Negative Probabilities in String Theory

[Suicidesoldier#1]

I remember reading somewhere that there were supposedly negative probabilities in some equation, which meant that for string theory to be true it would have to violate lorentz and/or have extra dimensions. But if those mathematical equations are accurate, it could simply be a misinterpretation of what the data applies to. Human error could be not understanding the mathematical anomaly.

But what is that equation, specifically? Since negative mass could theoretically have a negative probability pertaining to the outcome say, something, say a particle traveling faster than the speed of light, you wouldn't necessarily need for dimensions to compensate for say, dark matter, or negative energy.


Negative energy, or negative gravity, could in part be what slows down (or keeps the outside at the same speed as the inside) the rotation of galaxies and essentially, binds them together in a stabilized non destructive manner. With an equal permeation of the universe, the negative energy could in fact be what's stabilizing galaxies, and could stabilize them by sheer volume in what's supposedly empty space, in the given size of a galaxy, rather than actually it's relative density in "open space".

The thing is, it's likely that this negative gravity is actually coming from negative matter. Since negative matter would behave in a lot of ways that the opposite to regular matter, such as constantly traveling faster than the speed of light and not being able to interact with matter, directly, being "neutral", it's possible that this missing particle/effect is in fact of negative mass.


This might explain it's masslessness and it's infinitely small size relative to other particles, in that it's how it interacts with them phasing right through them.

But due to the small size and mass of sub-atomic particles, the minute interactions found in near backwards quantum physics could simply be a result of the spacetime bending, that is in fact, expanding space, rather than shrinking it, altering their effects and stabilizing them, or having whatever effect, somehow.


These particles could in fact be of negative mass, and there obviously could be more than one type. Given that large connected structures would be unlikely to form, and it would just be a bunch of particles, traveling faster than the speed of light, it's likely these particles would just be, a bunch of random particles permeating the universe. Since space time at these levels are supposed to be incredibly "bumpy" and chaotic, and somewhat counter to regular Newtonian mechanics, it could explain quite a bit.

Since negative matter could travel faster than the speed of light, bend space time in weird ways, and virtually have no mass, essentially, but potentially some kind of interaction with mass, it could explain a lot of unresolved issues with quantum mechanics without violating lorentz or requiring lots of extra dimensions, being an easier theory than string theory to connect with most laws of physics. But since I'm not entirely sure of the equations that lead to this "the probabilities can't be negative", I'm not entirely sure how this fits in.

[deep damage]

I think what your talking about is space distortion.
Though I'm not entirely sure.

[Suicidesoldier#1]

shultz96

I think what your talking about is space distortion.
Though I'm not entirely sure.

Well, I know that negative mass has the potential to bend timespace in a lot of weird ways.

It's just a random theory, but I wanted to see if there was an equation anywhere that explained where the supposed negative probabilities or extra dimensions came from. xp


Or if there are lots of equations.

Since string theory is largely based within itself and it's own hypothetical constraints I haven't really taken time to learn much, since a lot of it is based off of it's constraints and then the logical stuff that would follow. xp


I suppose I only mentioned a lot of what I said just to see if any more data could be derived. xp

[deep damage]

Ah, well if your just treading waters I would do more research.

[Layra-chan]

Equation 21 here is the one that explicitly spits out the negative probability.
The idea is that you look at the string as a bunch of harmonic oscillators, and when you quantize the harmonic oscillators in the context of strings the Lorentzian metric gives you a minus sign in the time-like component of the commutator relations for the raising and lowering operators; this minus sign doesn't show up for regular harmonic oscillators.
In turn, this minus sign shows up as the norm of the time-like component of the vacuum state, which gives us a negative probability for the vacuum state.
Note that while negative probabilities and negative masses and such are allowed in standard quantum field theory, they are unacceptable as possible observables.
From here, the usual thing to do is to switch our coordinate system (light-cone gauge) and get rid of the time-like component altogether, but that gives us the irritating anomaly that only disappears in dimension 26.
Frankly, that's my least favorite way of deriving D = 26 for bosonic string theory; the moduli space argument is better, and if I could understand the lattice argument, that would be better.
Of course, the best D = 10 argument is the 2+division algebra argument, but that one doesn't actually preclude D = 3, 4, or 6. It would need to be combined with something like a Majorana-Weyl spinor D = 8k+2 argument, but I haven't found a full version of that yet.

But string theory is a load of crock anyway, seeing as it is both perturbative and background dependent.

[Suicidesoldier#1]

Layra-chan

Equation 21 here is the one that explicitly spits out the negative probability.
The idea is that you look at the string as a bunch of harmonic oscillators, and when you quantize the harmonic oscillators in the context of strings the Lorentzian metric gives you a minus sign in the time-like component of the commutator relations for the raising and lowering operators; this minus sign doesn't show up for regular harmonic oscillators.
In turn, this minus sign shows up as the norm of the time-like component of the vacuum state, which gives us a negative probability for the vacuum state.
Note that while negative probabilities and negative masses and such are allowed in standard quantum field theory, they are unacceptable as possible observables.
From here, the usual thing to do is to switch our coordinate system (light-cone gauge) and get rid of the time-like component altogether, but that gives us the irritating anomaly that only disappears in dimension 26.
Frankly, that's my least favorite way of deriving D = 26 for bosonic string theory; the moduli space argument is better, and if I could understand the lattice argument, that would be better.
Of course, the best D = 10 argument is the 2+division algebra argument, but that one doesn't actually preclude D = 3, 4, or 6. It would need to be combined with something like a Majorana-Weyl spinor D = 8k+2 argument, but I haven't found a full version of that yet.

But string theory is a load of crock anyway, seeing as it is both perturbative and background dependent.

blaugh

Thanks a ton! blaugh

[Suicidesoldier#1]

Wait so, aren't massless particles traveling back in time though?!

So you could have negative time. ninja


I don't know how that would be observed though. O_o

[Layra-chan]

No, that's not the measurement of time passage for those states. That's the probability of a ghost state having a time-like component. Even if the ghost state is experiencing time backward, the probability should still be positive.

And no, massless particles are not necessarily traveling backwards through time. Antiparticles are traveling backwards through time, massless or not; massless particles themselves don't experience time and are often their own antiparticle, or at least cannot be distinguished from their antiparticles by anything observable.

[Suicidesoldier#1]

Ahh, that would make sense, since like, none of it seemed to do with time. O_o

So it's the probability of time being relative.


Which is in part why they believe it's pure dimensions doing things, I suppose.

Wait, if massless particles are their own anti-particles, could it cancel it out and mean time didn't apply to them?! xp


Herm...

What happens if mass in their equation becomes negative though?

[Layra-chan]

Photons, for instance, are their own antiparticles. As are gluons. In the "antiparticles are particles travelling back in time" interpretation, a photon-photon annihilation is really just a single photon turning around as a result of hitting an antiparticle (of the correct energy level), which itself turns around to become a particle. We see this as a photon-photon annihilation generating a particle-antiparticle pair. Similarly, a particle travelling forward in time and hitting a photon (of the correct energy level) travelling backward in time makes both turn around, the particle becoming an antiparticle and the photon becoming a forward-moving photon.
To be careful, though, backwards-moving photons look exactly like forward-moving photons, since photons don't care about time.

Negative mass, like negative probability, is, at least in quantum field theory, not observable. This is not to say that it doesn't come up in the calculations, but only in virtual particles. Well, that and Dirac's sea, which is not a notion I'm particularly happy with but whatever, the Dirac sea isn't observable either so I don't care.

If you want a better understanding of where all of this is coming from, you're probably going to need to learn quantum field theory, at least up until you get to the Feynman diagram stuff; the Standard Model is kind of an ugly, unenlightening mess. But the stuff about negative probabilities and negative masses in virtual particles and the meaning of square norms of the time-like components of the string oscillator operators are a lot clearer if you already have basic quantum field theory under your belt. I think that David Tong's notes are a pretty good way to learn, although I'm not sure because I already knew most of the material from disparate sources when I first found the notes.

[Suicidesoldier#1]

Well, it's debatable that they exist and you're right that they can never be observed.

But hypothetically speaking, if mass was negative, would that now mean there was a positive probability for time? ninja

[Layra-chan]

Nope. At least, not in the case of ghost states. The commutators in the page I linked don't involve mass at all; they spit out integers, just like any other number operator.

[Suicidesoldier#1]

Layra-chan

Nope. At least, not in the case of ghost states. The commutators in the page I linked don't involve mass at all; they spit out integers, just like any other number operator.

Herm... so what were all the symbols about? O_o

I mean I saw like, that weird u thingy, uh, mu, and various other things, but I guess none of them may have involved mass. So if it was negative mass, it wouldn't have made a difference? xp

[Layra-chan]

They're explained in the section on classical strings. It's the basic harmonic oscillator setup.

[Suicidesoldier#1]

Layra-chan

They're explained in the section on classical strings. It's the basic harmonic oscillator setup.

Oh, cool.

So how many of the physics symbols used are actually applied to real world physics symbols, other than string theory? ._.