Reference Frames

[Farsight]

REFERENCE FRAMES

 

You know I was talking about magnetic fields and electric fields? When you move through an electric field you see it as a magnetic field. That’s Relativity. It’s the same old thing really. The difference is down to you. Sometimes you don’t realise that things are the same because you see them a particular way. Because you walk around all your life wearing some very special sunglasses. They’re like Ray-Bans. You grow up with them, so much so that you don’t know you’re wearing them.

 

 

They colour your vision but you cannot see how. They stop you seeing the light for what it really is. I need to talk about them, because I want to get to the bottom of Special Relativity and talk about time, and I want to get to the bottom of General Relativity and talk about gravity. But the things that colour your vision aren’t sunglasses. What they are is reference frames.

 

Let’s have a little gedanken, a thought experiment. It involves my spaceship. Remember my spaceship?

 

 

You’re the copilot, and I’ve just taken you down to the cargo bay and shown you “the box”. It’s a ten foot canister sitting in front of the airlock. It’s comfortable, cushioned, equipped with an air supply so you don’t need a spacesuit, with thruster rockets for positioning and trim and emergency escapes. And as you may have gathered, you have to get in the box.

 

You climb in, find the light switch and turn it on, then I swing the hatch closed and give you a slam slam goodbye. You hear me leave and the pumps evacuating the air, followed by the grinding of steel as the outer doors open. There’s a jolt as the launch ram pushes you outside the ship, and then everything goes quiet. There are no windows in this box. There is however a radio so we can stay in touch. I call you up to say I’m pulling back a little, leaving you there in your box.

 

 

You say A-OK catch you later, and enjoy a few zero-gravity games, doing somersaults and pushing yourself from one side of the box to the other practising your racing turns. After a while you find the tennis ball in your jumpsuit pocket and throw it against the opposite wall, smiling when it bounces straight back into your waiting hand. The radio bleeps into life and it’s me, asking how you’re doing. Fine you reply, I ask if you can detect any acceleration and you say Nope. You’re cool, because you’re weightless, it’s fun. You're in the box. There are no windows. You chuck the ball across the inside of the box and it goes straight as a die, bounces off the side, and back into your hand. You are in an inertial reference frame. You can feel no gravitational force, and you can detect no gravitational force acting upon the ball. You are not accelerating.

 

I ask if you’d like to try a little acceleration, you say Sure! and then you feel and hear the thruster rockets burning. You find yourself pressed back, and now one side of the box feels like it’s the floor. You stand up and it’s like being on the surface of the moon, or shipside under artificial gravity. You can feel your weight. You throw the ball and it travels in a lazy arc towards the floor and bounces around a little before settling there. You are now in a non-inertial reference frame, and you know you’re accelerating. You can feel it, you can measure it locally, within your frame, within your box.

 

 

I shut off the thrusters so you’re back weightless again, floating in your inertial reference frame. You can no longer feel any acceleration. You can’t measure any. The ball flies straight as a die. As far as you are concerned, you are not accelerating.

 

Did I mention that you’re falling into a black hole? No? Oops. Sorry about that.

 

Here’s the deal: a body in freefall is not accelerating. If you say it is, you're mixing reference frames. You're looking at yourself from some reference frame out somewhere in space rather than from your reference frame, that of the body in freefall. Don’t be mistaken about this. The Principle of Equivalence between gravity and an accelerating box applies when you're standing on a planet, not when you're in freefall.

 

 

There really is no force acting on your freefalling body. You can't feel any, you can't see any, you can't measure any. Because there is none. If you looked out of a window to see a moon going backwards, you're mixing frames. This is why gravity is not technically a force. It exerts no force on you. In your reference frame you are not accelerating. You never can be, because in your reference frame your velocity must be zero. If you say it isn’t, you’re mixing frames. You really really are not accelerating, and that’s why you can throw that ball straight. And that’s why Einstein called gravity a pseudoforce.

 

Meanwhile I’m sitting pretty, out in space in the ship where the black hole gravity is so neglible that I can also consider myself to be in an inertial reference frame. All I have to do is switch off the ship gravity, and I can play ball games just like you. But when I look through the viewscreen I see you falling faster and faster towards the black hole, knowing that as far as you’re concerned, you’re in an inertial reference frame just like me. We’re both in inertial reference frames, but yours isn’t inertial as far as I’m concerned, and vice versa. What’s happening is that your inertial reference frame is changing and you can’t see it.

 

But you can detect something, if you have the right equipment. And that you do. Because the radio crackles and it’s me again, telling you open a concealed hatch and pull out an apparatus that looks like a long dumbell. I tell you to perform a "Pound-Rebka" experiment, and you follow my instructions and find that you get a photon blueshift reading when the instrument is pointed in a given direction. I tell you it’s pointed at the black hole, and what you’re measuring is a slight tidal force in that direction.

 

 

Note that a “proper” gravitational field is never uniform. Sometimes the tidal force is neglible, but it is never ever zero. If gravitational felds were uniform, they’d be hills without slopes, they’d be flat, so they wouldn’t be hills at all. The tidal force is always there because of a slight change in the gravity in a given direction. This is where the Principle of Equivalence isn’t quite perfect, because there is no tidal force in a simple accelerating box in free space. Einstein knew this, but people only look at what he generalised in 1911 and take it all too far. Here’s a quote from a guy called John R Ray dating from 1977:

 

The first thing to note about the 1911 version of the principle of equivalence is that what in 1911 is called a uniform gravitational field ends up in general relativity not to be a gravitational field at all – The Riemann tensor is here identically zero. Real gravitational fields are not uniform since they must fall off as once recedes from gravitating matter.

 

It’s really obvious when you think about it. But people never do. They never actually look at the reference frames that they look through. You’re in your box, and "gravity" is continuously changing your inertial reference frame. But you’re in it, you are immersed in your reference frame, you can’t see it, it’s what you look through to see the world, you can’t see it changing. All your photons are blueshifting, but you don’t notice it. Your time is dilating, but you don’t notice it. Your seconds are changing, and your metres too, but not to you, because you can’t see it.

 

Your reference frame is how you see the world, but it isn’t how the world is. Because in your reference frame, your velocity is always zero. And that simple fact means you are at odds with Copernicus, because in your reference frame, the sun goes round the earth.

 

 

I don’t like reference frames. They aren’t real, they don’t actually exist, they get in the way instead of making things clearer. People talk about them too much, more than Einstein did. Let’s use them less, and learn to look at the world the way it really is.

 

Is that the time? It’s time for tea. We will continue this gedanken another time. OK, thrusters on, full boost. Come on home, back to the ship. Time is of the essence.

[Farsight]

This is a new little "RELATIVITY+" essay/chapter that serves as a "lead in" to time, which is a toughie. If anybody can give me any feedback and put me straight on any errors/omissions/confusions I'd be grateful.

[Sayonara]

Let’s have a little gedanken, a thought experiment. It involves my spaceship. Remember my spaceship?

 

 

That's not your spaceship you thieving gypo. It's Malcolm Reynolds' spaceship, and he probably wants it back.

[Realitycheck]

So if there are no such things as reference frames, then what is your take on the clock experiment? How do you explain shortcuts through time? Surely, there is a good reason as to why it happens, not just that it happens.

[Farsight]

Sorry guys, I didn't mean to be rude, I've been busy.

 

Sayonara: there's more than one of them babies.

 

agentchange: there are no shortcuts through time, because there's no going "through" time at all. We only go through space.

[someguy]

no we go through time as well. not in the same sense and shortcuts are usually for space but we travel through time at different rates determined by our velocity.

[CPL.Luke]

the idea behind an inertial reference frame is that there is no way to make a preference between me traveling at 10,000 miles per hour towards you, and you traveling at 10,000 miles per hour towards me they are both identical situations.

 

also once you add a gravitational field in you no longer have an inertial reference frame, and you can make the distinction.

[insane_alien]

no we go through time as well. not in the same sense and shortcuts are usually for space but we travel through time at different rates determined by our velocity.

 

since your new, i'll explain something, farsight doesn't believe in time or much else other than space. he is, in honesty, nuttier that a squirrels bowl of crunchy nut cerial topped with peanutbutter with bits of peanut brittle in it with a coating of crushed nuts.