The Uncertainty Principle And It's Interpretation Fundamentally

[Aethelwulf]

I will skip many of the conventional interpretations of the uncertainty principle... reason only being that we have most of them at some point in our life, including the popularized interpretation that position is a complimentary observable to momentum. There is a different interpretation (if even not separate) which can be fundamentally described as saying that the uncertainty principle is actually saying the future is unknowable. The formulation of the ''future event'' of a quantum system appears spontaneous and random on many occasions. The inability to describe an entire system based on the future seems to be an inherent factor of nature but does not need to mean that the future is unknowable, only that we can only extract a certain amount of information about it.

 

 

What is of interest however is that the past and future can be collected as real things in nature if the present is the product of two wave functions, one coming from the past and another coming from the future. Not only would they be complimentary but also conjugates as you would find as [math]\psi \psi^{\dagger}[/math].

 

The reason why the past and future exist will therefore be reliant on where these ''waves'' coalesce. The probability of any one of these wave functions depend statistically on physical interactions or even observations made in either the future or past cone of the universe. We have evidence that this is what happens in an experiment called ''The Delayed Choice Experiment.'' Because of this, there is strong evidence that the past is shaped up by our actions in the present state statistically-speaking.

 

It is real science that we could be ''smears'' throughout every moment in existence, nothing more than a ''probability'' that has emerged itself. How insignificant then a single solid object in reality. It seems to be a collection of statistical averages and nothing more. And worse yet, statistical averages to which no future can be ascertained fundamentally-speaking if we attempt to measure that object!

Edited March 9, 2013 by Aethelwulf

[CraigD]

That’s some deep hinting at though experimentation, Aethelwulf, and delightfully devoid of the detailed math that’s so often required of the subject, and which I so struggle and usually fail. :( :thumbs_up :)

 

I gather what you’re saying is connection to the observation that some physical laws, including quantum mechanical laws, are time-reversible, working either in a forward or backward time direction – present state data can be used to calculate future or past states, which in quantum mechanics are ensembles of wavefunction values (conventionally written [imath]\psi [/imath], and related to real-number valued probabilities [imath]\psi \psi^*[/imath], “the complex conjugate of psi” – Aethelwulf is this what you meant by [math] \psi \psi^{\dagger} [/math]?), and available present state data constrained by the uncertainty principle. In principle, then, just as the uncertainty principle makes the results of future, predicted measurements uncertain, it makes the imagined results of past, “postdicted” measurements (necessarily, because unlike a predicted furture measurement result, we can’t actually wait and make the postdicted measurment) uncertain also.

 

There this, and similar time-reversed though experiments, get paradoxical for me, is when it collides with my intuitive certainty that we know the results of past measurements – we remember them, from recordings and documents and our brain-held memories, but don’t yet know the results of future ones. Practically, postdiction is usually not used to calculate the probability of a given past state of a system, but to test the goodness of the calculation against a certainly known past state. Some laws of physics work in both directions of time, but out intuitive perception of reality appears forward in time only.

 

I don’t believe this is a true, unresolved paradox, but its resolution isn’t intuitive.

 

We have evidence that this is what happens in an experiment called ''The Delayed Choice Experiment.'' Because of this, there is strong evidence that the past is shaped up by our actions in the present state statistically-speaking.

I don’t think the delayed choice experiment shows that our actions shape the past.

 

Key to this conclusion is consideration of exactly what “the past” is in the domain of the DCE. It’s the passing of a single particle – in real DCE experiments, a photon of visible light – though one or the other of 2 pathways. Per quantum mechanics, if it’s certain which path the particle followed – for example, is a “gate” of some kind is closed so that it only one of the 2 paths is possible – the particle doesn’t exhibit wavelike behavior. The DCE adds a wrinkle to this basic consequence of QM, by not making certain which of the 2 pathways the particle “chose” (or, if you prefer, reality chose for it) by closing the gate on one, but by detecting, after the particle has “made its choice”, which path it followed, or not detecting it. Words begin to fail me in this description, so here’s a picture (from this 2007 AAAS ScienceNOW article) or the famous (with this science fan, at least :)) 2007 Aspect DCE:

 

The original DC thought experiment, and action ones like that 2007 one, use elementary particles. The validity of its verified prediction depends on this. Consider, for example redoing the DCE using large composite particles –for dramatic effect, let’s say tour busses full of people, replacing the beam splitters in the Aspect experiment with forks in underground tunnels, the driver chooses with a fair coin toss or is forced to take by barricades set by the experiment. It wouldn’t work – regardless of what the experimenter did to have or not have certainty of which path the busses take, the drive and passengers would know, because unlike photons, they can record and recall such information.

 

Aficionados of quantum physics though experiments might be reminded by this of

the Wigner’s friend thought experiment/paradox. My intuitive “it wouldn’t work” conclusion is essentially an affirmation of the objective collapse theory resolution of the paradox mentioned in the linked article.

 

The point John Wheeler had in mind when he proposed the DC though experiment is not to suggest that the later choice of the experimenter to detect the path chosen earlier by the particle influenced (“shaped”) the particle’s choice, but that the view that such choices actually happen, in a usefully meaningful sense, is a wrong one. Metaphorically put, [imath]\psi \psi^*[/imath] is not a choice, the record of the roll of some cosmic dice, but rather a collection of probabilities (probability density functions, for the metaphor-phobic math purist ;)), a description of the exact nature of the dice.

 

There are other, deeper reasons to conclude that the “forward from the past to the future” direction of the “arrow of time” is not an arbitrary decision, the ones I know best rooted in considerations of the underlying mechanics that give rise to the emergent property described by the second law of thermodynamics. All these explanation seem to me to emerge from underlying mechanics common to both fundamentally deterministic (classical) and probabilistic (modern, quantum) mechanics.

 

It is real science that we could be ''smears'' throughout every moment in existence, nothing more than a ''probability'' that has emerged itself. How insignificant then a single solid object in reality. It seems to be a collection of statistical averages and nothing more. And worse yet, statistical averages to which no future can be ascertained fundamentally-speaking if we attempt to measure that object!

Yep - [imath]\psi \psi^*[/imath] is well-imagined as a smear.

 

Per objective collapse theory, though, big solid objects are very significant, because they’re big bundles of wavefunction-collapsing particle interactions. This, not mere statistical averaging of large numbers of individual probability density functions, is why the everyday macroscopic world we measure looks certain, not smeared out.

 

In principle (though not in practice, because the number of arithmetic operations required is too great), we can predict the future using quantum mechanics. That prediction, however, is not “certain” – consisting of wavefunctions with complex conjugate values of only 1 and 0 – but a [imath]\psi[/imath] collection of wavefunctions. Practically, the classical approximation approximates the likely outcome of these wavefuctions.

 

The uncertainty principle rules out a classical Laplace’s demon. It doesn’t rule out or ability to determine the future of ensembles of particles for practical purposes, or of single fundamental particles, if we are content to represent it with probabilistically, with a wavefunction.

 

 

The reason why the past and future exist will therefore be reliant on where these ''waves'' coalesce.

Assuming by “waves” you mean [imath]\psi[/imath], Aethelwulf, I don’t get your meaning here. As I understand it, the value of [imath]\psi[/imath] changes with time, and represents the addition of many individual wavefunctions, so can be though to “coalesce” for a given particle by describing a high probability of that particle being detected in a particular volume at a particular time. A wavefunction does not, however, give a probability density function for a particle being detected only at a specific duration of time. Put another way, particles are distinct in space – they have high probabilities of being where we detect them to be, low probabilities of being elsewhere – but not in time – the probability of a particle existing in some volume at every instant of time is 1. The wavefunction of a particle permits it to interfere with itself spatially, not temporaly, so I can’t understand what you mean by them “coalescing” at some instant in time distinguishing past from present. Can you elaborate :QuestionM

[LaurieAG]

Hi Athelwulf and CraigD,

 

In some of DD's posts I argued that the future becomes determinant if you use statistical probability at a middle point and claim absolute results that can only be ascertained as true or false at the end, i.e. infinity. The methodology (discard the false statements from all true/false statements at the middle point) makes this type of solution more of a logic error than anything else.

 

I actually think the inverse of the uncertainty principle means that directly observed exception to any rule, unaccounted for by that rule, means that as that rule stands it is not correct. Also, as this has been used to make quite complex mountains out of mole hills by tweaking and fiddling, both equations and data, to make things fit, the uncertainty principle and its inverse have copped considerable abuse from their originally pure and simple intentions.

 

This is even more important when you get to time directions as the Scholes Black method will, once again, cause major disruptions to the global financial system due to working both ways in 'time' to exploit regulatory deficiencies being accelerated by leveraged High Speed Trading (HST) set plays.

 

http://en.wikipedia.org/wiki/Black%E2%80%93Scholes

 

http://www.nanex.net/aqck/aqckIndex.html

 

This is the simpler terminology based on Kurt Gõdel's work and the image at the bottom shows what is happening in this type of unregulated, unsustainable and perpetually 'expanding' situation.

 

Consider a simple, balanced, Global system G, with internal systems G*, G** etc, based on the following rules:- B$ = Business Benefits gained, L$ = Leasing Benefits gained, D$ = Depreciation Benefits gained, U$ = 'User Paid' amounts gained etc. and Ax is the Axiom for the amount of leverage applied/yielded through each integer x greater than zero. At the lower end of the internal system limits of G* the key rule is

 

(1) B$ = L$ OR D$ OR U$ Therefore, because L$ = D$ = U$ we can say that L, D and U become redundant and

 

(2) B$ = Ax$ for all x greater than zero.

In the case of all regulated systems of this nature, A = 1 for all

applied x$. When the internal system G* is consolidated into the global system G we find that things have changed dramatically and key rule (1) now allows:-

 

(3) B$ = L$ AND D$ AND U$ ******************IMPORTANT**************************

 

Thus B$ = Ax$ = 3 per x$ and A becomes unregulated and equal to the sum of the number of elements x (not the sum of the elements) applied to the internal system G*, therefore

 

(4) A = the consolidated leverage applied across each internal system G* in G.

The B of G*, the 'Gross Yield' on 'Unregulated Leverage', now has the

following form from (2)

 

(5) B = Ax + c for all x > 0 and all A in x, where c = 0, in G** A = x, in G*** A = x squared etc. As the slope of any straight line is determined by m in the equation y = mx + c,

 

(6) the slope of the global system G line = A = (4) the consolidated leverage of G* in G.

 

The HST people may be masters of the financial universe but not in any genuinely regulated universe.

[Aethelwulf]

The thing concerning the experiment, is merely one interpretation that it means that the present can effect the past. It has been quite a popular one. A more simple thought experiment can be thought of as a photon travelling through space. According to quantum mechanics, the photon must travel every possible trajectory until something disturbs its wave function. According to us, a photon could have traveled to Earth since the dawn of the universe, with an undefined history; instead it has many possible histories. Only when something detects this photon in the lab, does a single history get chosen for the particle.

 

Again, just this simple thought experiment shows us, that the choices made in the present are somehow statistically shaping up the past. A popular way to envision this is by thinking of the universe like a double barrel gun - one positive wave function (and as you pointed out) a time reversed negative wave function. One major question about the beginning of time, is how the universe chose this state out of an infinite amount of possible start up conditions. One way to solve this is by saying that this state is being chosen today even by ourselves. As reality becomes more concrete in the future, it tampers with the wave functions on a quantum level and shapes up the past state of the universe.

 

The Transactional Interpretation is synonymous with talking about a two-time symmetry physics where a wave function comes from the past, another from the future and they converge every time anything physical occurs in the universe.

[LaurieAG]

That's just what DD would think.

[Rade]

The Transactional Interpretation is synonymous with talking about a two-time symmetry physics where a wave function comes from the past, another from the future and they converge every time anything physical occurs in the universe.

Another interpretation, one I use, is where a wave function inputs [a moment] from the past during a past time interval, while simultaneously another outputs [same moment] during a future time interval, and where the wavefunctions converge [within the moment] time does not exist, nor does anything physical exist that is not forever. But, this is only the explanation for matter wavefunctions, for antimatter wavefunctions the opposite occurs, the time arrow is from the future to the past (we learn this from Feynman, antimatter moves to past time, matter to future time). Comments pro or con welcome.

[Aethelwulf]

I'd agree with the mechanics there, until you said it converges to a non-existent time. I'd argue the past and future are non-existent whereas the present is very real.

[Rade]

I'd agree with the mechanics there, until you said it converges to a non-existent time. I'd argue the past and future are non-existent whereas the present is very real.

To clarify, for me, there is a concept of time associated with any moment, present, past or future, but is outside human measurement because the duration is Planck Time and thus the HUP applies. For me, what exists in time experienced by humans (e.g., the spacetime interval where ds^2 > 0, the distance between two events as timelike interval) are things with mass that have potential for change and/or movement. One exception is that which exists forever, which is by definition within the |moment| and thus outside time. For example, I would put the identity of the photon with no rest mass within the |moment| and outside of time. So, I would view the photon as a real quanta of energy that can be experienced by humans but cannot be measured by time. However, an electron or positron with small rest mass would have movement within past and future spacetime intervals that are intermediate between any two moments. Such moments are the same as events that divide the spacetime interval concept of Einstein, with dt = coordinate time difference between two events. For example, if event #1 [a moment in time] is the sound of a gun and a runner begins running down the track, and event #2 [a second moment in time] is the sound of a second gun when the runner reaches finish line, then both runner with motion, and coordinate time interval associated with the two gun sound events, are real. The reality of the runner as a physical entity with mass is superposed with the reality of time as a number that measures the motion of the runner, to the extent we would say mass as a number, and time as a number, are real.

 

I also suggest that what I present above best fits the 5 dimensional approach of the Kaluza-Klein Theory. The fifth dimension of Kaluza allows that gravity, thus motion, is associated with it, and Klein suggested that this fifth dimension has a very small radius = Planck length, which also means it has duration of Planck Time, and is the reason humans can never experience this 5th dimension. As known, this 5th dimension that is associated with gravity also can be perceived by experiments as the combined electromagnetic force. Thus Kaluza-Klein Theory unites Einstein general relativity force of gravity with quantum electromagnetic force. (as an aside, given that electromagnetic force has been united with strong force, it suggests that Kaluza-Klein Theory also unites gravity with strong force ?).

 

I suggest that the very small 5th dimension of Kaluza-Klein can be viewed to be associated with the concept of the |moment| of events (both quantum and classical) within spacetime. So, when we introduce a moving object within the timelike interval of spacetime that feels force of gravity, the following model is suggested: infinity from past...... |past moment of event #1 in 5th dimension|<--space-time, timelike interval of moving object that feels gravity (4 dimensions) -->|present moment of event #2 in 5th dimension|<--space-time, timelike interval of moving object that feels gravity (4 dimensions) -->|future moment of event #3 in 5th dimension|.....infinity to future. If this makes any sense, it would suggest the HUP is associated with measurement of the 5th dimension of Kaluza-Klein having radius of Planck length.

 

Let me know what you do, and do not agree with, thanks.

Edited March 13, 2013 by Rade

[Rade]

... there is strong evidence that the past is shaped up by our actions in the present state statistically-speaking.

Question. What do you mean by present state ? Is this some extended event ? So, for example, suppose the president gives a present state of union speech today at 8:00 to 9:00 pm. Could the past be shaped by that speech because the president took some action in the past knowing he wanted to mention the outcome at some future date, which happens today to be the present day state of the union speech ? If so, why would this effect of the present on the past have anything to do with statistics ?

[Aethelwulf]

The present state is a moment in so-called ''time.'' It is the only state a thing experiences anything in. For instance, an object does not exist in the past nor in the future. An object is always stuck in the present time.

 

As for the ''statistically-speaking'' part, I am referring to the wave function of matter.

[Rade]

The present state is a moment in so-called ''time.'' It is the only state a thing experiences anything in. For instance, an object does not exist in the past nor in the future. An object is always stuck in the present time. As for the ''statistically-speaking'' part, I am referring to the wave function of matter.

Thanks. It appears we agree, but let me ask a few more questions to make sure I understand you.

 

When you say the present state is the only state a thing (let us call it human brain) experiences anything in, this means there would be another state for the thing (lets call it non-present state) where it does NOT experience anything, yet the anything, as an object of potential experience may exist...correct ? (note: I use red and blue to highlight the difference between the terms thing and anything as you use them).

 

Next, the wavefunction of an object (the anything above) can 'exist' within a 'present state' that you also call a 'moment in so-called time'. Would your 'so-called time' also be the spacetime of Einstein. Is there any reason you would not agree with this ? Next, is it possible only the wavefunction of the object exists within a present state moment, but the object also has potential to exist as a particle and not wavefunction outside the present state moment(e.g., via concept of wave-particle duality of quantum theory)?

 

Next, would you agree that the duration of the present state moment where the wavefunction of anything can be found would have extension and duration of Planck length and Planck time and thus the reason humans as a thing can never experience the present state moment of interaction with anything, that is, the feeling we all get that the present moment is long gone before we can concentrate on it ?

 

Next, when you say that the object (the anything) does not exist in the past, are you saying (1) it did not exist in a past state moment in so-called time (or spacetime of Einstein) that once was a present state moment, (2) it did not exist as an object with potential motion in a past timelike interval of so-called time, (3) both 1 and 2 are true, (4) neither are true, (5) one is true but not the other ?

 

I appreciate any response because it will help me better understand your presentation and how it may or may not match my understanding of the HUP (or lack of).

Edited March 13, 2013 by Rade

[Aethelwulf]

Ok I won't beat around the bush here... how does the uncertainty principle come into play in the above?

 

According to three physicists, you can actually know the position and the trajectory of a particle - so long as your measure both complimentary values at different times; a process often called in physics as two-time measurements.

 

''Curious New Statistical Prediction of Quantum Mechanics''

 

http://prl.aps.org/abstract/PRL/v54/i1/p5_1

 

You might be familiar with David Albert, certainly Yakir Aharonov is well known but perhaps a little less known is Susan D'Amato.

 

So how does their idea work? Well, if you make a measure of a particles location in the past say and a measurement of it's momentum in the future, you can statistically know the momentum and position simultaneously in the present moment, seemingly violating the uncertainty principle!

 

But how do you actually make a measurement in the past and future and gather that information here in the present? I don't know if that is even possible, but what does seem possible is that something similar is happening with the wave function (on the fundamental level). Perhaps the past and future are actually influencing things here in the present moment. But what is the past if not once a present moment as well? It certainly doesn't exist ''now'' because it is past, so what is sending this signal to the present moment?

 

The answer must be that the past has it's ''own present moment.'' The same goes for the future. In fact you could argue that everything is stuck in an eternal present.

[Rade]

According to three physicists, you can actually know the position and the trajectory of a particle - so long as your measure both complimentary values at different times; a process often called in physics as two-time measurements.

 

''Curious New Statistical Prediction of Quantum Mechanics''

 

http://prl.aps.org/abstract/PRL/v54/i1/p5_1

Thanks, a very interesting paper that gets directly to what I was describing, what happens to quantum systems within the time-like interval between two moments (two measurement events). But I would add that the same can be asked of classical, non quantum systems, and my discussion of time above addresses both circumstances.

 

So how does their idea work? Well' date=' if you make a measure of a particles location in the past say and a measurement of it's momentum in the future, you can statistically know the momentum and position simultaneously in the present moment, seemingly violating the uncertainty principle![/quote']Your explanation here is very helpful.

 

But how do you actually make a measurement in the past and future and gather that information here in the present? I don't know if that is even possible' date=' but what does seem possible is that something similar is happening with the wave function (on the fundamental level). Perhaps the past and future are actually influencing things here in the present moment.[/quote']Well, this makes sense to me because, as I suggested in posts above, I see the past as associated with ----- spacetime ----> forming a begin boundary with the present moment ->| , while, simultaneously (within error of human measurement), future spacetime forms the end boundary of the same present moment |>-. The summary picture is past->|present moment|>-future. So yes, the present moment must be influenced by past and present spacetime intervals at the two boundary conditions of any moment | and |, and what is of interest, they both would influence the present moment at the same moment in time, that is, simultaneously.

 

But what is the past if not once a present moment as well?

Yes' date=' I agree in the context of moments. But, we also can say that the past "is" an interval of spacetime before any present moment ----> || because we can imagine the opposite, a future interval of spacetime after the same moment || ---->. So, for me, the past and future can be either a moment in time or an interval of spacetime between a set of measurement events (e.g., moments or nows).

 

It [the past] certainly doesn't exist ''now'' because it is past, so what is sending this signal to the present moment?

There are two aspects to the "now" as relates to time. In one sense it is the same, as we talk about the past, future, present moments (as a now) are the same, e.g., moments in time. But, to the extent that we can think of a set of nows in infinite succession, ( ....Now-1 Now-2 Now-3.....) they must differ in the order they are found within the set. Thus each now has dual attributes. When considered as a set of nows in succession, there must be something intermediate between any two nows (which must be the spacetime interval of Einstein) that has an entity with potential of motion, and each entity with motion at different spacetime intervals must be associated with different nows.

 

Thus, I would suggest that one possible answer to your question of what sends the signal to the present moment, is "an entity (defined or undefined) that exists with potential of direct motion, or potential to emit information signals, that can be measured by time". Thus, the now as a moment in spacetime corresponds to the entity that exists, while simultaneously, time and space corresponds to the motion of that entity that can be measured. Also, the same entity would be that from which a signal could be released from a present moment. The theory of cybernetics would help with the details of how signals emitted by entities could be received by the present moment or released from it.

 

The answer must be that the past has it's ''own present moment.'' The same goes for the future. In fact you could argue that everything is stuck in an eternal present.

I would modify to say the past HAD it's own present moment and the future WILL HAVE it's own present moment. So, yes, in this view there is only eternal PRESENT, although, as said above, a better view may be that there is only an eternal SET of infinite present moments as now ( ....Now-1 Now-2 Now-3.....). And this is what Einstein said in a letter after the death of his dear friend Besso ..."He has departed from this strange world a little ahead of me. That means nothing. For us believing physicists, the distinction between past, present, and future is only a stubborn illusion" (W. Isaacson, p.540). But Einstein was not referring to MOMENTS as "nows" in the sense that each moment can occur as a set of nows that must differ in virtue of having attribute of order ( ....Now-1 Now-2 Now-3.....).

 

Comments pro-con welcome.

Edited March 14, 2013 by Rade