Y!A: String and Quantum Theory

This is a question i answered for someone who seemed to be having some problem conceptualizing both String Theory and Quantum Mechanics in the same context. i can't say that i completely understood what he was asking, but i hope i gave him a good idea that these two concepts are very well related.

http://answers.yahoo.com/question/index?qid=20100824133230AAGX5rj&r=w#OpBoM23EKWK18mDD9Dq0

Q:
Simultaniously Conceptualizing String & Quantum Theory?
String theory says there are strings that are 1-dimensional slices of a 2-dimensional membrane vibrating in 11-dimensional space with variations in their vibrations resulting in the creation of all light, matter, gravity etc... in the universe. Quantum Mechanics says particles can exist in a super position until the wave function is collapsed, part of the particle wave duality. How can one stitch these two theories together conceptually? Are all strings in some type of super position as well until collapsed? Or another way of asking; If a particle is in super position, is the string also in a kind of superposition? 


Maybe the question is illogical. Like asking what's the marital status of the number nine. 


Help with conceptualizing this would be much appreciated!

A:
first of all, i think you know very well what strings and string theory are, and i compliment you on that knowledge!
one thing i want to clarify is how these strings create, as you say, "all light, matter, gravity etc... in the universe." the only thing that a variation in a string vibration produces is a different fundamental particle. that is, one specific vibration of a string is an up quark, while another is the gluon. then the interactions between these particles create light, gravity, etc... (and even mass, itself!)
but this i'm sure you know, and i just wanted to clarify.

these two ideas can be easily conceptualized as follows:
quantum theory does state that particles exist in a state of uncertainty until they are 'observed'. so, in short, yes, you can think of the strings being in a sort of quantum state as well. but remember that this quantum state applies only to properties of the particle like position, speed, etc... so it is essentially no different than thinking of the particles in this superposition. since these basic particles are, more fundamentally strings, it is just fine to thing of the strings adhering to the same rules as the particles! although i don't necessarily know what great insight this approach would yield.

one thing which would be wrong to say is that the vibration of the string is also in superposition. that is, the string can be vibrating in many different ways - and thus be many different particles - at the same time. although this may seem theoretically possible, remember that a particle remains in superposition only as long as it is not observed or measured. i would think that the universe is constantly checking on which particle a certain string is behaving as. i may be wrong however, but i have never heard of quarks suddenly turning into leptons and then turning into photons.

Y!A: Heisenberg's principle

this is a question i answered about basic knowledge of Heisenberg's principle. but i also tried to give the asker a good background on the subject and even a nice illustration of the meaning of the results at the end.

http://answers.yahoo.com/question/index;_ylt=AgUt5CPVFqxv56o4K4ZEV__ty6IX;_ylv=3?qid=20100805131936AA3iGQD&show=7#profile-info-KN1zv8xbaa

Q:

At a baseball game, a radar gun measures the speed of a 140 g baseball to be 137.32 ± 0.05 km/h.

(a) What is the minimum uncertainty of the position of the baseball?

answer in m

(b) If the speed of a proton is measured to the same precision, what is the minimum uncertainty in its position?

answer in m

please help me out i'm stuck it would be greatly apprieciated if you help me out..thanks

A:

a ) here you need the relationship between uncertainty in position and uncertainty in speed. unfortunately, no such one exists, but there's an equally useful one which relates uncertainty in position to uncertainty in momentum. it is one of Heisenberg's equations:

∆x * ∆p ≥ ħ/2

(where ħ is "h-bar" or h/2π)

(and ∆ means "uncertainty in")

it is good then that you are given the mass of the ball, so that p can be written as mv, with those 2 values given in the problem.

now, all that is left to do is solve for ∆x (or the uncertainty in position):

∆x ≥ ħ / (2*∆mv)

note that since there is no uncertainty in the mass, we can take it out of the ∆ operator - not a necessary step, but still worth noting.

∆x ≥ ħ / (2m*∆v)

so now all we have to do is plug in our known values for m, ∆v, and ħ (in the correct mks units, of course)

m = 140 g = 0.140 kg

∆v = 0.05 km/hr = 50 m/hr = 0.0139 m/s

ħ = 1.0546 * 10^-34 J*s = 1.0546 * 10^-34 kg*m²/s

thus we have:

∆x ≥ (1.0546 * 10^-34 kg*m²/s) / (2 * 0.140 kg *0.0139 m/s)

cancelling units and evaluating, we get:

∆x ≥ 2.71 * 10^-32 meters <<<<<<<<<<<<<<< (answer part a)

you'll notice that this is so small, it is not even perceptible - or anywhere near that! that is why you don't notice this phenomenon while watching a game of baseball.

b) for this problem, we need the same uncertainty relationship. ∆v is again 0.05 km/hr (or 0.0139 m/s). and the mass of the proton can be looked up and is approximately 1.6726 * 10^-27 kg (much much smaller than the baseball)

starting again with the basic relationship

∆x * ∆p ≥ ħ/2, and rearranging:

∆x ≥ ħ / (2m*∆v)

plugging in values exactly the same as last time:

∆x ≥ (1.0546 * 10^-34 kg*m²/s) / (2 * 1.6726 * 10^-27 kg * 0.0139 m/s)

again, all we are left with is meters, and the value of the expression is

∆x ≥ 2.269 * 10^-6 meters <<<<<<<<<<< (answer part b)

although this is still relatively small, it is many many many orders of magnitudes larger than the ∆x of the baseball.

consider also that it is roughly 2.27 * 10^-6 meters (2 micrometers). it is interesting to see this value compared to the approximate size of of an atom, which has a diameter of roughly 100 PICOmeters (a picometer is 10^-12 meters. or 100 of them is 10^-10 meters).

so the uncertainty in the position of this moving proton is almost 4000 times larger than the diameter of an atom!! so forget about it if you wanted to pinpoint the location of this particular proton among other atoms.

i hope this was helpful! and i'm always happy to answer more questions :]