Quantum Entanglement ?

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Posted (edited)
On 12/9/2017 at 8:04 AM, interested said:

I would not assume the pendulum clock had travelled in time if I accelerated it or if I changed the level of gravity it was experiencing, and time either slowed down or speeded up.

Exactly. The same effect can often be produced by more than one cause. An acceleration implies the application of force, and forces applied to things change how they behave.

6 hours ago, interested said:

Question is this link related to entanglement,

Yes. The last sentence in the article states "These include fundamental questions for our understanding of the universe like the interplay of quantum correlations and dimensionality..."

As I have described in other posts, the effect of "quantum correlations" can be produced by misinterpreting measurements made on a 1-dimensional object (a single bit of information) as being caused by measurements assumed to be made on the multiple vector components existing within a 3D object.

Edited by Rob McEachern
somehow this got posted before I ever finished typing

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Posted (edited)
17 hours ago, Rob McEachern said:

Yes. The last sentence in the article states "These include fundamental questions for our understanding of the universe like the interplay of quantum correlations and dimensionality..."

As I have described in other posts, the effect of "quantum correlations" can be produced by misinterpreting measurements made on a 1-dimensional object (a single bit of information) as being caused by measurements assumed to be made on the multiple vector components existing within a 3D object.

18 hours ago, Strange said:

However it could possibly be evidence for a possible effect that might be consistent with a 4d Hall effect.

So 4 spacial dimensions are definately possible, but not definitely proven.

Would anyone have any opinions on additional time dimensions, involved with entanglement?

Edited by interested

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Posted (edited)
1 hour ago, interested said:

So 4 spacial dimensions are definately possible, but not definitely proven.

Anything (almost) is possible.

And nothing is ever really proven.

1 hour ago, interested said:

Would anyone have any opinions on additional time dimensions, involved with entanglement?

Entanglement is explained without needing extra time dimensions. I’m not aware of any theories needing extra time dimensions.

It may be impossible:

Edited by Strange

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3 hours ago, interested said:

So 4 spacial dimensions are definately possible, but not definitely proven.

One has to be careful. The number of dimensions that are important, may be those existing in the logical space being used to describe the physical space, rather than those of the physical space (including time) itself. Consider the situation in numerical analysis, of attempting to fit an equation to a curve or to a set of data points. One may choose to fit an equation with a fixed number of parameters (logical dimensions) or a non-fixed number.  For example, if you choose to fit a straight line, then there are only two parameters required to describe the "best fit" line. But if you were to chose to fit a Fourier series or transform to the curve, there may be an infinite number of parameters required, to specify the "best fit". Gravitational theory is a "parametric" theory, in that it requires only a fixed number of parameters, to describe behaviors. But quantum theory is a "non-parametric" theory, requiring an infinite number of parameters (Fourier transforms) to describe behaviors. This is one of the reasons why it is so hard to make the two "play together" and it is also why it is so hard to find a common-sense interpretation for quantum theory -  a non-parametric theory may be consistent (sufficient to describe) virtually any behavior, and thus it may not be possible for it to eliminate any hypothetical cause for the behavior - anything goes - and weird interpretations and correlations (entanglement) may result from attempting to associate an incorrect "logical dimensionality" with the correct "physical dimensionality". The situation is further complicated by the fact that the physical dimensionality of an emitter may differ from the logical dimensionality of any emissions (observables) produced by the emitter. In other words, simply because an object has three physical, spacial dimensions, does not necessitate that its observables must also possess three logical dimensions (three independent parameters).

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On 30/07/2017 at 6:18 PM, interested said:

Can any one explain how quantum entanglement works, and the limits of what is achievable through quantum entanglement.

It's apparent, not real, much like a spirograph.

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5 minutes ago, dimreepr said:

It's apparent, not real, much like a spirograph.

Um, what? What sense of "real" are you using?

Entanglement has measurable results.

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Spirograph is also real.

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Uhmm...
Electromagnetism also requires a fixed number of parameters, and is, then, a parametric theory.
Yet quantum electrodynamics seems to work just fine.

I used to have a real Spirograph...

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12 minutes ago, MigL said:

Yet quantum electrodynamics seems to work just fine.

QED does not play very well with gravity, and unlike EM, it is non-parameteric; Nobody uses wavefunctions, in classical EM, as they are used in QED.

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Posted (edited)

I think you have it backwards...

Electromagnetism uses a finite set of parameters and is 'asymptotically free', such that a quantum field theory of electromagnetism ( QED ) still has a finite set of parameters  because it  is renormalizable.

Gravity has a finite set of parameters classically, but is perturbatively non-renormalizable, and at high energies, the parameters become intractable and will not go away.
Various methods around this obstacle have been attempted...
An effective field theory , which makes use of a 'cut-off' and basically discards un-needed parameters.
String theory, which is like QM, background dependant.
LQG, which like GR, is background independent.
And many other approaches

Edited by MigL

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Posted (edited)
20 hours ago, Strange said:

I’m not aware of any theories needing extra time dimensions.

String theories need at least 9 spacial dimensions,  and i understand some use more than one time dimension

20 hours ago, Strange said:

Tachyons are a bit like dark matter, they havent been detected.  3 space and 1 time dimension do not appear to cover the QM world which appears a little unstable a 4th spacial dimension is not stretching the realms of possibility, when string theory is taken into account.

9 hours ago, MigL said:

I used to have a real Spirograph...

Whats a spirograph, is this what you are talking about https://en.wikipedia.org/wiki/Spirograph aqnd what has that got to do with entanglement or an extra dimension

Edited by interested

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1 minute ago, interested said:

Tachyons are a bit like dark matter, they havent been detected.

Except we know dark matter(or, sigh, something that causes the effects that can be modelled as dark matter)  exists but there is no reason to think tachyons exist. And the existence of tachyons is irrelevant.

Quote

3 space and 1 time dimension do not appear to cover the QM world

Quantum field theory works perfectly well in 4D spacetime. Do you have any evidence to back up this assertion?

3 minutes ago, interested said:

the QM world which appears a little unstable

The universe still exists so I don't know what you are basing this idea of it being "unstable" on.

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9 hours ago, MigL said:

I think you have it backwards...

We are talking about two different things. I am talking about the number of parameters required to specify the solution to a problem. You are talking about the number required to specify only the equations. The solution also depends upon the auxiliary conditions like the initial and boundary conditions, in addition to the equations. A non-parametric solution does not require any correspondence between the number of parameters in the solution and the number in the initial conditions - think about the number of parameters in a best-fit line versus the number of *points* being fit. The significance of this, is that such a theory "loses track" of the number of particles it is supposed to be describing. Thus, it should come as no surprise that it cannot keep track of their detailed trajectories, when it cannot even keep track of their number. The number of particles that it actually does describe, ends up being an artifact of the description itself, rather that a property of the entities being described. And that is why particles are excitations of a field, in such a theory. This is the direct consequence of exploiting the mathematical principle of superposition in order to formulate a non-parametric solution. It worked great, when Joseph Fourier first developed his technique to describe a temperature *field*, but when physicists in the early twentieth century tried to apply it to the tracking of *particles*, they ended up losing track of them - because that is the inevitable result of choosing to employ a mathematical, descriptive technique, that is ill-suited to that purpose.

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Posted (edited)

Funny how there are  formulas in QFT that literally calculates the particle number density.  So I don't see how it loses track of them. The Bose Einsten and Fermi Dirac statistics is used to calculate the number density of a particle species from the blackbody temperature.

in QFT you use the Number operator given by

$N=\int\frac{d^3p}{2\pi)^3}a^\dagger_\vec{p} a_\vec{p}$

where $a^\dagger, a$ are the creation and annihilation operators. Several important cutoffs in QFT is the IR, UV and LSZ cutoffs to prevent infinities. The Lehmann-Symanzik-Zimmermann formula is used on the scattering amplitudes. In particular its application to path integrals.

$|\vec{p}\rangle$ is the particle, however its described via its momentum eugenstate,

The LSZ and QFT use the Klien Gordon as opposed to the Schrodinger equation which provides the second order of the space and time deriviatives

$-\hbar^2\frac{\partial^2}{\partial^2}\psi(\mathbb{x},t)=(-\hbar^2c^2\nabla^2+m^2c^4)\psi(\mathbb{x},t)$

The LSZ formula is extensive in its time ordered path integrals as you approach infinity in particular when you account for the number of vertex external lines on tree level diagrams. (lengthy topic of its own).  However the cutoffs provides the bounds.

(little sidenote when the operators above commute your describing a boson field, when anticommute its a fermionic field) ie via Pauli (another lengthy topic on how that works with above)

Edited by Mordred

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On 1/6/2018 at 8:25 AM, Strange said:

Quantum field theory works perfectly well in 4D spacetime. Do you have any evidence to back up this assertion?

The fact a mathematical model explaining the universe to some one living in flat land works perfectly well does not mean it is complete. Entanglement is simply explained for me by an additional spacial dimension that  can potentially connect different points in 4 dimension space time to another distant point in 4 D space time.

On 1/6/2018 at 8:25 AM, Strange said:

The universe still exists so I don't know what you are basing this idea of it being "unstable" on.

Quantum fluctuations and excitations can randomly appear to move around in space time, with an  extradimension this might not appear so random.

With the addition of one extra dimension as a minimum connecting points in space, it appears possible to me to explain many things.

15 hours ago, Mordred said:

Klien Gordon as opposed to the Schrodinger equation

Ahhh Schrodinger equation I actively avoided questions on this in my final exams, do you have any opinion on Kaluza Klein 5 dimensional space https://en.wikipedia.org/wiki/Kaluza–Klein_theory

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1 hour ago, interested said:

Entanglement is simply explained for me by an additional spacial dimension that  can potentially connect different points in 4 dimension space time to another distant point in 4 D space time.

You might want to look up Occam’s Razor.

Inventing something that is both unnecessary and undetectable is a waste of time. It might make you feel better but it isn’t science.

1 hour ago, interested said:

Quantum fluctuations and excitations can randomly appear to move around in space time, with an  extradimension this might not appear so random.

It is not random. It is deterministic but probabilistic.

1 hour ago, interested said:

With the addition of one extra dimension as a minimum connecting points in space, it appears possible to me to explain many things.

It might appear that way, but with no mathematical model there is no way to know. And I would guess it violates Bell’s inequality. As it is, we have explanations and that work.

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Posted (edited)
48 minutes ago, Strange said:

You might want to look up Occam’s Razor.

Occams Razor is an excellent tool, it has two edges, and cuts in many different ways.

For example

Cut 1:

For a Four dimensional creature living in 4 dimensional space and time

If two particles appear to be connected over a long distance, and appear to transfer information almost instantaneously, then they may be connected by an extra spacial dimension.  If a particle appears in two places at once, then it exists in both places at once and could be by an extra spacial dimension.

Cut 2:

For a flat lander living in 3 dimensional space and time

If two particles appear to be connected over a long distance, and appear to transfer information almost instantaneously, then a mathematical function in 3 dimensional space can explain it.  If a particle appears in two places at once, then a mathematical function in 3 dimensional space can explain it.

Cut 3 :

For anyone prepared to accept there may be more than 3 spacial dimensions and one time dimension

String theory, has extra spacial dimensions, an earlier theory involving just 4 spacial dimensions one of them invariant and a time time dimension was  https://en.wikipedia.org/wiki/Kaluza–Klein_theory ,

---------------------------------------------------

The FACT is modern science appears to require extra spacial dimensions to explain the real world. Cut 1 is simple, Cut 2 is for flat landers, Cut 3 is complicated.

I posted the question on Kaluza Klein as it introduces a 4th spacial dimension and did not disagree with relativity although it does have problems as indicated in the link. It is an early example of science contemplating an extra spacial dimension, possibly connecting other 3 dimensional spaces directly together, via an invariant spacial scalar dimension.

IF OCCAMS RAZOR IS APPLIED IN  ALL DIRECTIONS, extra spacial dimensions exist. However as you are aware using maths it is not difficult to reduce a four dimensional space to 3 dimensions for flat landers to understand.

Edited by interested

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7 minutes ago, interested said:

Occams Razor is an excellent tool, it has two edges, and cuts in many different ways.

1

No, it really doesn't.

9 minutes ago, interested said:

However as you are aware using maths it is not difficult to reduce a four dimensional space to 3 dimensions for flat landers to understand.

Go on then...

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Posted (edited)
18 minutes ago, interested said:

If two particles appear to be connected over a long distance, and appear to transfer information almost instantaneously, then they may be connected by an extra spacial dimension.  If a particle appears in two places at once, then it exists in both places at once and could be by an extra spacial dimension.

All Occam's razor says is that you should remove unnecessary entities. You are proposing unnecessary extra dimensions.

18 minutes ago, interested said:

The FACT is modern science appears to require extra spacial dimensions to explain the real world.

That is not a "fact". There is no actual theory (i.e. tested and confirmed by experiment) that requires extra dimensions.

And extra dimensions are not required (even in those speculative theories that include them) to explain entanglement.

Edited by Strange

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On 05/01/2018 at 5:33 PM, swansont said:

Um, what? What sense of "real" are you using?

Entanglement has measurable results.

I'm sure I understood what I meant at the time but due to one too many beers, I can't remember that post.

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On 1/6/2018 at 2:31 PM, Mordred said:

Funny how there are  formulas in QFT that literally calculates the particle number density.  So I don't see how it loses track of them.

The answer lies in the word density. First, density is only proportional to number, so the theory only needs to track the probability density (not the actual number) of particles being detected at particular locations and times, but not the trajectory they took to get there, or their actual number. Second, and much more interesting, is how this all relates to so-called quantum fluctuations, renormalization, and the error behavior of superpositions of orthogonal functions. Addressing these issues will quickly lead beyond the scope this tread’s topic,  so I will keep this brief, so as not to incur the wrath of any of the moderators - if you wish to pursue the matter further, I would suggest starting a new topic devoted to these issues.

Briefly, think of a Fourier series, being fit to some function, such as the solution to a differential equation. As each term in the series is added, the least-squared-error between the series and the curve being fit, decreases monotonically, which each added term, until it eventually arrives at zero - a perfect fit. Which means that it will eventually (if you keep adding more terms to the series) fit any and all errors and not just some idealized model of the “correct answer”. In other words,  it will continue adding in global-spanning basis functions, that decrease the total error, while constantly introducing fluctuating, local errors all over the place. In essence, it treats all errors, both errors in the observed data and errors in any supposed idealized particle model (like a Gaussian function used to specify a pulse that defines a particle’s location) as though they have actual physical significance and must therefore be incorporated into the correct answer. Hence, the series forces “quantum fluctuations” to occur, by instantaneously reducing what is being interpreted as the particle numbers at some points, while simultaneously increasing it at others, in order to systematically drive down the total error between the series and the curve being fit; all because the superposition of the orthogonal functions never demands that any particles remain on any trajectory whatsoever, in order to reduce the total error.  It ends up being much easier (and likely)  for the method to drive the error down, by constructing a solution that has supposed particles popping in and out of existence all over the place, in order to rid the solution of any and all non-local errors or noise.

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Posted (edited)

no it also keeps track of number density, not everything in QFT involves probability ie once you take a measurement.

Obviously your missing the importance of the cutoffs with regards to fourier analysis. In particular the significance between operators and propogators in terms of the Feyman boundary conditions. However thats a lengthy topic in and of itself that is best left for another thread.

Edited by Mordred

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1 hour ago, Mordred said:

Obviously your missing the importance of the cutoffs with regards to fourier analysis.

My point is that QM imposes no cutoffs, unless it is done in a completely ad hoc manner, because it cannot do it any other way; because any physically relevant cutoff would be dependent on the specifics of the detection process used to experimentally detect and thus count anything.

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Posted (edited)

What is adhok about applying a cutoff, there is always an established reasoning behind those cutoffs. For example it doesn't make much sense to define a particle that has energy levels too low to cause any observable or measurable effect. For that matter in order to be observable you must have some displacement hence operators as opposed to propogators. Though to fully understand an operator you must also define localization under LSZ which is a time ordered metric.

Have you ever truly looked at the reasoning behind each type of cutoff or boundary condition?

For example define when local action differs from non local effective action without applying a boundary to each of those two terms. Nothing arbitrary or adhok about having that requirement.

Another good example being boundary conditions imposed by other field potentials. Primary example being the Dirichlet boundary condition to describe the temperature on a surface as opposed to the Neumann boundary condition which describes the flux of temperature beneath said surface. These boundaries aren't adhok. For example the Poission equations are elliptic so the Direchlet boundary condition is appropriate while the Neumann boundary condition applies to parabolic. In the above case a Green's function is defined not only with respect to an equation and its boundary conditions, but also with respect to a particular region. However more importantly the Greens function provides a limit between measurable "Observable" via ODE's to infinitisimal which are units so small they cannot be measured PDEs (partial differential equations)

As far as probability or density functions go well a natural boundary is the set of Real. After all the sign doesn't matter for density. Negative probability via imaginary numbers doesn't particularly make sense either. (not to be confused with correlation functions. This applies to the limits of a domain. Infinity for example is not a number and cannot be manipluated algebraically. It only makes sense with an applied limit on a given function. Limits is a lengthy topic, ie limits of vertical and horizontal asymptotes, limits of the numerator and denominator, limit of quotient which all applies to graphs.

I fail to see where you feel QM limits are adhok considering those same limits arise in differential calculus. Good example limit to the slope of a curve. Though under QM the slope is a discontinous wavefunction (discrete units) though thats not only form of discontinuos  wavefunctions.

Edited by Mordred

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Posted (edited)
14 hours ago, Mordred said:

As far as probability or density functions go

14 hours ago, Mordred said:

I fail to see where you feel QM limits are adhok

The problem lies within the difference between the properties of the territory (reality) and the properties of the map (mathematics - specifically Fourier transforms) being used in an attempt to describe the territory. I am of the opinion that all the well known, seemingly peculiar properties of quantum theory, are merely properties of the map and not properties of the territory itself. This begins with the assumption that quantum theory describes probabilities. It actually describes the availability of energy, capable of being absorbed by a detector; this turns out to be very highly correlated with probability. This happens, because of the frequency-shift theorem pertaining to Fourier transforms: in the expression for the transform, multiplying the integrand by a complex exponential (evaluated at a single "frequency") is equivalent to shifting (tuning - as in turning a radio dial) the integrand to zero-frequency and the integral then acts like a lowpass filter to remove all the "signal" not near this zero-frequency bin. Thus, the complete transform acts like a filterbank, successively tuning to every "bin". Subsequently computing the sum-of-the-squares of the real and imaginary parts, for each bin, then yields the (integrated) energy accumulated within each bin (AKA power spectrum). If this accumulated energy arrived in discrete quanta, all of the same energy per quanta, then the number of quanta that was accumulated in each bin, is simply given by the ratio of the total accumulated energy divided by the energy per quanta. In other words, in the equi-quanta case, this mathematical description turns out to be identical to the description of a histogram. Which is why this description yields only a probability distribution and why all the experiments are done with monochromatic beams. If there is "white light", then there may be no single value for the energy per quanta within a single bin, to enable inferring the correct particle count, from the accumulated energy.

So, quantum theory never even attempts to track the actual motion (trajectory) of anything, either particle or wave, it just, literally, describes a set of detectors (a histogram) at some given positions in space and time, that accumulate the energy arriving at those positions in space and time - energy that enables an exact inference of particles counts (probability density) whenever the energy arrives in equal-energy quanta within each bin.

The mathematical description is thus analogous to the process of a police officer attempting to catch a thief that is driving though a community, with many roads, but with only one way out. Rather than attempting to follow the thief along every possible path through the community, the officer simply sits at the only place that every path must pass though (a single bin/exit), in order to ensure being detected. If there are multiple such exit-points, then multiple bins (detector locations) AKA a histogram is required, to ensure that the probability of detection adds up to unity. - every way out must pass through one detector or another.

Edited by Rob McEachern
Correct typos