Physics often uses the sign of a frequency to indicate the direction of travel with regard to a reference frame.
E.g. 2 Hz is a wave oscillating two times per second and travelling to the right, -2 Hz is the same travelling to the left.
In some cases direction isn't really meaningful (standing waves, or the height or pressure of a medium as seen by a stationary observer). In others, the direction of propagation can be quite significant.
For me, this is easiest to see through the equation Velocity = Frequency x Wavelength. Negative frequency is algebraically equivalent to negative wave velocity (which already means opposite direction), or negative wavelength (which already means opposite direction). There are several different ways that you could try to interpret "negative frequency," but by shuffling the negative sign around it becomes clear it must be equivalent to a wave of the same absolute frequency, where the wavelengths point the other way.
Is a -2 Hz wave travelling to the right the same as a 2 Hz save travelling to the right, but going backwards in time?
Could there be something to John G. Cramer's transactional interpretation of Quantum Mechanics? Instead of probability waves collapsing instantaneously, could everything be mediated by photons going backwards in time?
"Is a -2 Hz wave travelling to the right the same as a 2 Hz save travelling to the right, but going backwards in time?"
Yes, all other things being equal. It's a bit less confusing if you leave the signs off and just say that "a wave travelling to the right at f in t is the same as a wave travelling to the left at f in -t.
This is also very much in the "spherical cow" sense of physics - it's true of many ideal cases on chalkboards, but it gets fuzzy in practice due to thermodynamics and other nonidealities. Plus, you can only observe things from the perspective of time moving forwards.
"Could there be something to John G. Cramer's transactional interpretation of Quantum Mechanics?"
There's nothing I'm aware of which is implicitly wrong with a transactional interpretation - you just have no way to empirically prove that it's a valid "why." In physics, we are very often limited to "how" and "what."
It looks to have some ideas in common with Feynman's reaction diagrams and path integrals, so it may be an interesting approach if you're partial to those. The catch is that wavefunction collapse is equally true: it's a model which makes accurate predictions about observable experimental outcomes.
They found a solution with a negative w and negative k, so it travels forward. They "neglect" the solutions that travel backward (with negative w and positive k, or positive w and negative k). The more clear parts about this is the Fig 1(a) (page 2) and the paragraph below it.
The problem with such interpretations is that they violate causality.
Check out Wheeler-Feynman absorber theory for history.
Concepts such as collapse of a wave function aren't necessary when you stop treating the observer in a special way and start considering observer-particle as a big quantum system.
So is this saying that a portion of the waves of energy are reflected back towards the source, that this energy has a negative frequency, and that it has an effect that has been elusive because it has little chance to interact with the positive frequency waves? I'm curious what some of the implications might be.
This is not true. A wave propagates both in time and space. You're mixing these two. A negative frequency is like a wave travelling backwards in time, not left/right spatial direction.
Not quite. A wave going left forward in time is equivalent to a wave 'going right' but backwards in time. Since it is further right in the past than now, it is actually going left.
There's a lot of similar effects in Physics, especially with time and/or antimatter.
Save me the trouble an learn some basic physics.
Read Jackson's Classical Electrodynamics, Chapter 7.
If it's too complicated for you, read about waves. See how they propagate in time and space, and pay special attention to what happens to the equation when you change the sign of t. If it's too difficult to imagine, try plotting using a program.
And anti-matter is not matter travelling backwards in time. See my post below.
Are we talking about the same thing?
I'm talking about particle waves, or wave functions of particles, not a function which satisfies the wave equation (a photon happens to satisfy the wave function, but I'm trying to be general here) and with frequency, I mean energy. Try changing the sign of t in Schrodinger equation and see if it simply amounts to changing the sign of your momentum vector or not.
I guess not. I had an impression of you talking about particles from the start of your comment, but then you went into "read about waves" and said to make a plot, which made it sound like you were talking about basic math. I only understand a few of the effects of altering time on physics so I'll shut up.
Which is exactly why the book has that title. The book by Jackson is required reading for any physics graduate in a field where EM radiation plays a role.
I have seen a negative sign grouped with frequency. Which was used to distinguish directionality. Most of the time it is understood from context what is meant, if not the speakers fall back on to more something more formal to ensure understanding.
E.g. 2 Hz is a wave oscillating two times per second and travelling to the right, -2 Hz is the same travelling to the left.
In some cases direction isn't really meaningful (standing waves, or the height or pressure of a medium as seen by a stationary observer). In others, the direction of propagation can be quite significant.