# How does a body "know" how to move??!!

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An interesting propositional experiment is as follows:

A planet bound observer watches an astronaut approach and fly past in a spaceship at 0.8c relative velocity.

The astronaut is holding straight out in front of her a 6 foot ruler, marked in feet.

What will the planet observer see?

Will he see all 6 foot markings?

How long will he think the ruler is?

If the astronaut rotates the ruler through a right angle as she passes

What will the planet observer see happen to the ruler?

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I don't think observing length connection (which is not easy) would tell you anything about direction.

Of course, I was wrong. Doh.

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What will the planet observer see happen to the ruler?

It will trace a circle, if the astronaut is more or less moving straight towards the observer??

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An interesting propositional experiment is as follows:

A planet bound observer watches an astronaut approach and fly past in a spaceship at 0.8c relative velocity.

The astronaut is holding straight out in front of her a 6 foot ruler, marked in feet.

What will the planet observer see?

Will he see all 6 foot markings?

How long will he think the ruler is?

I’m not convinced that this is the correct approach to looking at the question. Making this a question that involves only lengths doesn’t fully express the problem.

Our official forum position is that spacetime is simply a volume with time added as an additional coordinate. I don’t think that anyone has much skepticism about this position being correct. The controversy is over the meaning of volume in this definition.

What you are attempting with your experiment is to decouple the three dimensions that make up a volume into some two-dimensional components. I think this is intended to simplify the question, but is has a fatal flaw. Some of the characteristics of Euclidean 3-space cannot exist in a two-dimensional model. In other words, volume has some properties that are more than what can be attained by simply arranging three planes orthogonally. The two-dimensional question that you’re posing isn’t a valid one (except perhaps in some mathematical constructs that do not model nature.)

Surely a metre cube ,say, would yield an image with different edges contracted by different amounts, for some arbitrary motion of the cube?

This question is a better one because the cube represents the three-dimensional space of spacetime. Instead of looking at the edges, it may be better to focus on the corners. Each corner is a direction and distance from the center of the cube. The direction is JUST AS IMPORTANT as the distance. We tend to ignore this fundamental certainty, most likely because of the way we do the math. But in order for Euclidean 3-space to hold together, direction and length are inextricably interconnected in a unique way.

If the astronaut rotates the ruler through a right angle as she passes

What will the planet observer see happen to the ruler?

This is a trick question. The correct answer is that she will not exist in our frame when she passes perpendicular to her direction of travel. That’s how spacetime wraps back on itself. Our notions about transverse Doppler only consider the distance aspect of the question. We need to consider the direction aspect, too.

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Three replies (I think) to my post#126 so far.

One poster realised that length contraction alone can give direction information.

One poster was realised that something would happen on turning the ruler from parallel to the direction of motion to being perpendicular to it, but was unsure what.

(The guess was incorrect)

One poster completely missed the point that my post was a response to the issue of difficulty in observing length contraction.

No it was not a trick question.

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Three replies (I think) to my post#126 so far.

....

One poster was realised that something would happen on turning the ruler from parallel to the direction of motion to being perpendicular to it, but was unsure what.

(The guess was incorrect)

.....

mmmm not sure you explained the situation clearly...

"The astronaut is holding straight out in front of her a 6 foot ruler, marked in feet.

.......

If the astronaut rotates the ruler through a right angle as she passes"

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One poster completely missed the point that my post was a response to the issue of difficulty in observing length contraction.

No it was not a trick question.

What do you think happens to the cube when it undergoes length contraction?

Do the corners remain at 45° referenced from the center?

This question does have a correct answer.

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An observer co-moving with the cube will not measure ANY length contraction, to this observer the cube will show no change.

A stationary observer will measure the cube (and its markings) contracted in the direction of motion.

The same stationary observer as above will "see" the cube rotated about an axis perpendicular on the direction of motion (see the Terrell-Penrose effect).

So, the issue is quite complex and depends on:

-the motion between cube and observer

-whether we are talking about "measuring" or "seeing"

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An observer co-moving with the cube will not measure ANY length contraction, to this observer the cube will show no change.

A stationary observer will measure the cube (and its markings) contracted in the direction of motion.

The same stationary observer as above will "see" the cube rotated about an axis perpendicular on the direction of motion (see the Terrell-Penrose effect).

So, the issue is quite complex and depends on:

-the motion between cube and observer

-whether we are talking about "measuring" or "seeing"

There is a set of directions in the local coordinate system, just as there is a set of lengths. We seem to pretend to understand the length contraction part by ignoring any questions about the direction part of the system. The two must jibe with one another. Anything that affects length will also affect direction. So the question is "how do all of the directions in the local coordinated system remain coherent when we throw length contraction into the mix?"

This question can't really be answered by simply choosing between measuring or seeing. The effect of length contraction is a real effect caused by the requirement that spacetime has to be isotropic and time moves only in one direction.

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There is a set of directions in the local coordinate system, just as there is a set of lengths. We seem to pretend to understand the length contraction part by ignoring any questions about the direction part of the system. The two must jibe with one another. Anything that affects length will also affect direction. So the question is "how do all of the directions in the local coordinated system remain coherent when we throw length contraction into the mix?"

This question can't really be answered by simply choosing between measuring or seeing. The effect of length contraction is a real effect caused by the requirement that spacetime has to be isotropic and time moves only in one direction.

You need o stop posting rubbish and trying to pass it as science. What I posted is textbook science.

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You need o stop posting rubbish and trying to pass it as science. What I posted is textbook science.

Look, there isn't any dispute that the corners of the cube are events in spacetime while at the same time they are positions in our reference frame. All that I'm talking about is the math that connects these things to one another. Have you seen the math? Do you understand the math?

If the math is incorrect then, yes, the math is rubbish. If it's correct then it's simply math. I don't understand the hatred for math.

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Look, there isn't any dispute that the corners of the cube are events in spacetime while at the same time they are positions in our reference frame.

Events and positions are two different things. Get your facts straight.

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Now we have a response from someone who actually knows what they are talking about.

Steve you should listen to ZZtop.

The purpose of the ruler was to avoid the complication of a 3D object such as a cube and all the arguments that will ensue.

The planet observer will not view the cube as a cube, only the rocket observer will do this.

The ruler will appear to to the planet observer to grow in length when the rocker observer turns it vertical or horizontal but perpendicular to the direction of motion.

Thus the planet observer will be able to witness the effect of length contraction.

Because lengths perpendicular to the motion are not contracted but those parallel are directions are affected in a measurable or calculable way.

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Events and positions are two different things. Get your facts straight.

That is exactly my point. They are different things. But they do relate to one another in a spatial sense. Since both cases comprise Euclidean 3-space they each have a volumetric relationship with one another. Do you know what this relationship is?

Now we have a response from someone who actually knows what they are talking about.

There hasn't been any response to my question.

Do you understand the math that I'm talking about?

If you don't understand, why not?

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Look, there isn't any dispute that the corners of the cube are events in spacetime

The cube has 8 vertices, events in spacetime are points in a spacetime 4-manifold i.e. uniquely specified by 4 Real numbers

Events and positions are two different things. Get your facts straight.

Hmm. Is this true when I choose coordinates such that, say, the spatial coordinate $x^4 = ct$? Not being a physicist I had always understood that a "point" in spacetime was an "event" as used in common parlance.

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The cube has 8 vertices, events in spacetime are points in a spacetime 4-manifold i.e. uniquely specified by 4 Real numbers

Hmm. Is this true when I choose coordinates such that, say, the spatial coordinate $x^4 = ct$? Not being a physicist I had always understood that a "point" in spacetime was an "event" as used in common parlance.

Points are observer dependent, ie they depend on the coordinate system.

Events are agreed by all eg the twins meet again or they don't.

But different observers will differ as to the point at which this happens just as with my cigar example the observers differ as to the point when the cigar burns out.

Another 'point' about points and events.

We are treating all bodies as 'point particles' when discussing events concerning them.

This may or may not be appropriate, just as in classical mechanics.

@steveupson.

I introduced a particular example to answer someone else's question about whether we can observe length or time contraction or not, not to discuss your pet direction obsession.

Edited by studiot
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Points are observer dependent, ie they depend on the coordinate system.

If you are using spatial coordinates here. Yes

Events are agreed by all........... But different observers will differ as to the point at which this happens

Now you are using spacetime coordinates.

Is it not the case that, given spatial coordinates $x,\,y,\,z$

and time-like coordinate $ct$ then under some arbitrary transformation that

$x^2+y^2+z^2 \ne x'^2+y'^2+z'^2$

$(ct)^2 \ne(ct')^2$

and yet $x^2+y^2+z^2-(ct)^2=x'^2+y'^2+z'^2-(ct')^2$.

Edited by Xerxes
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Hmm. Is this true when I choose coordinates such that, say, the spatial coordinate $x^4 = ct$? Not being a physicist I had always understood that a "point" in spacetime was an "event" as used in common parlance.

No, it is no longer true in 4-space but this is not what he was talking about. Please do not encourage the troll.

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If you are using spatial coordinates here. Yes

Now you are using spacetime coordinates.

Is it not the case that, given spatial coordinates $x,\,y,\,z$

and time-like coordinate $ct$ then under some arbitrary transformation that

$x^2+y^2+z^2 \ne x'^2+y'^2+z'^2$

$(ct)^2 \ne(ct')^2$

and yet $x^2+y^2+z^2-(ct)^2=x'^2+y'^2+z'^2-(ct')^2$.

I can't for the life of me see how what I said could have given you that impression, but I am sorry if it misled you.

Read inertial frame for coordinate system if you will. Personally I don't like the term (inertial) frame as it means something quite different to me, but it is well used.

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Is it not the case that, given spatial coordinates $x,\,y,\,z$

and time-like coordinate $ct$ then under some arbitrary transformation that

$x^2+y^2+z^2 \ne x'^2+y'^2+z'^2$

$(ct)^2 \ne(ct')^2$

and yet $x^2+y^2+z^2-(ct)^2=x'^2+y'^2+z'^2-(ct')^2$.

My current understanding is that there will be one unique case in any reference frame where this relationship occurs. The triplet x,y,z can be ordered in any of six different ways and everything will still commute. When we add the time coordinate it doesn't commute. This is why I understand this relationship to be unique.

If I'm wrong, I'm sure someone will correct me. If I'm right, I'm sure someone will still correct me.

When I say that the coordinates commute, I mean that both length and direction commute. The problem with the two-dimensional ruler example is that in two dimensions length always commutes and direction is always its inverse. And that's exactly how we deal with it mathematically.

The coordinate system that contains the x,y,z triplet has some previously unknown relationships that don't exist in two dimensions. All of the normal two-dimensional geometric rules still exist, only they must exist side-by-side with another three-dimensional set of geometric rules.

Adding time to the manifold establishes constraints on this ability to commute, possibly due to the fact that time is divided into the past, now, and the future. All of the events that share the same now must have a geometric relationship to one another that is in addition to a common time coordinate. Also, everything that the skeptics are saying about me seems to be true, except for the parts where they claim that the math isn't the math. I honestly don't think they understand the math.

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Read inertial frame for coordinate system if you will.

No, never!

Personally I don't like the term (inertial) frame

I agree in general, I think. Would you accept the following........

.....a coordinate set is referred to as an inertial reference frame iff for a body considered in inertial motion relative to one coordinate set, there exists a global orthogonal transformation that brings our body the rest relative to these new coordinates.

This seems to be the case in the Special Theory, as far as I understand it.

Of course, in the General Theory, global coordinates do not exist, so the term "inertial reference frame", by the above ad hoc definition, is not appropriate.

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Think of a body moving as in Newton's first law - in a straight line at a fixed speed say. I have been wondering where is the information for the body to "know" how to move? One could argue that the motion itself is the "information", but that is somewhat unsatisfactory from an information theory point of view.

I understand that information theory is being suggested as a possible way of looking at fundamental physics, so my question might be relevant, even though I am only a novice student of theoretical physics.

I kind of always thought of it as a distribution of probability. For instance, I am holding a ball in my hand, that ball can exist everywhere in space that it is possible for it to exist, but the circumstances of probability of the reality that it exists somehow made it more likely that it is there in my hand. Think of the ball in my hand as a fractal pattern radiating out in every perceivable space that it could exist. As you look further from where the ball actually is, it become less likely that it is there because it would require more energy in order to displace it from its current probable position. e.g. It would take a enormous amount of energy to place that ball in orbit, because it is far less probable for it to be there than where it sits. As I move the ball with my hand, I'm affecting the distribution of probability to shift and create a new position that is more probable. This can be said about my hand as well, in fact, my whole body including my head and brain. It's consciousness that has the ability to manipulate this distribution, because it is consciousness that creates a reality that is more probable than another. Otherwise, without it's awareness, energy and matter always interfere with themselves through the double slit.

If you were to ask me to speculate, I would theorize that shifting the probability doesn't "slide" the matter through space, but it actually destroys and creates the matter along an infinite limit from one point to another. Think of one of those novelty sliding needle things you can imprint your face on. I believe matter moves through space kind of like moving an image across one of those. Heisenberg's Uncertainty Principle would not only allow for this, but actually make it mathematically more probable.

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That was the sort of crazy speculation I had hoped for, though I'm not sure about the essential role of consciousness....

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That was the sort of crazy speculation I had hoped for, though I'm not sure about the essential role of consciousness....

Well, if the Universe is infinite in space, that would stand to reason that every possible outcome for every piece of matter is also possible. So why do we perceive it at only one place... because our awareness increases the probability, even if only very slightly, that it is there. So essentially, since your consciousness is the very thing that reduces an object from infinite possibility to finite probability, it is also the thing that can manipulate that perception thereby shifting the distribution of probability.

I think of everything being everywhere all the time, and when I move it I'm just shifting my perception of it's location. I don't think of it as a sliding analog motion, but more of a shifting digital one. I'm just perceiving it through all it's potential locations, and the further away I alter it from it's most probable location in my perception, the more energy that is required because I'm perceptually creating the matter with only my awareness of it. The further I move it, the less probable that it is there, so I need to put more energy into doing it.

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Well, if the Universe is infinite in space, that would stand to reason that every possible outcome for every piece of matter is also possible. [ .....]

Is "every piece" meaningfully labelled though? Especially if continually being destroyed and recreated as you said earlier...

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