# Strings and QFT: particles moving backward in time?

New question: In string theory and QFT, do particles travel back in time? Not related to antimatter: Do they travel back and forth in time in reality or are these just interpretations of mathematical formulas used to make sense of calculations?

This is a different question (from this one) as it concerns strings and not antimatter...

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It really is the same question. The "going backward in time" notion is a alternate way of thinking about anti-matter. It is intrinsically quantum mechanical, and strings are quantum mechanical objects. You can't duck this, but I am going to leave it to one of my fellow moderators to close (or not close) this as they see fit. –  dmckee Mar 26 at 19:27
–  dmckee Mar 26 at 19:28
Finally, you can merge your several accounts using physics.stackexchange.com/help/user-merge –  dmckee Mar 26 at 19:29

The "motion backwards in time" is often mentioned in popular texts/shows about physics but it can't be understood literally. All processes in the Universe are taking place forward in time. An essential subtlety in the previous sentence is the tense – "are -ing" (present progressive), in this case – which automatically includes the information about what is happening with time during the process described by the word: it is increasing from $t$ to $t+dt\gt t$, and so on.

We may look at the history of a process backwards in time, but that's something else than that the process is actually happening. It is always "happening" while time is doing the same thing: going forward.

Instead, what this "back in time" stuff means in physics is that certain objects – in particular, antiparticles – may be related to other objects – particles. And the relation is such that the processes involving antiparticles are naturally the time-reversed (back-in-time interpreted) processes involving the original particles.

This map may be literally applied to Feynman diagrams. In Feynman diagrams, antiparticles are given by the same line as the particles except that their presence in the initial state must be represented by the original particle's presence in the final state and vice versa (and energy has to flip the sign). This trick is related to the Dirac sea for fermions: a positron is a hole in the Dirac sea of negative-energy states, and a hole/positron that disappears from A and appears in B is the same change as an electron that disappears from B and appears in A (because the occupation numbers are reverted).

These relationships between particles and their antiparticles hold in string theory, too. A string moving backwards in time is described by locally the same pieces of strings, the same world sheet, but the orientation may get reflected. For example, when a string is wound around a circle $w$ times, its antiobject has the opposite charge $-w$, so it's wound in the opposite direction. The winding number is an example of a charge. If we revert the orientation of time inside the world sheet, it switches the overall orientation of the world sheet which may be compensated by another switch of the orientation of the spatial direction, too – and that's what changes $+w$ to $-w$ and replaces particles by antiparticles etc.

So physics doesn't support any other "real and impressive" interpretation of "motion back in time" except for its being a good interpretation of the motion of antiparticles that makes some of the properties of antimatter – why they're related to properties of matter – manifest. It's really a way to visualize a certain symmetry but the particles and antiparticles are still doing the same thing and the only right way to "look" what's going on is to look at everything as time goes forward.

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So rons comment as in the other thread that states that point particles can reproduce the quantum field if they are allowed to go backwards doesn't mean the point particles go backwards in time? –  Peter Mar 26 at 19:55
Lubos or other you there? –  Peter Mar 26 at 23:30
The statement "something goes backward in time" only makes sense if you parameterize the motion of "something" by yet another time that isn't the same time as the time in the sentence "backward in time". So the world lines of these objects in spacetime may be parameterized by $\tau$, a different coordinate along the lines than the $t$ coordinate in the spacetime, and the relationship between $t$ and $\tau$ may be either increasing or decreasing. The decreasing case means "backward in time" and it's useful when one describes antiparticles. –  Luboš Motl Mar 27 at 7:08
But if one only talks about one time $t$, the phrase "something is happening back in time" is meaningless. What's happening is always described as some functions of $t$ and higher $t$ means future, lower $t$ means past, and the right interpretation of any sentence about a process is that it starts with a lower $t$ and goes to higher $t$: this is really a rule of grammar. There's no way to qualitatively change any process so that it would happen back in time. Whatever the process is, it's a qualitatively the same function of $t$ that should be read from low $t$ to high $t$ when we "live it". –  Luboš Motl Mar 27 at 7:10
Thank you lubos so I now understand it that particles don't literally have to go back in time to recreate the quantum field as Ron says –  Peter Mar 27 at 7:34
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