Some questions about String theory

[ShayanJ]

Hi people
I have 2 questions about string theory

1-I've read that string theory tells us that we can ignore the fluctuations of space time in sub Planck scale and so enables us to use general relativity in such small scales.Also we know that GR says Gravity is not a force but a cause of space time curvature.If string
theory wants to use GR,So it should accept that gravity is not a force.But instead,it introduces Graviton as the messenger string for gravity which obviously shows us String theory is taking gravity as a real force which is in conflict with GR.What's the problem here?

2-In standard model,particles are said to be zero dimensional.As I understood,it means they have no extension in space.Now in string theory,Strings are said to be 1 dimensional.Is it something that we should take in account just mathematically or,like about particles,it has a non mathematical meaning too?
I ask this because I can't understand how a closed string,which is absoulatly 2 dimensional,is called 1 dimensional in string theory.

thanks

 

[bapowell]

With regard to question 2 -- yes, strings are physically 1-dimensional. A closed string is in fact a 1-dimensional objects, because its topology is fully defined in 1-dimension: it's a line segment with a 'rule' that says connect the two ends. If you were an ant walking along the string, you would have 1 dimension (direction) in which you could walk. By analogy, the surface of the Earth is a 2-dimensional manifold, even though we are used to envisioning the Earth as embedded in a higher (3-D) space. You must be careful not to confuse the dimension of the manifold with the way it *looks* when you embed it in a higher dimensional space.

 

[bapowell]

With regard to question 1 -- Regardless of whether one considers gravity to be a an actual force mediated by bosons, gravitational radiation does indeed exist. Quantization reduces the gravitational wave to a superposition of spin 2 particles.

 

[ShayanJ]

Thanks about the second question.
But as I know,Gravitational radiation can be explained by the sudden in the space time curvature or changes in the amount of mass.There is no need for a boson.

 

[bapowell]

Thanks about the second question.
But as I know,Gravitational radiation can be explained by the sudden in the space time curvature or changes in the amount of mass.There is no need for a boson.

But it's a spin 2 wave, and all oscillating radiation fields can be quantized. Are you suggesting that gravitational radiation isn't quantized?

 

[ShayanJ]

Well now that I read about quantization I understood what you mean.but If this is the case,because gravitational radiation is a wave in space time,we should say that graviton is the quantum of space time.Which is a strange result.

I think my problem is that I don't know what is a spin 2 wave or particle.
You know my mathematical knowledge is hardly beyond multi variable calculus and I read non mathematical articles about physical theories so if mathematics is the only way of answering my question,tell me to wait till I learn enough math.
thanks

 

[bapowell]

Sure, some more knowledge of mathematics would be helpful, for example, understanding Fourier transforms. However, if you understand electromagnetic radiation then gravitational radiation can be gotten to by analogy. We know that EM radiation can have a polarization. It turns out that an EM field is really just a summation of a bunch of oscillating fields with different momenta. The excitations of these fields are quantized, and these packets are the photons. The polarization of the EM field can now be more fundamentally attributed to the fact that the photon has spin (spin 1 ). This is the usual spin that you learn about in QM. Now, the gravitational wave also has polarization, but it's more complicated. Whereas the polarization of an EM wave is dipolar, that of the gravity wave is quadrupolar (see, for example, http://en.wikipedia.org/wiki/Gravitational_wave#Effects_of_a_passing_gravitational_wave). When you look at the constituent oscillating fields of the gravity wave, you find that the quantized excitations must have a higher spin to account for the more complex polarization of the gravity wave -- spin 2.

However, if gravitational radiation isn't quantized, then the decomposition into component oscillators is not appropriate, and there is no need for gravitons. I don't know whether gravity waves *must* be quantized. Perhaps someone else can chime in on this point.

 

[Coin]

Perhaps a dumb question, but is it really correct to say particles are 0 dimensional, lacking extension in space, in a QFT?

 

[bapowell]

Perhaps a dumb question, but is it really correct to say particles are 0 dimensional, lacking extension in space, in a QFT?

That's not a dumb question. Yes, in QFT particles are zero dimensional field excitations. I think the best place to see this is in the Lagrangian formulation of the free particle -- the path of the particle is a worldline as opposed to a higher dimensional surface, like in string theory. This is why particle paths in Feynman diagrams in QFT are lines.

 

[ShayanJ]

I didn't completely understand your explanation(I think I can't till I pass my electromagnetism courses or read some more articles so don't try more)I just want to tell you the thing I've understood from your answer to coin and ask you if its right.
You say particles are 0 dimensional field excitations.does it mean that if take an infinitly small(not same with the thing in calculus)of our force field,such that it can be thought of as nothing,that part is called the messenger particle of our force?
(I know this is one is dump.because by taking some part of space we mean there is a dimension.But I can't get it some how else and I feel something true in this explanation.Otherwise existence of graviton can't be compatible with GR)
thanks

 

[dimensional]

The graviton is just our own way of describing the quantized force of gravity, which GR posits to be actual deformations in the topology of space-time. Yes, gravity is not a traditional force like the others, but it is still measurable in a sense and theoretically allows itself for observable quantization. The existence of the graviton is compatible with GR in many ways, but in others it is not because GR is itself in ways incompatible with QFT.

By the way, I'm just learning this stuff as well so don't take my words as authoritative.

 

[bapowell]

I'd be careful with this description of a graviton as being a deformation in the topology of the universe. The term 'topology' has a very specific meaning in this context -- I think you mean 'topography'? The topology of spacetime is a fixed entity in Einstein gravity.

Gravitational radiation is a perturbative phenomenon in GR. What this means is that the gravitational wave propagates about a background geometry that it does not couple to. In other words, the gravity wave can be taken to be separate from the geometry of the spacetime to a large extent. Gravitons are compatible with GR in so far as you wish to quantize the gravity wave into spin 2 excitations; however, GR is not compatible with gravitons as means of describing the gravitational force in general. (The analogy here would be that if EM theory is capable of describing quantized EM radiation, but not capable of describing quantized static E and M fields.)

However, all of this is essentially moot, since we know that GR as a QFT in which the graviton acts as the force mediator does not work. String theory has yielded perhaps the most successful program for understanding the perturbative interactions of gravity with matter; in this theory the graviton is a closed string of dimension 1.

 

[dimensional]

Yes you're right, I used the wrong term. I'm still memorizing all of the field lingo that I've been mostly unexposed to until recently :)

But when you start talking about strings and vibrations, I'm all over that! From my production/musical composition background I am instantly ingratiated towards this concept of the ultimate cosmic symphony.