String theory and reference frames HELP

[Libohove90]

I am reading The Elegant Universe...and I have bumped to possibly the first part of the book that I can not understand.

When an electron and a positron pop out of existence, they soon annihilate each other with a "bang"...emitting a photon.

If fundamental substance of universe are considered point particles, the 2 particles would bump to each other and emit a photon. That means they have a precise location and moment in time in which they annihilate each other that all reference points can agree.

However, string theory says that if the fundamental substance of the universe are vibrating strings...the two strings "merge" forming a vibrational pattern that creates the photon. However, since the strings are TWO-DIMENSIONAL...two observers cannot agree on the location and precise moment in time in which they annihilate each other.

That last statement I do not understand. It is relativity applied to strings. I don't understand why two observers do not agree in the location and time the two strings annihilate each other...just because they are two-dimensional. Plz offer me a clear explanation. Thank u

 

[Demystifier]

I am reading The Elegant Universe...and I have bumped to possibly the first part of the book that I can not understand.

When an electron and a positron pop out of existence, they soon annihilate each other with a "bang"...emitting a photon.

If fundamental substance of universe are considered point particles, the 2 particles would bump to each other and emit a photon. That means they have a precise location and moment in time in which they annihilate each other that all reference points can agree.

However, string theory says that if the fundamental substance of the universe are vibrating strings...the two strings "merge" forming a vibrational pattern that creates the photon. However, since the strings are TWO-DIMENSIONAL...two observers cannot agree on the location and precise moment in time in which they annihilate each other.

That last statement I do not understand. It is relativity applied to strings. I don't understand why two observers do not agree in the location and time the two strings annihilate each other...just because they are two-dimensional. Plz offer me a clear explanation. Thank u

The explanation is much easier to draw than to explain by words. And the pictures are actually drawn in the book (Figures 6.8, 6.9, 6.10).

 

[Libohove90]

The explanation is much easier to draw than to explain by words. And the pictures are actually drawn in the book (Figures 6.8, 6.9, 6.10).

All right.

Why is Gracie's plane different? Just because she is moving the plane is tilted? What is the plane anyway...a plane of simultaneity?

 

[Demystifier]

What is the plane anyway...a plane of simultaneity?

Exactly.

 

[Demystifier]

Why is Gracie's plane different? Just because she is moving the plane is tilted?

This a question about special relativity, not about string theory. If you have problems with understanding the basics of special relativity, I suggest you to ask this on the Forum specialized for relativity.

 

[Naty1]

Whoa!, before we toss this to another thread, I'd appreciate any insights regarding the representations of the strings in the figures referenced...

I had the same "issue" reading Greene's book as Libo...I still do. I thought Greene's explanation was long winded and did not make clear just what he was picturing. He does state clearly as noted above that the "...plane ...slices though all events in space that occur at the same time" is the once he is attempting to picture.

The place where I fell off the description was a page earlier, page 159 where Greene says there is an unambiguous point in quantum field theory where particles interact, fig 6.6, (How can anything be unambiguous in QUANTUM theory?) then he says, pg 160 and goes on to say what happens if "particles" are one dimensional strings...but pictures them as tubes and claims the point of interaction disappears...he does not picture them as one dimensional... they sure look two or three in those figures depending on what he's approximating...the whole thing seemed unclear to me, but I took him at his word (p163) that strings smear out interactions spreading out forces and eliminating infinites...that single sentence would have made me happy...

Does he mean the one dimensional elongated frame is the one that becomes "relative" ...(I could get that) but picturing it as a tube distracted me a lot...and given that quantum mechanics is so Heisenberg "uncertain" I really don't see much of an argument distinguishing the two...especially since strings are vibrating like crazy all the time quantum jitters plus characteristic vibrations plus thermal vibrations...

 

[humanino]

given that quantum mechanics is so Heisenberg "uncertain" I really don't see much of an argument distinguishing the two...especially since strings are vibrating like crazy all the time quantum jitters plus characteristic vibrations plus thermal vibrations...

The "quantum fluctuation" picture does not change the nature of the string. Freeze time : its a one dimensional object. Switch time on and represent it vertically : you get a space-time sheet. If the string is closed, that's a tube.
http://upload.wikimedia.org/wikipedia/commons/2/25/World_lines_and_world_sheet.svg
If you think of the above as real picture of what's happening, the fluctuations would appear as rapid changes in (say) the curvature of the above object along the vertical direction (time). But topologically they stay the same. However, this is not an actual picture of what's happening. This is a graphical representation for a Taylor-like series of terms, different terms being topologically inequivalent (Feynman diagrams just allow us to keep track of the topologically different terms).

To me there are two basic important points to realize at this level, one fairly general and one rather specific and technical. The rather technical point is that strings do not suffer from the t-channel versus s-channel "duality". The easiest way to see this is to take the particle diagrams for both channels :
http://upload.wikimedia.org/wikipedia/en/7/75/S-channel.svg http://upload.wikimedia.org/wikipedia/en/b/b0/T-channel.svg
and imagine that you expand each line into a tube instead. Topologically, you end up with the same surface : basically a sphere with 4 tubes attached. If the stringy transformed diagrams are topologically equivalent, that is to say for string perturbation they count as just one. This is how things work close to the actual calculation.

In fact, the above observation runs even much deeper into the second important point I wanted to mention. The QFT of point particles needs some sort of principle to fix the interactions. It may be as elegant as a a choice of gauge group. Of course string theory has a lot of things to define itself, but there is one marvelous miracle : once you have the free theory, you do not need to add any choice for the interactions : they come along automatically.