One aspect of this is that, if you sub `t -> -t'`, that's just as good a solution too. Which would suggest any solution with a positive time direction can have a negative time direction, just as easily. Is this widely assumed to be true, or at least physically meaningful?
There's also Wick rotations, where you can sub `t -> it'`, and then Minkowskian spacetime becomes Euclidean but time becomes complex-valued. Groovy stuff.
I'm not much of a physics buff but I loved reading Julian Barbour's The Janus Point for a great treatment of the possibility of negative time.
The craziest thing I've seen though is the suggestion that an accelerating charge, emitting radiation that interacts with the charge itself and imparts a backreacting force on the charge, supposedly has solutions whose interpretation would suggest that it would be sending signals back in time. [0]
> Which would suggest any solution with a positive time direction can have a negative time direction, just as easily. Is this widely assumed to be true, or at least physically meaningful?
It's widely assumed to be true and not at all physically meaningful. If you sub x -> -x then that's just as good a solution as well, i.e. just as you can count x as running from west to east or east to west and the results will be the same, you can also count time as increasing away from the big bang or as decreasing away from the big bang and all your calculations will be the same.
How much of this is just the mathematical model permitting such things?
Has any of this been experimentally fit to reality?
> sending signals back in time.
First encode stock movements. Then technological discoveries. If it works like many-worlds, then even NP hard problems.
With sufficient bandwidth and time delta, you'd also have to hope that the future isn't sending anything nefarious that could lead to your demise. A future adversary could final destination you pretty easily and use you as a pawn to enrich itself, and there's not much you could do except stop listening - but it'd know you planned that too. A future adversary would be the scariest adversary.
And then you get in a car accident when driving a time you otherwise wouldn’t have been, wherein you maim the otherwise grandfather of a founder of the mega corporation temporally exploiting you — thereby eliminating the whole event.
Messing with your own history, given that most systems are chaotic, seems inherently risky. Even in warfare, you’d have a hard time predicting the outcome over more than a short interval.
No, that's just life. If you are afraid of changing something and decide to do nothing, you are still changing things by not acting as a beeing with agency.
Atomics? Climate Change? Technology advances? Ineffective appeals to the better angels of our nature, that clearly go extinct first the moment a resource window snaps shut ?
Should have written queries into the data mountain of humanity,learn about whats possible and whats not possible. The time we could reuse from ineffective public appeals to work on solveable problems
If I toss a ball at a 45 degree angle then the motion it describes is a quadratic parabola. That means the solutions for where it hits the ground is going to be either a positive t, and a positive x (It lands somewhere in front of me, after a second or so), but also a negative t and negative x (it lands right behind me, right before I threw it). But the equation having those solutions doesn't mean there is any physical meaning to that solution. Isn't this (possibly) the same thing?
The second solution doesn't have the ball land behind you before you throw it... It has the ball emerge from the ground, from the orbit it was in, on its way up to your hand.
What both solutions correspond to is the completion of the orbit the ball is briefly in while it is in free fall, in both directions. Every body in free fall (ignoring air resistance) is for that time in orbit around the center of gravity of the Earth. It's just the the body can not complete that orbit due to the fact it impacts the ground, and in the time-reversed direction, couldn't have come from that orbit initially because of the ground.
It's not mystery getting in the way of the equations, it's the physical ground.
(There are many other deviations from the highly idealized "orbit the Earth as if it was a stationary body in perfect Newtonian physics" but compared to air resistance you will not be able to witness any of those effects with anything you can throw with your arm from the ground.)
I guess then, why is what that solution lacking physical meaning versus the normal one - in some sense that means what it corresponds to is something other than a part of physics, but then what is that?
The arc describes the full motion, and the solution we seek is when F(x)=0 which is when the ball hits the ground. There is no mathematical curve that starts at my hand at (x=0m, y=1m) and ends at the ground. We use the full quadratic curve just because its a suitable model for the motion, on the part of the motion we know the ball takes.
The use of a quadratic to solve the throw is a mathematical model. We say that "the value x describing the when the ball lands must satisfy the quadratic equation F(x)=0" but that does NOT imply the opposite, which is "all x that satisfy F(x)=0 describe a valid motion of the ball."
So when we get two answers, e.g. F(-1)=0 and F(15)=0 for the two points when the ball is at ground level, that means only this: if I had thrown the ball from ground level to follow the same curve land in the same place at x=15, then I would have stood 1m further back when I threw it. It does have physical meaning, but there is nothing curious about the physical meaning.
This throw is symmetrical in time though, in the sense that if I throw the ball with the same speed in the opposite direction starting at x=15 then it will land exactly in my hand. (But the equation here is y=F(x) and not parametrized on time).
The equation we use to describe the motion does not contain a term for the ground being there. That assumption exists outside of the model described by the equation, and you use that assumption after the fact to reject a solution that would otherwise be valid, and describe the movement of the ball that's pulled down by gravity.
In this form, it doesn't really describe a proper orbit, just a trajectory of being pulled down by a constant force. I believe this would correspond to an infinitely-ish heavy object located infinitely far below. The proper equation that gives you an orbital curve has the force of gravity proportional to inverse-square distance and point at the center of the body, which is what makes it possible to describe a circular or elliptical motion this way. Parabolic orbits exist too, but they're interpreted as failed orbital capture - "object is moving so fast that it'll curve around and fly away to infinity before turning around and coming back".
And in all cases, the solutions make physical sense (+/- infinity), on the assumption the trajectory doesn't cross the ground, as there's no term for it there :). If you want, you can describe the ground as another equation (or inequality), and solve the resulting system - it'll then be clear what exactly is it that rejects some of the solutions.
The Minkowski metric is time reversal symmetric. The bigger question in particle physics is "what are the symmetries of the action?"
It's not time reversal symmetric, but it's probably [CPT][1] (charge-parity-time reversal) symmetric.
If you forget about quantum field theory and consider classical physics in Minkowski space (or Cartesian space), then t -> -t indeed doesn't change the physical laws. You could tell the two apart, though, provided that the system is far from thermal equilibrium (e.g. "why is this egg uncracking spontaneously?").
Greg Egan wrote a science fiction book in a world with two timelike dimensions - that is, two terms in the Minkowski metric are negative. It's a fascinating world to explore. The book is titled Dichronauts.
Barbour is criminally underrated as a physics author. He’s published a lot of interesting ideas regarding the role of time, or lack thereof, in modern theories! (The End of Time, and its treatment of Causality as a direct substitute for time in any future theory of everything, was very fun)
Someone came up with a very similar theory (two arrows of time diverging from the same point, the big bang). They even gave their theory the same name: Janus.
the metric only tells you distances. it says the distance between today and yesterday is the same as the distance between yesterday and today (swapping doesn't negate).
it doesn't say anything about time evolution because it isn't something you solve. given a spacetime, you can lay down axes and the metric tells you intervals between events.
it says nothing about allowed trajectories through spacetime.
> We generalize Einstein's General Relativity (GR) by assuming that all matter (including macro-objects) has quantum effects. An appropriate theory to fulfill this task is Gauge Theory Gravity (GTG) developed by the Cambridge group. GTG is a "spin-torsion" theory, according to which, gravitational effects are described by a pair of gauge fields defined over a flat Minkowski background spacetime. The matter content is completely described by the Dirac spinor field, and the quantum effects of matter are identified as the spin tensor derived from the spinor field. The existence of the spin of matter results in the torsion field defined over spacetime. Torsion field plays the role of Bohmian quantum potential which turns out to be a kind of repulsive force as opposed to the gravitational potential which is attractive [...] Consequently, by virtue of the cosmological principle, we are led to a static universe model in which the Hubble redshifts arise from the torsion fields.
Wikipedia says that torsion fields are pseudoscientific.
> If gauge symmetry breaks in superfluids (ie. Bose-Einstein condensates); and there are superfluids at black hole thermal ranges; do gauge symmetry constraints break in [black hole] superfluids?
There's also Wick rotations, where you can sub `t -> it'`, and then Minkowskian spacetime becomes Euclidean but time becomes complex-valued. Groovy stuff.
I'm not much of a physics buff but I loved reading Julian Barbour's The Janus Point for a great treatment of the possibility of negative time.
The craziest thing I've seen though is the suggestion that an accelerating charge, emitting radiation that interacts with the charge itself and imparts a backreacting force on the charge, supposedly has solutions whose interpretation would suggest that it would be sending signals back in time. [0]
[0] https://en.wikipedia.org/wiki/Abraham–Lorentz_force