The Best and Easiest Reading on Quantum Physics?

Uncertainty Principle

The uncertainty principle in quantum physics (usually associated with Heisenberg) is a fundamental limitation of nature and has nothing at all to do with our ability to make measurements of limited precision. Indeed, the principle can be derived entirely from pure mathematics, with no input from physics at all (i.e., Fourier Transforms and Uncertainty, The Mathematical Uncertainty Principle). Despite the fact that mathematics is an invention of the human mind, it appears nevertheless that the universe around us obeys the principles of mathematics at a very deep and fundamental level (i.e., Tegmark, 2008; follow the arXiv link to a PDF of the original).
 
Tim Thompson said:
The uncertainty principle in quantum physics (usually associated with Heisenberg) is a fundamental limitation of nature and has nothing at all to do with our ability to make measurements of limited precision. Indeed, the principle can be derived entirely from pure mathematics, with no input from physics at all (i.e., Fourier Transforms and Uncertainty, The Mathematical Uncertainty Principle). Despite the fact that mathematics is an invention of the human mind, it appears nevertheless that the universe around us obeys the principles of mathematics at a very deep and fundamental level (i.e., Tegmark, 2008; follow the arXiv link to a PDF of the original).
Click to expand...

Excellent posts, tim.
 
eirik said:
It's possible I don't understand your post here, but my understanding is that the a Schroedinger's box is a thought experiment(but possible) that shows how quantum physics can interact on a macro scale. I don't see how the double split experiment has anything to do with cats.. except that they are made of atoms.

The S-box has a quantum mechanical trigger, a radiation source who randomly and unpredictively shoots electrons on a detection device, which at some point releases a deadly gas, killing the cat. Did I miss anything?
Click to expand...
Well as I understand it the idea is that electrons that haven't been measured are actually superpositioned - i.e. we simply do not know their exact location. So in theory until we measure them they are actually in multipe states.

Schrodingers thought experiment was to show that this didn't scale up, so he create a 'ludicrous' example where a cat was introduced into the system and whether it was alive or dead was directly related to whether the electron had triggered the poison release. Since this was unknown until measured the electron and thus the life of the cat, was in both states at once.
Since this was impossible I thought the thought experiment was meant to show how the weirder aspects of QM did not scale up to macroscopic objects.

But I was informed on these forums that this was not the case.

It would be easier to explain if I could find the darned thread. :(
 
reason1 said:
Well, check the following post:
reason1 said:
This is a very good question. It varies from entity to entity, and also it depends on the level of abstraction of the stimulus, for example :
Questions consist of words , which consist of letters, which consist of sounds , which consist of waves that have frequency and amplitude.
If an entity can memorize and recall certain number of waves as a sound , it's conscious in regard to hearing.
If an entity can memorize and recall certain number of sounds as a letter, it's conscious in regard to language.
If an entity can memorize and recall certain number of letters as a word of certain language, it's conscious in regard to this particular language.
If an entity can memorize and recall certain number of words as a question, it's conscious in regard to grammar.
And so on, the more a stimulus is abstract, the more is the delay to construct a unit for it before it can be memorized in the area which is reserved for this particular stimulus kind.
And then after a unit of stimulus is recalled, comes the appropriate response, which can be internal (e.g.: more abstraction) or external (e.g.: replying to the question).
Click to expand...
Click to expand...

eirik said:
reason1 said:
Well, check the following post:


[snipped for crazytalk]
I'm very close to violating Heisenberg's uncertainty principle, very close than you've ever imagined!.
Click to expand...
Ok. Sorry for disturbing.
Click to expand...
OK :).
 
Are the threads in 2006 and 2007 missing from the search function?

I get results for 2008 and 2005, but never anything between.
 
Ashles said:
Well as I understand it the idea is that electrons that haven't been measured are actually superpositioned - i.e. we simply do not know their exact location. So in theory until we measure them they are actually in multipe states.

Schrodingers thought experiment was to show that this didn't scale up, so he create a 'ludicrous' example where a cat was introduced into the system and whether it was alive or dead was directly related to whether the electron had triggered the poison release. Since this was unknown until measured the electron and thus the life of the cat, was in both states at once.
Since this was impossible I thought the thought experiment was meant to show how the weirder aspects of QM did not scale up to macroscopic objects.

But I was informed on these forums that this was not the case.

It would be easier to explain if I could find the darned thread. :(
Click to expand...

I thought it showed that it CAN be scaled up to the macro world, and that your statement marked is inncorrect. But I'm no expert at all. Hmmm. Anyone else on this? Tim?
 
From wiki:
Schrödinger wrote:
One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.[2]

​
Click to expand...
Although he describes it as "quite ridiculous" I am unclear whether he then, or later, or others then or now consider the experiment to be, if not actually do-able, then at least scalable in principle from micro to macro.
 
Ashles said:
From wiki:

Although he describes it as "quite ridiculous" I am unclear whether he then, or later, or others then or now consider the experiment to be, if not actually do-able, then at least scalable in principle from micro to macro.
Click to expand...

I think he means ridiculous in terms of unethical. Is not that the reason this has never been done? Isn't the point of the contraption to let the destiny of a macro sized cat be determined by the 'whims' of an electron? This is the strangest part, but I'm pretty sure the cat literally is neither dead or alive untill someone opens the box and checks. I tried reading up on this,but then my brain hurts..
 
Quantum to Classical

eirik said:
I thought it showed that it CAN be scaled up to the macro world, and that your statement marked is inncorrect. But I'm no expert at all. Hmmm. Anyone else on this? Tim?
Click to expand...
Well, you have seen what Gell-Mann thinks. It all depends on what you mean by "scaled up". The laws of quantum mechanics are laws of physics, and like any other law of physics, they apply everywhere & everywhen, always. But in the macroscopic world, their effect is simply too small to worry about. Consider the De Broglie wavelength. In the example from the linked Wiki page: "Given the enormous momentum of a person compared with the very tiny Planck constant, the wavelength of a person would be so small (on the order of 10−35 meter or smaller) as to be undetectable by any current measurement tools. On the other hand, many small particles (such as typical electrons in everyday materials) have a very low momentum compared to macroscopic objects. In this case, the de Broglie wavelength may be large enough that the particle's wave-like nature gives observable effects."

So what really happens when you "scale up" to the macroscopic world is that the tiny effects of quantum mechanics are swamped by the relatively enormous effects of the classical world. It works much the same way when you "scale down" the classical world. An electron has a mass, so it exerts a gravitational force, but it's mass is so small that the classical world gravity of the electron is swamped by the relatively enormous forces of the quantum world. It really gets interesting where classical meets quantum, in solid state electronics, for instance, where classical electronic effects and quantum physics effects play against each other on an "equal footing" to result in the zoo of electronic devices we now have available.

Seek out an old book from the 50's, Mr. Tomkins in Wonderland (or maybe it's Tompkins), by George Gamow. He talks about relativity and quantum mechanics disguised as a story about a bank teller who attends science lectures in the evening, falls asleep, and dreams of strange worlds where the effects normally unseen in the classical world become big. It's still quite entertaining & instructive, I think.

You might also try Speakable and Unspeakable in Quantum Mechanics by J.S. Bell (the same Bell of Bell's Theorem fame), Cambridge University Press 2004, 2nd edition (1st edition dates from 1987). It's a collection of papers, articles & Essays by Bell, not all of which require a background in physics to understand. It might help to elucidate some of the weirder aspects of quantum physics.

Unfortunately, I am not really up on the literature in quantum physics for non physicists. I don't even know if there is much along those lines that is trustworthy, simply because of the invasion of "new-age" and other shoddy thinking into the popularization of the field. That's one reason I shy away from philosophical interpretations. I am too hard headed. If you just assume that you only really know what you can observe & measure, you are safe.
 
So could (in theory, in admittedly specific artificial conditions) a macroscopic object (e.g. a cat) be fired through the double slit experiment and yield the same unusual results as a subatomic particle?
 
Ashles said:
I asked if in theory a cat could be fired through a macroscopic version of the double-slit experiment and yield the same results as the subatomic results and he said yes.
Click to expand...
I bet you $1,000,000 that the cat's wave form collapses to that of a dead cat having every appearence of having been forced through two very narrow slits. The challenge of course would be distinguishing between that and a cat that had only been forced through one narrow slit. Still, it would be for Science, I'll go check....
 
Lengthy discussion, awesome, yet.. it's still too technical and hard for me to digest anything. And I haven't been able to find what I need too in the internet. Uh.. :(
 
True-Gossiper said:
Lengthy discussion, awesome, yet.. it's still too technical and hard for me to digest anything. And I haven't been able to find what I need too in the internet. Uh.. :(
Click to expand...

If you wait a little you might become disinterested, as I think I'm about to shake the quantum mechanics from its foundation :cool:. But I'd like to help you If you ask a specific question.
 
Last edited:
Tim Thompson said:
The uncertainty principle in quantum physics (usually associated with Heisenberg) is a fundamental limitation of nature and has nothing at all to do with our ability to make measurements of limited precision. Indeed, the principle can be derived entirely from pure mathematics, with no input from physics at all
Click to expand...

Uh, no, it can't. That's an absurd statement. First of all, mathematics is not a form of physics. Mathematics has no power to say anything at all about the universe. Mathematics would remain valid in any conceivable universe which maintained internal consistency. It's completely aprioristic.

Second, you are confusing the fact that the physics is codified in mathematical language -- in this case Hamiltonian language -- with the idea that it is the mathematics which makes the physics valid, rather than the physics making the mathematics meaningful.

Third, mathematics alone has absolutely no concept of certainty or uncertainty. In pure mathematics, either a postulate is true or false. It is not probably true or false, and it is not true or false with a given uncertainty. Mathematics must be applied to a probabilistic universe for the concept of uncertainty to even be invoked, and when that happens your "no input from physics at all" stipulation fails.

Fourth, the uncertainty principle depends expressly on Planck's constant, which couldn't be known unless physically derived, given E=hν. (That's a Greek nu, not a Latin vee).
 
rlr said:
Uh, no, it can't. That's an absurd statement. First of all, mathematics is not a form of physics. Mathematics has no power to say anything at all about the universe. Mathematics would remain valid in any conceivable universe which maintained internal consistency. It's completely aprioristic.

Second, you are confusing the fact that the physics is codified in mathematical language -- in this case Hamiltonian language -- with the idea that it is the mathematics which makes the physics valid, rather than the physics making the mathematics meaningful.

Third, mathematics alone has absolutely no concept of certainty or uncertainty. In pure mathematics, either a postulate is true or false. It is not probably true or false, and it is not true or false with a given uncertainty. Mathematics must be applied to a probabilistic universe for the concept of uncertainty to even be invoked, and when that happens your "no input from physics at all" stipulation fails.

Fourth, the uncertainty principle depends expressly on Planck's constant, which couldn't be known unless physically derived, given E=hν. (That's a Greek nu, not a Latin vee).
Click to expand...

I totally agree ;).
 
You must log in or register to reply here.

Back
Top Bottom