Non-locality again

[orange31]

Hello, I'm new to the JREF, it looks like a great site and I'm pleased to be here.
For a few months I've read about EPR, Bell's Inequality, etc using the well known books for laymen by Pagals, Green, and the more recent experimental work by Aspect.

It seems most physicists stop at the inexplainable point, as it seems professionally indiscreet for a physicist to speculate about FTL potential mechanisms.

So here's my question: Isn't the only possible "explanation" for Quantum nonlocality (regardling simultaneous spooky action at a distance) the existence of another dimension? (Not that that would prove another dimension). Or are there other explanations I've missed?
Thanks for your time and consideration!

[Molinaro]

I don't think the extra dimensions are suggested as solutions to the action-at-a-distance problem. It's not as if some motion is suposed to occur through these other dimensions resulting in us observing an effect that seems to not travel through the known dimensions.

From what I've understood, the extra dimensions are suggested as a means of unifying the forces and as a means of deriving their relative strengths using the underlying geometry of the universe as a basis for the calculations.


I like the explanation given by the transactional interpretation of QM to do away with the mystery of the Aspect experiment and other double slit stuff.

[Moochie]

Yep.

M.

[godless dave]

Keep in mind that when physicists talk about extra dimensions they're not talking about parallel planes of existence like what you see on Star Trek. They're using "dimension" in the mathematical sense.

[sol invictus]

So here's my question: Isn't the only possible "explanation" for Quantum nonlocality (regardling simultaneous spooky action at a distance) the existence of another dimension?

No - not at all.

First of all, no "explanation" is necessary. Quantum field theory is a perfectly consistent mathematical description of nature, which coincides with experiment to 12 significant figures (the greatest accuracy of any theory in the history of science). It contains these phenomena, and so that is probably just the way the world works. Beyond that I'm not sure what you would mean by an explanation. It does not contain any extra dimensions (and it is consistent with special relativity, in case you're wondering).

Secondly, adding an extra dimension or dimensions to the theory (which is often done, but for reasons that have nothing to do with this) does not affect these phenomena in any interesting way.

[orange31]

Thanks - a few questions-

I like the explanation given by the transactional interpretation of QM to do away with the mystery of the Aspect experiment and other double slit stuff. - Molinaro
I checked out some of that, quite interesting, but Cramer is forthright in saying it's untestable. It may also involve the use of 'hidden time' or hidden space-time, which is kind of problematic ;).

First of all, no "explanation" is necessary... Quantum field theory is a perfectly consistent mathematical description of nature,....that is probably just the way the world works...etc -Sol invictus

I realize no explanation is necessary, as QM always checks out right. Are you saying that "explanation" is actually not possible because our macroscopic classical day to day life and analogies just can't wrap around QM?

[Fnord]

... the extra dimensions are suggested as a means of unifying the forces and as a means of deriving their relative strengths using the underlying geometry of the universe as a basis for the calculations.


I agree.

Too often, people use see the term "Extra-Dimensional" and think "Alternate Universe". I guess this comes from the tropes of pulp science-fiction.

[orange31]

I only meant "extra dimension" in the geometric sense of a real dimension, and how a 5th one could 'explain' simultaneous particle actions that are separated great distances/time in our 4 dimension world, by the particles being side-by-side in dimension 5.
No, I was not thinking of a star-trek 5th dimension as another world with it's own set of 4dimensions.

[sol invictus]

Are you saying that "explanation" is actually not possible because our macroscopic classical day to day life and analogies just can't wrap around QM?

More that the theory is the explanation.

For example, the orbits of planets are not particularly intuitive to people (the fact that the earth is always falling towards the sun, and yet never hits it). But once you understand the theory it becomes easy to understand and quite intuitive.

Quantum mechanics is another order of weirdness, but still, once you understand the mathematics, it becomes easier to comprehend.

I only meant "extra dimension" in the geometric sense of a real dimension, and how a 5th one could 'explain' simultaneous particle actions that are separated great distances/time in our 4 dimension world, by the particles being side-by-side in dimension 5.

But that doesn't help at all. If they are far apart in our 4 dimensions, being close in the 5th doesn't make them any nearer.

Imagine two points, very close together along the x-axis, but very far apart in the y direction. They're still very far apart even though they are close in x. The distance between them (put one at the origin) is the square root of x^2 + y^2, so if y is large, the distance is large regardless of x.

[orange31]

But that doesn't help at all. If they are far apart in our 4 dimensions, being close in the 5th doesn't make them any nearer.


Woops- I sketched out an example on an XYZ graph (point 2,4,0 and point 2,4,-8 ) and of course you're right. I tripped up on the semantic concept of 'sharing' a coordinate(s). Thanks.

So nonlocality is even wierder than I thought. I guess you're a Copenhagen guy and not too taken with the transactional concepts of offer waves, confirmation waves, hidden time, etc; - best just to stick to the math?

[arthwollipot]

Strange - this is the second time I've seen transactional QM raised in these forums this week.

[nathan]

But that doesn't help at all. If they are far apart in our 4 dimensions, being close in the 5th doesn't make them any nearer.

All that adding a 5th dimension can do is make them _further_ apart :)

[sol invictus]

All that adding a 5th dimension can do is make them _further_ apart :)

Unless

a) the extra dimension is like time, in which case distance squared is x^2-t^2, or

b) the extra dimension is curved and we're stuck mostly to a subspace. That is, imagine we are stuck to the inside surface of a cylinder, but some particles can propagate through the bulk of the cylinder. Two antipodal points are separated by pi R along the surface, but only by 2 R through the bulk, so events there can influence each other more quickly than someone who can only see the surface would expect.

Neither of those help with the OP's question, though.

[nathan]

a) the extra dimension is like time, in which case distance squared is x^2-t^2,

could you clarify this? I don't follow ...

[sol invictus]

could you clarify this? I don't follow ...

In relativistic theories, the difference between time and space is a factor of i (where i^2=-1). That means the norm - the length of a vector - is not positive definite. It can be zero or negative.

So if you have two points, one at t=0, x=0 and one at t=t, x=x, the squared "distance" between them is x^2-t^2 (or t^2-x^2 depending on convention). Points connected by null rays (paths along which light can move) are zero distance apart.

Just as rotations preserve radial distance (x^2+y^2), Lorentz transformations preserve this distance (x^2-t^2).

EDIT - by the way, every time I write "t" I mean "ct", where c is the speed of light.

[nathan]

In relativistic theories, the difference between time and space is a factor of i (where i^2=-1). That means the norm - the length of a vector - is not positive definite. It can be zero or negative.

Thanks, I'd not appreciated that i came into it. BTW I recall some Scientific American article a few years back which discussed (amongst other things), how many large-scale spatial and temporal dimensions are conducive to a complex universe. It had a graph of spatial-dimensions vs temporal ones, and comments about what a universe of each particular combination would be like. (unfortunately I cannot recall the date of publication). Anyway, IIRC it claimed that exactly 1 large-scale temporal dimension was a necessity and at least 3 spatial ones. I can't recall the upper bound on spatial dimensions, it may have been 3 or 4.

[sol invictus]

Anyway, IIRC it claimed that exactly 1 large-scale temporal dimension was a necessity and at least 3 spatial ones. I can't recall the upper bound on spatial dimensions, it may have been 3 or 4.

As far as I know no one really understands theories with more than one time dimension. But for spatial dimensions there are some interesting arguments.

With 1 spatial dimension things are truly boring. The only possible interaction is a head-on collision.

With 2, you can't have a mouth connected to an anus without splitting yourself in half :), and so it's not very clear whether there's enough "room" for life. You also probably don't have any chemistry (see below).

3 is very special - a hydrogen atom has a discrete set of possible energy levels for its electron, allowing complex and interesting chemical bonds to form between atoms.

In 4 the potential of a proton is 1/r^2 and electrons have a continuous energy spectrum, meaning no chemistry (probably - I haven't thought very hard about it, and this particular case is rather subtle).

In 5 and higher, the energy of the electron is unbounded from below and you have major problems.

Of course none of these arguments really prove anything, primarily because I'm assuming that the only thing we can change is the number of dimensions (and not the rest of the theory). Also this is kind of "proof by lack of imagination" - there may well be other forms of chemistry or some other kind of complexity which we just haven't thought of.

Is that the kind of thing the Sci Am article discussed?

[sol invictus]

So nonlocality is even wierder than I thought. I guess you're a Copenhagen guy and not too taken with the transactional concepts of offer waves, confirmation waves, hidden time, etc; - best just to stick to the math?

I think the Everett interpretation is probably the correct one. It is fully consistent with everything we've observed, and (unlike Copenhagen) it is logically complete.

[nathan]

Is that the kind of thing the Sci Am article discussed?

Yes. some time between Feb 2002 and 2005?

[Fnord]

All that adding a 5th dimension can do is make them _further_ apart :)


... assuming that each dimension is somehow orthogonal to all the others.

[slyjoe]

... assuming that each dimension is somehow orthogonal to all the others.

But isn't that true by definition? We can't visualize it, but the math works out. Otherwise, you wouldn't need another dimension.

[orange31]

Strange - this is the second time I've seen transactional QM raised in these forums this week.


Que ominous sounding background music ;)

[Molinaro]

Strange - this is the second time I've seen transactional QM raised in these forums this week.

That would have been me both times :)

I'm re-reading "To The Beat of a Different Drum: The Life and Science of Richard Feynman" by Jagdish Mehra. I am just finishing up reading the section about his Doctoral Thesis were his transactional methods were first derived.

[Fnord]

But isn't that true by definition? We can't visualize it, but the math works out. Otherwise, you wouldn't need another dimension.


I had understood that some dimensions "wrap around" the three orthogonally-aligned space dimensions, like the sheath of insulation around a wire, and that they do not interact with time in a way that "we" fully understand.

But since all of my work is on atomic-scale materials and E/M waves, I may not ... certainly do not ... have a complete understanding of dimensions beyond the "Big Three" and time.

[arthwollipot]

That would have been me both times :)Wow! What were the chances of that? :D

[Cuddles]

I had understood that some dimensions "wrap around" the three orthogonally-aligned space dimensions, like the sheath of insulation around a wire, and that they do not interact with time in a way that "we" fully understand.

But since all of my work is on atomic-scale materials and E/M waves, I may not ... certainly do not ... have a complete understanding of dimensions beyond the "Big Three" and time.

It's important to remember that dimensions are essentially a human construct. It is entirely possible to define a different set of dimensions that describes the universe just as well, all that is really fixed by the universe is the minimum number of dimensions. Defining orthogonal dimensions is just the simplest way way to do things. However, in the case of dimensions "wrapped around" others, they are still orthogonal. Just think of cylindrical coordinates, for example. You have two cartesian coordinates and a third effectively wrapped around them, but they are all orthogonal to one another.

[arthwollipot]

I had understood that some dimensions "wrap around" the three orthogonally-aligned space dimensions, like the sheath of insulation around a wire, and that they do not interact with time in a way that "we" fully understand.

But since all of my work is on atomic-scale materials and E/M waves, I may not ... certainly do not ... have a complete understanding of dimensions beyond the "Big Three" and time.Actually, in "standard" string theory (as if there is any such thing), the extra dimensions are not actually wrapped around other dimensions - they are tightly curled up, and therefore do not have the same spacial extent as the regular three spacial dimensions that we are used to.

The metaphor used in Brian Greene's The Elegant Universe (which I recommend) is that of a garden hose stretched over a canyon. From a long distance away, the hose appears to have only one dimension, and it would be assumed that a hypothetical ant walking on the hose would have only one dimension in which to move - left and right. But when you get closer, you can see that the hose actually has a second dimension, tightly curled up. The ant can move left and right along the length of the hose, but can also move around the hose.

Extend this metaphor to three dimensions and you'll get the idea. At every point in the three extended spacial dimensions, there is one or more other dimensions which are tightly curled up (into a calabi-yau manifold if you want to get technical).

Anyway, I think this is getting a little off-topic.