String-mass near the speed of light

[Mike2]

If the mass of a string/particle increases with the vibrational frequency of the string, and if time slows down when you travel near the speed of light, then wouldn't it appear to a stationary observer that the frequency of the string and thus the mass of the particle was decreasing as it neared the speed of light?

 

[Mike2]

If the mass of a string/particle increases with the vibrational frequency of the string, and if time slows down when you travel near the speed of light, then wouldn't it appear to a stationary observer that the frequency of the string and thus the mass of the particle was decreasing as it neared the speed of light?

I couldn't find anything about this in either of zwiebach's book or in Hatfield's book, or even in Relativity by Hans Stephani. Yet this seem like a very fundamental question. I wonder why it is not addressed?

 

[Mike2]

If the mass (or some other property) of a string/particle increases with the vibrational frequency of the string, and if time slows down when you travel near the speed of light, then wouldn't it appear to a stationary observer that the frequency of the string and thus the mass (or some other property) of the particle was decreasing as it neared the speed of light?

What... this is the most straight forward way of testing the vibrational nature of extended objects as particles, and you are not talking about it? Are we all in denial, or what? :grumpy:

 

[RingoKid]

by the same token to an observer traveling at the speed of light it would appear stationary and of fixed mass ?

 

[humanino]

Is this not the wrong forum ? That could explain the few answers.

 

[LURCH]

If we are talking about a vibrational frequency, I should think that this frequency would appear to increase to an observer that the string is traveling towards, and decreased to an observer of the string is traveling away from. However, this is only an attempt to apply a familiar concept from electromagnetics (red shift and Blue Shift) to string theory, and I am not at all certain that one can do that.

 

[Mike2]

If the mass (or some other property) of a string/particle increases with the vibrational frequency of the string, and if time slows down when you travel near the speed of light, then wouldn't it appear to a stationary observer that the frequency of the string and thus the mass (or some other property) of the particle was decreasing as it neared the speed of light?

If we are talking about a vibrational frequency, I should think that this frequency would appear to increase to an observer that the string is traveling towards, and decreased to an observer of the string is traveling away from. However, this is only an attempt to apply a familiar concept from electromagnetics (red shift and Blue Shift) to string theory, and I am not at all certain that one can do that.

I would think that if the string gave off photons at a regular rate, then this would appear redshifted when receding and blueshifted when approaching. However, we are talking about the perception of a single particle with relativistic speeds with respect to some observer.

 

[nitin]

I would be extremely cautious in trying to apply relativistic effects to a string that straightforwardly. Nevertheless, we can at least try to think about such a thing. I think we haven't considered the effect of length contraction here (whatever that means in the context of strings). We assume that the (non-extensible) string is moving with constant (relativistic) speed (no GR effects, only SR). The only oscillations would be transverse. If we assume the string is moving in a direction perpendicular to that of the oscillations (that is in the direction of its extension), then, according to my understanding, the "stuff" that makes up the string suffers no relativistic effects (and the frequency remains the same, hence the mass is unchanged). Now, we work in the direction of motion of the string to make sure everythings holds. The string is contracted in its direction of motion, and its length appears smaller to the observer. Now, we must be clear about what frame we are referring to... as I understand Mike, he's talking about the frame of the string. The oscillations on the string are stationary (for the sake of argument), hence the velocity of the wave traveling to the right of the string is equal to the velocity of the wave traveling to the left...but we have a shorter string... but hey, now there's the effect of time dilation.. that is the velocity remains the same for the observer (and for the string). Thus, no change in frequency, hence no change in mass (assuming Mike's hypothesis of mass is proportional to frequency is correct). We can also speak in terms of "tension", but I am hungry... Maybe someone can work the maths out.. it should be straightforward! Now, we can argue to infinite lengths about all I have just said.. what is this "stuff" which makes strings, etc... hence, I believe that the idea of trying to think about strings as "things" that actually behave in classical relativistic manner does not hold (hence the need for a quantum gravity theory, or whatever it might be called).

 

[Mike2]

Now, we can argue to infinite lengths about all I have just said.. what is this "stuff" which makes strings, etc... hence, I believe that the idea of trying to think about strings as "things" that actually behave in classical relativistic manner does not hold (hence the need for a quantum gravity theory, or whatever it might be called).

As far as the perception of fast moving QM effects to stationary observers, I suppose the same issues arise if one were to take the particle in an infinite well and make that system travel near "c". What would change? Would a stationary observer perceive the energy levels of the particle in the well to increase, decrease, or stay the same? So at least it is relevant to ask such questions.