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]

I've been writing further essays which I intend as chapters of a popular science book. This one started life as a mention within GRAVITY EXPLAINED, and grew via a thought experiment I was talking to Zanket about. I then expanded it within a chapter on black holes, and have now juggled things around and made it a little lead-in chapter all on its own.

I'd be grateful if anybody could point out any errors herein, and otherwise I hope it proves useful.

[sanctus]

I have to say it was a very interesting read Popular, but there is one thing missing an alternative...I really wonder how you want to explains things without reference frames? Isn't it enough, as you point out very well, to know that all is relative to the considered reference frames and formulate everything in a covariant form (so that no new things happen when you change reference frame)?

[Farsight]

I'm not saying we shouldn't use them at all, sanctus, just less. And we need to remember what it is that we're talking about.

For example, imagine a hypothetical charged particle, a "point particle", just sitting there doing nothing. It has an electrostatic field extending outwards. It has no magnetic field. But if you zip past it, or it zips past you, it does. It had an electromagnetic field all along, which you view an an electric field and/or a magnetic field. How you see it depends on your relative motion, and your reference frame compared to it. But the particle hasn't changed at all.

It's similar with length contraction. If you travel at .99c you will measure all distances as if they're contracted sevenfold in the direction of travel. You would measure the entire universe as being contracted sevenfold in the direction of your travel. But the universe hasn't changed one iota.

All this ties in with the "ontological viewpoint" that I use in my various essays.

[Qfwfq]

Originally Posted by Popular

Here’s the deal: a body in freefall is not accelerating. If you say it is, you're mixing reference frames.

I'd say that you are choosing a reference frame.

Originally Posted by Popular

The Principle of Equivalence between gravity and an accelerating box applies when you're standing on a planet, not when you're in freefall.

It's always valid. In a differential sense, of course. When in free fall, you simply "don't need" it because you're "already" in free fall. But then, you can use it the other way around, to say that the falling ball simply "isn't being accelerated upward" and that is where gravity becomes a pseudo-force, or apparent force, exactly like all inertial forces.

Newton stated it only for a uniform gravitational field (with a remark about approximation for nearly uniform cases) but GR states in in general, in differential terms. Before SR and Minkowskian geometry, all attempts to do this had failed.

Originally Posted by Popular

In your reference frame you are not accelerating. You never can be, because in your reference frame your velocity must be zero.

True, this is so even when the thrusters are going. That's why you say that the ball is accelerating, instead of the spaceship.

How sure is John R Ray that the Riemann tensor in a uniform gravitational field is identically zero? The spatial submanifold is flat, but space-time isn't.

Originally Posted by Popular

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.

And how is the world, really? The whole point of the principle of relativity is reference frames. They were the whole point that Einstein was addressing.

[Farsight]

Thanks for the feedback, Qfwfq.

Originally Posted by Qfwfq

I'd say that you are choosing a reference frame.

Noted. I'll see about working that in.

It's always valid. In a differential sense, of course. When in free fall, you simply "don't need" it because you're "already" in free fall. But then, you can use it the other way around, to say that the falling ball simply "isn't being accelerated upward" and that is where gravity becomes a pseudo-force, or apparent force, exactly like all inertial forces.

Hmmn. I wrote what I did because I'd been talking to somebody who compared the freefall acceleration to the acceleration in a rocket-powered box. I'll check my wording to make it clearer.

Newton stated it only for a uniform gravitational field (with a remark about approximation for nearly uniform cases) but GR states in in general, in differential terms. Before SR and Minkowskian geometry, all attempts to do this had failed.

Please can you clarify this?

How sure is John R Ray that the Riemann tensor in a uniform gravitational field is identically zero? The spatial submanifold is flat, but space-time isn't.

I can't speak for him. But I will say this: there is no such thing as a uniform gravitational field. It's a contradiction in terms. Like a flat hill. And I would hazard a guess that spacetime curvature is something that you take for granted and can not actually explain. I could talk at length about this, and it might take us some way off this topic, so I'll leave it there. I came across the quote by Ray in an interesting paper Einstein’s Gravitational Field by Pete Brown. See page 20. There’s also a quote by Synge:

http://xxx.lanl.gov/ftp/physics/papers/0204/0204044.pdf

“... I have never been able to understand this principle…Does it mean that the
effects of a gravitational field are indistinguishable from the effects of an
observer’s acceleration? If so, it is false. In Einstein’s theory, either there is
a gravitational field or there is none, according as the Riemann tensor does
not or does vanish. This is an absolute property; it has nothing to do with any
observers world line … The Principle of Equivalence performed the essential
office of midwife at the birth of general relativity, but, as Einstein remarked,
the infant would never have gone beyond its long clothes had it not been for
Minkowski’s concept [of space-time geometry]. I suggest that the midwife be
buried with appropriate honours and the facts of absolute space-time faced.”

And how is the world, really? The whole point of the principle of relativity is reference frames. They were the whole point that Einstein was addressing.

It's pure marble. If you catch my drift.

[snoopy]

Yeah popular,

I think I have to agree with the moderators on this one,

You need to pick a frame of reference its absolutely fundamental to living in a relativistic universe.

Newton had thought about relativity then rejected it on the grounds of points similar to the ones you are making but as it turns out Newton was wrong.

You need to pick a frame of reference to make relativity work and in the elevator/space rocket thought experiments Einstein was trying to say forces that are similar are actually the same.

It doesn't matter which frame of reference you pick you could pick the earth and have the entire universe moving relative to it. Or pick the rest of the universe and have the earth move relative to it.

But you must pick one, relativity doesn't work if you don't.

[jungjedi]

is that spaceship the serenity from firefly
Serenity (Firefly vessel - Wikipedia, the free encyclopedia)

[Farsight]

Noted snoopy. I'll think carefully about what you said.

jungjedi: yep. I've used it before when talking about "my spaceship" to illustrate a point.

[Qfwfq]

OK Popular, I needed to shake a few cobwebs out of my differential geometry, over the weekend I gave a quick read through a translation of Die Grundlagen der allgemeiner Relativitätstheorie. In a uniform field the intrinsic curvature is zero, only the embedding into is curved. I was somewhat confusing things. Actually, the doubt had already crossed my mind, due exactly to the trivial argument Einstein gave, it's the very first remark he makes after introducing the Riemann tensor with four indices. All the same, I don't get the drift about the equivalence principle.

Now the principle is obvious enough for a uniform field; in Newton's Principia it is one of the corollaries (I think VI but I can't remember for sure) after the three axioms. Einstein's Ansatz is that, given a point, even if the principle can't be applied in a finite region, there is a coordinate choice which is locally inertial for that point, meaning that SR is valid to the first order in a neighborhood of it. There is absolutely nothing wrong with this principle (except that it would obviously not apply at a singularity such as that of the Schwarzschild solution).

Before Einstein, some had thought of using the same idea in a 4-D euclidean space-time to describe gravity but attempts failed. I read somewhere that someone eventually proved that it can't be done, so it's only with Minkowski's metric that the idea works and not with Euclid's.

Originally Posted by Popular

It's pure marble. If you catch my drift.

No, I don't catch it, sorry.