# String theory: why can't strings move at the speed of light?

The tension in the strings is supposed to be high - one would have to suspend a mass of two Andromeda galaxies at the Earth's surface to approach it...This is correct. But may I ask how you obtained these figures? It would make a real nice addition to my project :)f

Hi guys,

So I'm a bit confused about why strings can't move at the speed of light. I understand that the end points do if the string is open, but the rest of it doesnt.

To paraphrase, really I want to know why you must have timelike and spacelike tangent vectors to a point on the world sheet of a string. Why is it unphysical to have all tanget vectors point in spacelike directions, with just a single lightlike one pointing in the direction of travel?

To paraphrase a final time: I know that if the string moves at the speed of light, then a point on the string at time t = 0 is mapped exactly to a point at time t = t, which we can keep track of. So: traveling at the speed of light means we can keep track of each point on the string. But this is not allowed. Why?

I'm a noob with this stuff so please try to dumb your knowledge down as much as possible so I can understand. Thank you!

• Dr. Watson
Yea, that's good question. It seems that since the string is vibrating at very high frequencies, there would be points on the string that would be moving very fast. And this would limit the whole string from moving near the speed of light. The theoretical limit of a point particle would be the speed of light. But a vibrating string would have to be limited to quite a bit less than the speed of light because some points on the string would be moving very fast with respect to the rest of the string in the direction of motion. Is this a proof that strings are not the correct description of particles?

We are reminded here often of the problems with using classical concepts about quantum behavior; particularly, thinking of points as locations is going to be problematic...

If I recall correctly, a typical uncertainty of position of a hydrogen atom is about six diameters.
Strings are much smaller - the size of a string compared to the diameter of a proton is supposed to be about the same proportion as the size of a man to the distance of Andromeda galaxy. The visualizations of strings being open or closed, having lengths, or having vibrations as displacements of location are classical conceptions.
The tension in the strings is supposed to be high - one would have to suspend a mass of two Andromeda galaxies at the Earth's surface to approach it...

Trying to get a casual feel for strings just promotes a cascade of thoughts that make increasingly less sense.
I'm an outsider... just suggesting that trying to conceive strings apart from the math in the theory is likely to always go in an unconceivable direction...

Interesting discussion :)

Yea, that's good question. It seems that since the string is vibrating at very high frequencies, there would be points on the string that would be moving very fast. And this would limit the whole string from moving near the speed of light. The theoretical limit of a point particle would be the speed of light. But a vibrating string would have to be limited to quite a bit less than the speed of light because some points on the string would be moving very fast with respect to the rest of the string in the direction of motion. Is this a proof that strings are not the correct description of particles?

Okay I do have a bit more questions about this though. Basically what you're saying makes sense if the string was vibrating in the direction of propagation, like for example a longitudinal wave. But what if its a transverse vibration?

The tension in the strings is supposed to be high - one would have to suspend a mass of two Andromeda galaxies at the Earth's surface to approach it...

Yes this is correct. But may I ask how you obtained these figures? It would make a real nice addition to my project :) Also yes I think this is the short answer. Since the strings have tension, they can't move at the speed of light? but why?

I don't recall where I ran across the two Andromedas estimate, but you might be able to figure it...

If you look around you will see figures like this:

size of a string about 10^-33 centimeters
tension is the energy per unit length of the string about 10^52 Newtons
tension is also mass of unit length times c^2, so strings are heavy 10^25kg/m
Andromeda mass 1.5x10^12 solar masses
Solar mass is about 2 x 10^30kg

c^2 is the ratio of the string tension to the string mass per unit length, so that may be important to your question...

So I'm a bit confused about why strings can't move at the speed of light
Why do you think that they can't move at the speed of light? They can. Some quantum modes of string oscillation are massless, implying that they move at the speed of light.

Interesting discussion :)

Okay I do have a bit more questions about this though. Basically what you're saying makes sense if the string was vibrating in the direction of propagation, like for example a longitudinal wave. But what if its a transverse vibration?
Still, there would be some directions for which other particles could not travel near c with respect to the string because some points on the string would be moving faster than c with respect to that other particle. Is this the death nail of string theory?

No, it is trying to kill a classical approach to string theory which never lived anyway.

Why do you think that they can't move at the speed of light? They can. Some quantum modes of string oscillation are massless, implying that they move at the speed of light.

I don't see how a string can travel at the speed of light - what happens to the tension in the string in this case?

I'm starting to think maybe there is no real concrete answer as to why the strings can't move at the speed of light :O !

I don't see how a string can travel at the speed of light - what happens to the tension in the string in this case?

I'm starting to think maybe there is no real concrete answer as to why the strings can't move at the speed of light :O !
Note that I am talking about quantum string. In your question you probably have a classical string in mind, but classical string cannot move at the speed of light.

By quantum string are you referring to a relativistic string?

I'm talking about the relativistic (open) string; that its endpoints move at the speed of light. Apparently according to Barton Zwiebach, only the end points move and speed v = c but the rest of the string doesn't. I was wondering why...

I'm talking about the relativistic (open) string; that its endpoints move at the speed of light. Apparently according to Barton Zwiebach, only the end points move and speed v = c but the rest of the string doesn't. I was wondering why...
That doesn't sound right. Wouldn't the ends of the string then outpace the rest of the string, causing it to stretch? The string tension in string theory is a real tension, but it is constant. This suggests that the whole string travels at the same speed.

By quantum string are you referring to a relativistic string?

I'm talking about the relativistic (open) string; that its endpoints move at the speed of light. Apparently according to Barton Zwiebach, only the end points move and speed v = c but the rest of the string doesn't. I was wondering why...
"Relativistic string" is either another name for or a sub-type of quantum strings, I'm not sure which but they are definitely encompassed by the term quantum string. These are the "strings" from String Theory, as opposed to a classical string which is just a piece of rope or twine or whatever. This IS what you are talking about, right (quantum strings) ?

That doesn't sound right. Wouldn't the ends of the string then outpace the rest of the string, causing it to stretch? The string tension in string theory is a real tension, but it is constant. This suggests that the whole string travels at the same speed.

I'll quote Barton Zwiebach: "The end points move with the speed of light. The endpoints move transversely to the string. On the interior of the string, the notion of a velocity is ambiguous. For the string end points, however, the velocity is well defined - there is no ambiguity defining the velocity of the end points!"
If you wish you can check out page 124 of chapter 6 in his book: a first course in string theory.

This IS what you are talking about, right (quantum strings) ?
Yes, this is what I'm talking about! But I can't understand why/how the string moves and at what speed! I'm so confused!

I'll quote Barton Zwiebach: "The end points move with the speed of light. The endpoints move transversely to the string. On the interior of the string, the notion of a velocity is ambiguous. For the string end points, however, the velocity is well defined - there is no ambiguity defining the velocity of the end points!"
If you wish you can check out page 124 of chapter 6 in his book: a first course in string theory.

Yes, this is what I'm talking about! But I can't understand why/how the string moves and at what speed! I'm so confused!
First, the chapter you are referring to is about classical strings, not about quantum strings.

Second, given that the end points move with the velocity of light (which is indeed derived in the book) it is easy to understand why other parts of the string should have a different velocity. It is a simple consequence of the fact that the string oscillates. Think of a guitar string - when it oscillates it is clear that different parts of the string have different velocity. But don't be mislead by guitar: a string attached to a guitar has fixed ends, while here we are talking about a vibrating string the ends of which are free. Since the ends are free, they can move faster than other parts of the string.

Third, you are referring to the second edition of the Zwiebach book, but note that the first edition contains more details on this topic.

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The string tension in string theory is a real tension, but it is constant. This suggests that the whole string travels at the same speed.
The guitar string, for instance, also has a constant tension, yet different parts of the guitar string have different velocities. The catch is that here "tension" is not the tensile force (which, of course, is not a constant). Instead, the "tension" is the force per unit stretch, the unit of which is N/m.

By quantum string are you referring to a relativistic string?
In general, just as any other object in physics, a string may be either of the four below:
i) non-relativistic and classical
ii) relativistic and classical
iii) non-relativistic and quantum
iv) relativistic and quantum
The Zwiebach book considers the cases i), ii) and iv), but in the chapter you are referring to he considers the case ii).

The guitar string, for instance, also has a constant tension, yet different parts of the guitar string have different velocities. The catch is that here "tension" is not the tensile force (which, of course, is not a constant). Instead, the "tension" is the force per unit stretch, the unit of which is N/m.
Yeah, I think I should have said instead that the average of the velocities of all points of the string is equal to the velocity of the end points.