered property of ensemble as that would be tying it to particular interpretation. It can reflect in ensemble in the same way as all other probabilistic properties.

[Rodd]

On 08/12/2018 at 10:34, vlaiv said:

So Heisenberg uncertainty principle stems from nature of wave function of system,

precisely--it is tied to the very fabric of reality (whatever that means), and has nothing to do with the often touted explanation that---something like... "one can't know both the position and velocity because when you take a measurement you affect the system because the act of measurement involves bouncing a photon off the particle which changes its velocity".  Or something like that.  It is often explained that the act of observing somehow interferes with one or the other measurement when in actuality, it is more fundamental.  That is why a method CANNOT be devised to know both.  feynman discussed this at length.  

Rodd

[andrew s]

On 08/12/2018 at 15:34, vlaiv said:

The simplest way for me to think about ΔxΔp≥ℏ/2 is in terms of Fourier transform and a single wave.

One just needs to observe two extreme cases to get the sense of how it works:

How can one tell which state the wave is is without a measurement ?

2 hours ago, Rodd said:

It is often explained that the act of observing somehow interferes with one or the other measurement when in actuality, it is more fundamental.

It is very fundamental and at the core of QM.  It is a fact that some operators in QM are such that the results of the measurements they represent depend on the order they are applied to the "wavefunction" so if A and B re two such operators |AB - BA| > 0 one example is position and momentum another is the components of angular momentum of say a hydrogen atom lx, ly or lz. However, lx ( or ly or lz) and the total angular momentum L commute so |lxL - Llx| =0. 

You have to look at a sample (ensemble) of results to establish the result ΔAΔB≥ℏ/2. experimentally and thus compare it with the theory derived from the action of the various operators on the wave function. Recall the Δx is a statistic, notably standard deviation.

It might also be noted that not all QM states have a "wavefunction" representation, e.g. electron spin where you need a matrix representation (Pauli matrices) and the intuition from classical wave theory does not obviously apply but the Uncertainty Principle does.

Regards Andrew

 

 

[andrew s]

This is a simple experiment anyone can to to see how observing, i.e. passing light through a linear polariser, effects the "state" of the light passing through. 

Take a light source and observe it through one polariser.

The take the second and rotate its plane of polarisation so that it blocks the the light from the first (This wont be perfect as these are real word devices.)

Take the third polariser and place it between the first two and rotate it you will find positions which maximises the through put from all three well above the blocked level!

This can only happen if the polarisers directly change the polariation of the light in a non classical way  i.e. the state of the system is changed by the observation in accordance with QM.

Regards Andrew

[vlaiv]

14 minutes ago, andrew s said:

How can one tell which state the wave is is without a measurement ?

You certainly need to measure it or prepare it at some point. Later on, state is determined by evolution of system - QM equations tell you how system will evolve with respect to time.

As for ensemble interpretation - well that is one interpretation - my guess is that it draws upon equivalent interpretation of probability.

I personally advocate position that wave function of system is part of reality not just mere description of the system. Ensemble is not complete interpretation of probability, I'm much more in favor of propensity interpretation, although I also find it somewhat lacking. In similar line of reasoning, if we accept that wave function is part of reality, then Heisenberg uncertainty principle stems from reality and it is only reflected in measured data in the same way that coin has 1/2 probability of landing heads, and any sort of measurement will only get us ever so close to this value.

[andrew s]

11 minutes ago, vlaiv said:

if we accept that wave function is part of reality, then Heisenberg uncertainty principle stems from reality and it is only reflected in measured data

I am not sure what this means but I don't want to get drawn into a philosophical discussion on the interpretation of QM. However, as I said above not all states have a wavefunction representation so you would have to accept for example the "reality" of Pauli Matrices to maintain your view. Is one representation more real than another where you have both wavefunction and matrix representation? These are plilosophical question which I am not competent to answer.

All I can say is that the Heisenberg uncertainty principle is derived in QM by looking at the action of operators (which represent measurements) on the state of the system. You have to have both the operators and the state of the system. 

Regards Andrew

 

[George Jones]

I have not forgotten about this thread. I had intended to make a longer post on the weekend, but I go a bit snowed under by family life, including loads of ice skating with my 12-year-old daughter. Now I have stuff to do at work, but I hope soon to make a longer post.

I would like to say, though, that I most certainly have not used any particular interpretation of quantum theory in my above post on the uncertainty principle. I have used a particular interpretation of probability (independent of quantum theory), the frequentist interpretation. 

[vlaiv]

7 minutes ago, andrew s said:

I am not sure what this means but I don't want to get drawn into a philosophical discussion on the interpretation of QM. However, as I said above not all states have a wavefunction representation so you would have to accept for example the "reality" of Pauli Matrices to maintain your view. Is one representation more real than another where you have both wavefunction and matrix representation? These are plilosophical question which I am not competent to answer.

All I can say is that the Heisenberg uncertainty principle is derived in QM by looking at the action of operators (which represent measurements) on the state of the system. You have to have both the operators and the state of the system. 

Regards Andrew

 

I agree, and by wave function I implicitly mean vectors in Hilbert space (so both matrices and functions), or simply state of system (linear combination of vectors in Hilbert space).

My point was in relation to uncertainty principle - it is fundamental property of state of system. It is our mental image and extrapolation of it that led us to believe that there should be both precise position and momentum (or other observables). Simply because we measure both quantities in macroscopic objects with certain precision led us to believe that it should be so at any scale.

Quoted simple wave function in two distinct states - as infinite sine wave and delta function, paints another mental image - one that describes how properties can be interlinked in such way that if we increase "precision" of one - other one becomes less determined and vice verse.

This intrinsic property of system state reflects in many ways - in formalism of QM via non commuting operators, in naive explanation that we can't measure position of a particle with enough precision because it requires high energy photon to hit it, there by scattering it (and we need two position measurements to determine momentum, thus we alter system by first measurement, and our second becomes less precise), in the fact that we can measure spin of electron in one axis only - there is no such thing as magnetic field with intersecting lines to do measurement in multiple axis at a time, and in ensemble of measurements where standard deviations of variables follow stated rule.