> If you really want a reference frame to compare to, you can use the one you started in before leaving.

Nah, the analogy is fine there -- you "wake up" in a new reference frame, and weren't able to make any measurements to compare it to your old one. Whether you can measure your motion against the old reference frame starting from this situation is actually the question!

Oh, that's not what I meant. I meant use the reference frame from when you first woke up. But I'll make a more detailed scenario:

* Wake up in the void. Label your current reference frame R0.

* Notice that there is no real way to label 'speed' vs. void.

* We can however measure angular speed via tension on body parts, it seems to be 0.

* Accelerate somehow

* * for some magical reason it's forbidden to have more than one object, so I thought up a couple minimally-magic ways to do it that I am pretty sure don't cause physics problems by themselves.

* * * You could throw something then immediately pretend the thing you threw doesn't exist, forbidding it as a reference frame.

* * * You could make a punching motion and use magic to cause your arm to disappear.

* * * You could swing all your limbs away from your body and use magic to reverse the direction of one of them.

* Now you are in reference frame R1 because you accelerated.

* Hooray you accelerated without any other objects to compare to. If you insist on comparing to a reference frame, use R0.

>* * * You could swing all your limbs away from your body and use magic to reverse the direction of one of them.

No you can't, this leads to the twin paradox. Assume you could use magic to simply reverse the direction of an object. Take two clocks, and have one travel away from you at relativistic speeds, then turn around and come back. Because of time dilation, when the clock returns, it will have observed less time pass then you, because it was moving at relativistic speeds. However, from the clocks perspective, you were moving at relativistic speeds, so you will have observed less time pass. The resolution to this paradox involves the fact that the clock was accelerated in order to turn around.

An interesting side point is that in the hypothetical void, you actually have no way of knowing weather or not you are accelerating. For example, the space station is currently in free fall towards the earth, but from within the station you cannot detect this fact. Similarly, if you are in a plane that is descending at the rate of gravity, you will appear to be in zero-g. The mathematics behinds this is considerably more difficult than special relativity.

You're talking about accelerating. The original passage was just talking about simple constant motion. The point being that you can't distinguish constant motion from remaining perfectly still without something else to measure against. That's really all I was trying to say. Obviously I failed!

For what it's worth I think you did a good job overall, but flaws are pretty much inevitable when your word choice is so restricted.

The point the original author is implicitly trying to make is that you can't compare to your original frame, where you went to sleep.

This is the part I'm objecting to:

To move, you have to move to or away from ... well, from what? You'd have to say that you don't even get to use a word like "move" when you are the only body in that void.

You can move. You can have a delta v. You don't have an absolute position or velocity, but you don't need those to move.

I don't see any comparison to the pre-sleep state, this is a statement about the void, and it overreaches.

This is a metaphor breakdown because you pushed it too hard, rather than a real problem with the idea. In the ideal case you are a floating point, and you haven't got discrete parts of yourself to fling away, but of course that's an abstract step too far away for the target audience of this piece.

Reflections on Relativity [1] in fact does build up to a generalize concept of relativity (not just Einsteinian relativity) starting with points in an unknown space (building up to a concept of distance, rather than assuming such a thing), but it's a mathematical treatment of the problem rather than an intuitive one. And certainly not in words of one syllable.

[1]: http://mathpages.com/rr/rrtoc.htm , the part I'm referencing starts right off at 1.1.

I think I haven't made it clear enough what my objection is. In my opinion it is the article that pushed the analogy too far. It works great to show that you can't tell what is moving. But when the analogy tries to claim that you can't move, well, it's pretty much begging the question. Of course a floating point can't move, and it says nothing about physics. That's why I assumed some mechanism for trying to cause motion: you can't see if you failed if you didn't try.

I guess I wasn't clear (no sarcasm). My point is based on the idea objecting that an analogy doesn't stand up to being pushed "too far" isn't a useful one; analogies always break down when pushed too far. If they didn't, they wouldn't be analogies, they'd be explanations. Analogies are dangerous ways of thinking, but again, this is generally targeted at people for who that is all they have available.

The analogy is useful, I agree there. The problem is that the article first uses the analogy for something it fits, then uses the analogy again for something it doesn't fit. The conclusions drawn from the second use are invalid. I don't object to the analogy, I object to that second use.

I had the same objection as the op actually - if you wake up at "rest" with just yourself and a bed, and accelerated away from the bed, you can in fact know whether "you are moving" or "the bed is moving". It is because one of the two have only been in 1 reference frame, while the other has been in 2.

Basically the same issue as the twin "paradox". I can appreciate the assumption of a constant velocity on wake though, as a way to simplify the story.

I don't think you can accelerate in an empty universe - no speed, no speed difference.

Without a reference frame, what experiment can you perform that would tell you that you're accelerating?

I guess the GP understood special relativity, but not general ;)

Well, to be really pedant, if you were spinning around yourself, you'd feel an acceleration.

There will be 'gravity' -a force- in the opposite direction you are accelerating in. You should know the feeling, it happens when you accelerate in a car, or when a plane lifts off. If it's really you floating around, you will be able to feel it. (I reckon you could even guess at the amount by comparing it to the acceleration of 9.81 m/s^2 that you're used to.)

>There will be 'gravity' -a force- in the opposite direction you are accelerating in.

Wouldn't there be a force in the direction you are accelerating in?

Anyway, when you accelerate a car, you are not feeling acceleration, you are feeling the force of the car on you. Imagine being inside of a box that is in free fall. What experiment could you run to determine if you were accelerating?

>Wouldn't there be a force in the direction you are accelerating in?

Well, yes, that would be the standard way to look at it. Sorry for being confusing.

>Anyway, when you accelerate a car, you are not feeling acceleration, you are feeling the force of the car on you.

According to [Force = Mass * Acceleration] you can take them as equal (apart from the constant factor of your mass). In the freefalling box that is accelerating (and thus no longer in free fall) you'd also feel a force. No need for experiments if you have your normal senses. You'll be pressed against one side of the box. (And if the acceleration is 9.81 m/s^2 you couldn't distinguish it from a box on earth.)

That is actually the basic premise of general relativity - the equality of 'inertial mass' that resists against acceleration and 'gravitational mass' that happens because of, well, gravity. It's like the idea of constant speed of light for special relativity.

edit: Unless you're talking about gravity, which accelerates all parts of the setup equally, thus no force results.. but that would need something else in the experiment, either a great amount of matter or energy. But then you'd have a reference frame right there. (Mathematically. As for an experiment.. hm. Check for perturbances from space-time distortions that result from rotating gravity sources, maybe.. most gravity sources in this universe are rotating. There's an experiment done that checked that for Earth.[1])

[1] https://en.wikipedia.org/wiki/Gravity_Probe_B

drop something? If it accelerates away from you, you are accelerating (or held stationary in a gravity field, but AFIAK, those are the same things).

That wouldn't work.

If you dropped something it would simply stay right next to you, even if you were accelerating - both of you are accelerating at exactly the same rate.

Why? What's making it accelerate? I wasn't trying to talk about some kind of universal/aether acceleration. I meant you and only you should accelerate.

And how do you accelerate - do you have a rocket attached to your feet?

It doesn't really matter. But there should be some mechanism. A rocket attached to your feet works quite well if you ignore the exhaust for purposes of reference.

If you want a useful thought experiment about physics then you need to give reasonable physics tools. Otherwise you get something like "Pretend you are an inanimate green blob. You can't climb a hill, can you? Therefore climbing a hill is an illusion."

If you have a rocket on your feet why do you need to drop something to figure out if you are accelerating? You can feel the pressure on your feet.

The only type of acceleration that is undetectable is gravity - and gravity will effect the dropped object exactly as much as you.

Great! You just simplified the experiment!

Dropping something was only one idea, but feeling pressure is much simpler.

Yes, but when you drop something, you're creating a reference frame, aren't you?

Ah, you're misunderstanding the term reference frame as it's being used here. A reference frame is like a coordinate system for velocity; it's not something physical.

No. When you drop something nothing whatsoever happens.

And as shardling said, a reference frame isn't a physical thing that is created and destroyed - it's simply the zero point for your system of measurement - but the measurement would work just fine if you started with any number, zero is just convenient.

I understand a frame of reference doesn't have to be physical. However, if you're in an apparently empty and dark universe, and you're interested in knowing whether you're accelerating or not, postulating a frame of reference is not going to be of much help.

I may have missed the point of dropping an object, though. I thought the idea was to create a physical point we could anchor the coordinate system to, and in that way be able to measure acceleration.

Dropping an object that won't get accelerated is one way to measure acceleration, but not the only way. If you are the actor causing the acceleration on yourself, as I originally intended, then presumably you already know / measure-by-doing how much you have accelerated, and you can use dead reckoning to watch the earlier reference frame fly by.

If the force is external and doesn't apply pressure then you have to drop an object.

If the force affects the entire universe the same way then that's aether and can't be measured / doesn't exist. But that was not the kind of force I was using to disprove "you can't move".

> If the force is external and doesn't apply pressure then you have to drop an object.

What kind of force is external and doesn't apply pressure, and also doesn't affect the dropped object? There is no such force, and therefor no such test.

> However, if you're in an apparently empty and dark universe, and you're interested in knowing whether you're accelerating or not

You can't. There is absolutely no test that can tell you this.

You can't "drop" anything - whatever force is accelerating you also accelerates the object, so letting go of it tells you nothing.