4 ms·
But if you just hold out a ball and drop it, it won't look the same in reverse.
by zeven7 8y ago
But if you just hold out a ball and drop it, it won't look the same in reverse.
- ridiculous_fish 8y agoIt will! Imagine the ball right before it hits the ground: it will have a large downward velocity. Reverse time and the ball acquires an upwards velocity, that slows as it reaches your hand, exactly as if it's accelerating towards the earth. If you know some calculus, observe that Newtonian gravity is coupled to acceleration but NOT velocity: d^2 x / dt^2 = a = g Now run time backwards: let dt be negative. This doesn't change a, because dt is squared and squaring a negative is still positive. The acceleration is independent of the direction of time. To show this isn't just mathematical hand-waving: consider a magnetic field. This does couple to velocity. Reverse time, and the magnetic field pushes the other way. Electromagnetism is not time symmetric, it's time ANTI-symmetric. Gravity is different from EM in this respect.
- zeven7 8y agoOk, interesting. The gravity part makes sense. I don't understand the difference with magnetism though. Let's say you have a positively charged item and you're standing on top of a large negatively charged surface. You "drop" the positively charged item. How does its velocity over time differ from the gravity example? And how is it different with time reversed? Seems like it would be the same to me... In forward motion, it would accelerate until it collided with the surface. With time reversed, it would start with a fast velocity and slow down over time. Edit: I googled this. It sounds like the motion of magnetized bodies is time symmetric, but when the charge of the electric field produced by the motion is taken into account it has to be reversed. Is this correct?
- ridiculous_fish 8y agoIn classical electromagnetism, we separate the electric field E and the magnetic field B. If we isolate E, we get rest: electrostatics. Charged particles exert an attractive or repelling force in proportion to their charge, just like gravity, except charge instead of mass. So E is time-symmetric. This applies to your example. Now consider just B. A positively charged particle is moving to the left, through a magnetic field that points inwards. By the right-hand rule, the force on the particle is up. Reverse time: now the particle is moving to the right, so you rotate your hand 180 degrees and the force is downwards. This magnetic field produced an upwards force forwards in time and a downwards force backwards in time: it's antisymmetric. Put mathematically we have: F = qv x B where q is the charge, v is the velocity, B is the field. Reverse time and the velocity gets a minus sign, so F reverses. So E is symmetric and B is anti-symmetric.
- blueprint 8y agoWhat makes it the right-hand rule rather than the left-hand rule?
- ridiculous_fish 8y agoPositive charges obey the right hand rule, while negative particles obey the left hand rule. Classical EM doesn't distinguish between these, and we might as well reverse the signs and hands. QM does so distinguish, for reasons way beyond me.
- blueprint 8y agoSeems like a very important/foundational answer to know, though. Do you happen to know of anything I can read about why charged particles behave by that rule?
- snarfy 8y agohttps://www.youtube.com/watch?v=0mXW1zPlxEE https://www.youtube.com/watch?v=0mXW1zPlxEE https://en.wikipedia.org/wiki/Sterile_neutrino https://en.wikipedia.org/wiki/Sterile_neutrino
- snarfy 8y agoHow does that work in relativity where d = sqrt(x^2 + y^2 + z^2 - ct^2). If it is moving backwards in time, it seems the spacetime interval would point the other direction. It would also have to be moving faster than c. I'm basically arguing that anti-matter is anti-mass/anti-energy, which is not true but still fun to think about.
- ridiculous_fish 8y agoWell intervals by definition don't point anywhere, they're scalars! Relativity says: E^2 = m^2 - p^2 If we treat antimatter as normal matter moving backwards in time, with negative energy - then energy reverses sign, so any time we connect back to experiments we get positive energy. Ok, cool. Even in this view nothing moves faster than c. If we permit faster than c, then either E or M has to become imaginary to get a negative sign after squaring. Imaginary energy is even weirder than negative energy and is well above my pay grade; google "John Baez tachyon" for more.