Quantum continuum.

[peter]

I'm struggling a bit to hang my understanding of what quantum theory has to say (if anything) about the existence of otherwise of continua in the universe. I always understood the electromagnetic spectrum as a continuum - but if energy comes in little indivisable packets, it can't be can it? Am I correct in thinking that quantum theory effectively precludes the existence of continua? Space is not one - the plank length and granular nature of the stuff at the quantum level preclude this, light I said about above. But hang on; of continua are precluded by quantum mechanics - why can they exist in mathematics - or can they? Does there exist somewhere down there a 'planc number' beyond which further divisibility is impossible? Help!

[Vraith]

I'm struggling a bit to hang my understanding of what quantum theory has to say (if anything) about the existence of otherwise of continua in the universe. I always understood the electromagnetic spectrum as a continuum - but if energy comes in little indivisable packets, it can't be can it? Am I correct in thinking that quantum theory effectively precludes the existence of continua? Space is not one - the plank length and granular nature of the stuff at the quantum level preclude this, light I said about above. But hang on; of continua are precluded by quantum mechanics - why can they exist in mathematics - or can they? Does there exist somewhere down there a 'planc number' beyond which further divisibility is impossible? Help!

Well, it has a lot to say, and depends on which version you're talking about. We all, it seems, make that error around here for convenience. We say "Quantum Theory" as if it was all one big thing. It ain't.

And all the versions have their own claims and inherent contradictions/paradoxes...although they all have one thing in common: though they use a plethora of mathematical tools, and can't be done/understood without those tools, the fundamental levels of none of them are actually mathematically rigorous. [[some people are trying to make them so]].

Anyway: any PARTICULAR photon, depending on frequency, wavelength, can only interact at/with specific discrete energy quanta. BUT light can be any frequency/wavelength. [[though total available energy obviously creates an upper practical limit. I don't think there is a lower limit?? Theoretically, I guess the lowest would be one that is EXACTLY one wavelength that is the size of the entire universe---but it would always be getting lower/longer due to expansion...I think. Maybe. I think somewhere at some time I ran across someone suggesting standing waves in all directions the size of the universe. ]].

The Planck length is NOT the smallest size/distance that can exist. [[though some say it is]] It is the smallest length we can MEASURE. [[Due to energy required and uncertainty.]] Planck time is similar---it is how long it takes something moving at light speed to travel a Planck length. It doesn't mean that 1/2 a "Planck second" doesn't exist...just that it cannot be measured meaningfully.

Try this--just for autotelic reasons--you have a sphere of Planck diameter. What is its radius? Does that thinking imply anythings/prompt speculations? I ask cuz it does weird things to me.

And, more just for fun...though I really mention it cuz I was gonna do so in other threads, because it relates tangentially to emergent properties, and might relate to what consciousness is [at least analogically fruitful, I think], and some other things...

We, almost all of us, keep talking about quantum in terms of particles, and "force carriers" and such, as if [among other things] particles CAUSE fields and forces. That isn't really the case, though, it's more of a convenience/useful tool. At a fundamental level it seems the opposite is true: particles, to the extent they even exist, are created by/states of the fields.

[[[All errors in the above are because I'm talking from a point way way out in the fuzzy/misty territories of my brain-power, data, and exposure]]].

[wayfriend]

I always understood the electromagnetic spectrum as a continuum - but if energy comes in little indivisable packets, it can't be can it?

You're mixing metaphors there. Although it may just be the way you phrased it.

The electromagnetic spectrum is a purely mathematical+nomenclature construct, which describes the range of possible frequencies an EM wave may have, and assigns names to different subranges. It's like an FM radio dial, going from 88 to 108. Any given radio station will be at one specific frequency, but the dial represents the range where that station might be. The electromagnetic spectrum is a range of frequencies which an EM wave might have.

What an EM wave moves through is actually something else entirely. AFAIK it is nothing except space (the three dimensions). But QP may have a more refined answer.

[Hashi Lebwohl]

Anyway: any PARTICULAR photon, depending on frequency, wavelength, can only interact at/with specific discrete energy quanta. BUT light can be any frequency/wavelength. [[though total available energy obviously creates an upper practical limit. I don't think there is a lower limit?? Theoretically, I guess the lowest would be one that is EXACTLY one wavelength that is the size of the entire universe---but it would always be getting lower/longer due to expansion...I think. Maybe. I think somewhere at some time I ran across someone suggesting standing waves in all directions the size of the universe. ]].

All matter is a standing wave, or more accurately a collection of standing waves--*you* are a standing wave. At the macro level, though, wave motion is so small that it may be dismissed entirely...unless you are creating a Bose-Einstein condensate, in which case quantum effects start to manifest at the macro level, but then things get weird when that happens.

Anyway, the Planck length is significant because below that threshold all normal definitions and ideas about space, length, and time lose their meaning--at that point you are reducing spacetime itself to a quantum nature. For comparison, the charge radius of a typical proton is less than 1 fm (femtometer, or fermi, at 10^-15 m) and the Planck length is 20 orders of magnitude (10^-20) smaller than that (I forget the exact value but you can look it up in about 30 seconds). To put this in perspective, if the charge radius of that proton is the age of the observable universe (10^16 s), then the Plank length is a tenth of a millisecond (10^-4 s).

[Zarathustra]

Wave/particle duality is real. It's not a mathematical construct. In experiments, matter behaves as either, depending on how you conduct the experiment. There are many ways to interpret this, but I do not believe any sort of reductionism is going to do it justice.

[Vraith]

Wave/particle duality is real. It's not a mathematical construct. In experiments, matter behaves as either, depending on how you conduct the experiment. There are many ways to interpret this, but I do not believe any sort of reductionism is going to do it justice.

Reductionism...probably not. Because the meaning of reduction has been "reduced." 50/100 can be "reduced" mathematically to 1/2. BUT there are innumerable ways that 50/100 is NOT the same as 1/2...or the same as 49/98...
OTOH [or maybe on the same hand, but we're saying similar things in different terms/comprehension spheres] the duality is only real-ish, perhaps. IF [I'd actually lean towards WHEN] we come up with a different kind of experimental basis, it might well be particle/wave/?? triplicity. And then particle/wave/??/** quadracity. Because it is not "dual" it is something else that is neither.

[peter]

If I can make an example of what I'm thinking (and thanks for the posts guys - it'll take me a bit to read the links, but I will), my wallet can hold any degree of money - but I can only add to it a pound at a time, or whole multiples thereof (say). Therefore whatever money it holds will be in multiples of pounds - no half or quarter pounds etc. Now won't the same be true of the frequency values that light will be found to hold down at the quantum level of accuracy of measurement? Are not continua a bit like Newtonian mechanics, a good descriptive tool at macro levels, but which have no meaning in a quantum description of the world. Or (most likely is this just plain wrong, and continua ....... errr ...... continue even down at this smallest level - is they actually do represent how light-waves are in reality.

(A third possibility is that these descriptions are just simply that - descriptions - waiting to be superceded by a new, more encompassing description in which continua and quantum will be unified into a single description of greater explanatory power.)

[Vraith]

but I can only add to it a pound at a time, or whole multiples thereof (say). Therefore whatever money it holds will be in multiples of pounds - no half or quarter pounds etc. Now won't the same be true of the frequency values that light will be found to hold down at the quantum level

Not really, no.
The notes in your wallet COULD have any value whatsoever. The printer/government just decided to label it. [[not to mention, the actual value of every pound varies all the time]].
Photons can have any frequency/wavelength whatsoever between nothing and infinite.
I've seen some speculation there MIGHT be endpoints, but we can't measure, even in principle, to know for sure. But there definitely are not gaps between. All wavelengths/frequencies are possible.

[peter]

Fair comment V. All part of the process of learning: continua and quanta, room for everything!