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Grimble
2009-Dec-09, 06:21 PM
http://img682.imageshack.us/img682/4396/movingtrain.jpg (http://img682.imageshack.us/i/movingtrain.jpg/)

How do these observers line up in relation to each other when A' passes A?

We know that from the train's reference frame B' will be adjacent to C and that from the embankment's frame C' will be adjacent to B, but as there is only one train and one embankment and as each has only a single physical existance and can only physically exist in one place at one time, how do they 'really' line up as they pass.

Now I can appreciate that time dilation and length contraction are perceived effects, distortions if you like due to the relative velocity of the participants, and that that perceived 'distortion' of time and space is reciprocal (as it must be, being due to their relative velocity).
And I can also appreciate that, to the observers in their reference frames those 'distortions' are the 'real' measurements they perceive; much as the pitch, of the sound of a passing car, being higher as it approaches and lower as it recedes, is real to an observer, whilst the actual pitch of the sound produced does not vary. It is once again an effect (albeit entirely different in nature) due to the relative velocity.

Now can we say that if we could calculate their relative positions, rather than 'observing them' from one or other of the reference frames, we would see them align, observer to observer?

Grimble :confused::confused:

Grey
2009-Dec-09, 07:02 PM
How do these observers line up in relation to each other when A' passes A?It depends on which observer you ask.


We know that from the train's reference frame B' will be adjacent to C and that from the embankment's frame C' will be adjacent to B, but as there is only one train and one embankment and as each has only a single physical existance and can only physically exist in one place at one time, how do they 'really' line up as they pass.There is no way that they "really" line up. Differently moving observers will have different views about how they line up, and each of those views is equally valid. It's true that those different observers will disagree about when things happen (like the various observers passing each other), but you need to remember that simultaneity is different for different observers, too. For example, C and C' will not agree on when exactly it is that A and A' meet. So if you ask the two of them where they are relative to each other at "that moment", it's not surprising that you'll get different answers, because they are talking about different moments.


Now can we say that if we could calculate their relative positions, rather than 'observing them' from one or other of the reference frames, we would see them align, observer to observer?No. There may be other reference frames where they align observer to observer at some moment in time, but that will not be the case from either the reference frame of the train or of the embankment, and none of those reference frames should be viewed as being any more "what really happens" than any other.

WayneFrancis
2009-Dec-09, 11:03 PM
what grey said. The hardest thing, in my opinion, to get around with SR it the fact that all frames are valid and all frames can show different answers. The beauty of it is if you run the different answers through the maths of SR you get consistent answers.

Grimble
2009-Dec-10, 12:09 PM
Hello Grey and Wayne, I appreciate all that you have said but please bear with me on this.:)

We know that if the embankment or the train were considered on their own, each being an inertial reference frame examined from within its own reference frame, then the lengths AC and A'C' would be identical (Einstein's 1st postulate).
Then, as they pass, their lengths, referenced from within their own frames, would be unchanged.
It is only when referenced from another frame that length contraction occurs and, as it is a function of the relative velocity, it is perceived by each of them equally.
This is all perfectly straightforward. A and B exist and have well defined dimensions. When A views B the dimensions that A perceives are a function of their relative velocity and vice versa.
The dimensions that A perceives are 'real' to A, and those that B perceives are 'real' to B. (cf. the sound of the car in my OP).
However this does not and cannot mean that A actually possesses different dimensions, unless we are venturing into the realms of multiple realities/existences, but that their relative velocity effects how they are perceived and that those perceptions are 'real' to the perceivers.

And yes Wayne:
The hardest thing, in my opinion, to get around with SR it the fact that all frames are valid and all frames can show different answers. but this is not due to some mysterious property of SR, it is due to 'straightforward laws of physics that are the same for all inertial reference frames'.:confused:

Grimble

hhEb09'1
2009-Dec-10, 12:40 PM
And yes Wayne: but this is not due to some mysterious property of SR, it is due to 'straightforward laws of physics that are the same for all inertial reference frames'This seems to be advocating that special relativity is somehow wrong in its interpretation. That's a non-mainstream view, of course, and would have to be moved to ATM to discuss it.

Grey
2009-Dec-10, 04:55 PM
It is only when referenced from another frame that length contraction occurs and, as it is a function of the relative velocity, it is perceived by each of them equally.
This is all perfectly straightforward. A and B exist and have well defined dimensions. When A views B the dimensions that A perceives are a function of their relative velocity and vice versa.
The dimensions that A perceives are 'real' to A, and those that B perceives are 'real' to B. (cf. the sound of the car in my OP).
However this does not and cannot mean that A actually possesses different dimensions, unless we are venturing into the realms of multiple realities/existences, but that their relative velocity effects how they are perceived and that those perceptions are 'real' to the perceivers.You seem to be suggesting that the measurement of the length of an object made by an observer in the rest frame of that object is the "real" one, and that the measurement of the length of an object made by some observer moving relative to that object should be discounted as not "real" in the same way. Special relativity makes no such distinction, however. It considers any measurement made by any inertially moving observer to be a valid measurement. If you make a measurement, it's "real". That is the length of the object. It is true that this means that differently moving observers will report different lengths for the same object. As far as special relativity is concerned, each of those measurements is just as accurate, and the math of relativity allows you to take your measurement, and from that work out what some other person might measure, given their movement relative to you.

Perhaps you can see where your idea would run into problems by considering how you would measure the distance between two objects that are moving relative to each other. Should you determine the "real" distance by thinking of object A as stationary, or B as stationary? Or maybe you should take the average velocity, and measure the distance between them by considering the midpoint between the two as stationary. You won't get the same result for any of those measurements.

NorthernBoy
2009-Dec-10, 05:31 PM
This attempt to pick one frame's values as "real" has been done recently by several other posters here, and always leads to problems, because invariably it will end up with a measurement from one frame being applied in another, giving nonsensical results.

Trying to define any one measurement as "real" shoudl just be avoided from the off. If you want to have a term for a quantity measured in an object's rest frame, perhaps use "proper length", and note that "proper" here is the same word as used in "property", and is not to be taken to mean "correct".

You may not like this analogy, but it is actually a perfectly apt one in this circumstance. Imagine that a box is placed on your desk, and you measure its width to be 30cm, and its height to be 20 cm. Yo then throw it to your friend, and he measures it too, and finds that its width is 20cm, and its height is 30cm.

You are both measuring the same box, but there is no way in which one of you gets the "real" numbers, and one gets false numbers. You both measure reality, but you measure it from a different perspective to one another.

The same is true of the train. In one frame it has length X, in another frame it has length X', and both are equally real.

Grimble
2009-Dec-10, 06:05 PM
This seems to be advocating that special relativity is somehow wrong in its interpretation. That's a non-mainstream view, of course, and would have to be moved to ATM to discuss it.

I must admit that I am not sure, myself, whether this is ATM or not.

Let me say that I feel that somehow, Einstein's theory is not what relativity seems to have grown into and that we should hand it back to him!

Right from the start of my investigations I came across the idea that, if we are dealing with two bodies of reference, then all measuments ("spacetime magnitudes") can be expressed as relative to the other body, and that one could swap between the reference bodies and the relationship would still be valid. Is it a natural consequence of relativity, that seems to have become lost in the more and more complex and involved attempts, to make relativity comply with possible misconceptions that have become the de facto standard? Building relativity into something far from the simple elegant little jewel that Einstein described.

Instances I would cite are:

the idea that time dilation and length contraction are somehow opposites, rather than two views of the same thing, albeit from slightly differing standpoints;
With respect to the Relativity of Simultaneity: Einstein said "Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)."
That, to me, implies that the same events could be simultaneous with reference to the train but not, from the same reference frame, with respect to the embankment. (reciprocality).
in Minkowski diagrams used to depict the 'twin paradox' as here (http://en.wikipedia.org/wiki/File:Twin_Paradox_Minkowski_Diagram.svg) there is a 'jump' in the plane of simultaneity at the turnround. (I have seen this described as a 'temporal disconuity') but careful examination reveals that this is solely due to the disortions of the scales used.


So I have undeniable differences with the 'Mainframe view', but, I believe, non with Einstein's theory as he described it.

Grimble

Grimble
2009-Dec-10, 06:18 PM
When I am referring to 'real' I am referring to the measurements taken by an observer that is at rest with the body measured.
Any measurement that is taken by an observer in motion with respect to the measured is altered by a function of that velocity. So which would one consider real if any?
As you say all measures are real to the measurers and there is nothing wrong with that, but what you seem to be arriving at is that there is no absolute size.

I quite understand that all measurements, of any kind are relative - relative to the standard of the scale used and that as the scale is changed so are the measurements but the magnitude (if I may so use the term) remains.

An atomic particle has a certain magnitude and will always have that magnitude however we measure it.

NorthernBoy
2009-Dec-10, 06:34 PM
An atomic particle has a certain magnitude and will always have that magnitude however we measure it.

But this is not true. If you want to pick, for example, the "magnitude" of its life in seconds, then moving particles have different ones to stationary particles.

No-one is saying that you cannot pick the particle's rest frame and work everything out in that, if you choose, but they are saying that there is nothing revolutionary about that, and that it is totally arbitrary for you to define that one as real.

I think that you need to explain more clearly what you think is new, or different here, or what you disagree with. So far, it seems that you are saying nothing more than that you personally prefer to work in the rest frame of whatever object you are considering. Where's the beef?

Grey
2009-Dec-10, 06:36 PM
...but what you seem to be arriving at is that there is no absolute size.Yep.


An atomic particle has a certain magnitude and will always have that magnitude however we measure it.Nope. Not if it's moving relative to us (or we're moving relative to it). As long as the relative motion is well below the speed of light, we can ignore that, but if it's comparable to the speed of light, we'd measure a different size for an atom, at least in the direction of motion. If you're thinking of subatomic particles, like an electron, well, as far as we can tell, an electron doesn't have a size in the first place. Electrons behave like point particles*. If it does have some nonzero size, it's much too small for us to measure, let alone tell how it changes at relativistic velocities.


* Well, point particles subject to the wacky laws of quantum mechanics, which makes it harder to talk about just where it is and what it's doing with any kind of meaning.

Sam5
2009-Dec-10, 07:07 PM
When I am referring to 'real' I am referring to the measurements taken by an observer that is at rest with the body measured.
Any measurement that is taken by an observer in motion with respect to the measured is altered by a function of that velocity. So which would one consider real if any?




Instead of using the terms “real” and “not real”, in a 1907 paper Einstein used the terms “geometric shape” and “kinematic shape”, in his paper “The Relativity Principle and Conclusions Drawn From it.”

http://i50.tinypic.com/54eg5s.jpg

http://i48.tinypic.com/kc1j7m.jpg

You can probably order a copy of this paper through your interlibrary loan system. It is in the Paperback (English Translation) Vol. 2, pages 252 – 311, “The Collected Papers of Albert Einstein,” Princeton Press. You must specify the Paperback English Translation version or you will receive a copy of the Hardback German original.

pzkpfw
2009-Dec-10, 07:58 PM
When I am referring to 'real' I am referring to the measurements taken by an observer that is at rest with the body measured.

I am at rest with respect to my desk, and measure it to be about 5.5 lengths of my ruler wide.

But I'm on Earth which is spinning, and orbiting the Sun, and ... (we've all heard this before). So why should I consider my measurement "more real" than any one elses? (Say, an observer at rest with respect to the Sun.)

Further, If I and my desk board a rocket that shoots off at a very high velocity relative to what appeared to be it's "stationary" location in my office, I would still measure it to be 5.5 units of my ruler wide.

...but my co-worker with the same desk, back in the same office where I was before, would observe my desk to be different to his, and vice-versa.

That all seems contradictory... but from that I find it very natural that there is no one "real" reality; everyones view of reality is "real", just that it may differ from someone elses view.


(The other side of this is when people try to suggest that there is some underlying absolute to which we could become stationary (somehow at rest with respect to the overall Universe??) and then this would give us a view of the "real" reality. That's a whole new kettle of ATM fish.)

Hornblower
2009-Dec-10, 09:03 PM
Once again, the cosmos (with all of its included observers, desks, rulers, trains, tracks, etc.) is what it is and does what it does, and it does not care whether or not it makes sense to all of us.

WayneFrancis
2009-Dec-10, 11:30 PM
I'll point to my original post (http://www.bautforum.com/space-astronomy-questions-answers/97865-how-does-moving-train-line-up-embankment.html#post1639702) in this thread.

Now for the longer discussion. How are we making the measurements we are making? What can we use as a ruler? Light! So if you take your 632.8 nm helium-neon laser and measure the desk while travelling with it you'll measure the distance different then I do if I'm not travelling with it. Now we both use the same laser and both see the frequency exactly the same but the time it takes to traverse the length of the object will be different.

I find that very often people get caught up in trying to justify a absolute frame and why SR is wrong because of this frame but inevitably they always fail just as a person jumping out of a plane claiming they fall away from the Earth always fails.

I do find it curious how some people that do the maths and see the answers then try to reinterpret SR in a way that isn't actually consistent with the maths or observations.

Grimble
2009-Dec-11, 12:11 PM
I am at rest with respect to my desk, and measure it to be about 5.5 lengths of my ruler wide.

But I'm on Earth which is spinning, and orbiting the Sun, and ... (we've all heard this before). So why should I consider my measurement "more real" than any one elses? (Say, an observer at rest with respect to the Sun.)

Further, If I and my desk board a rocket that shoots off at a very high velocity relative to what appeared to be it's "stationary" location in my office, I would still measure it to be 5.5 units of my ruler wide.

...but my co-worker with the same desk, back in the same office where I was before, would observe my desk to be different to his, and vice-versa.

That all seems contradictory... but from that I find it very natural that there is no one "real" reality; everyones view of reality is "real", just that it may differ from someone elses view.

Absolutely! I have no problem whatsoever with that!

But in this post:
When I am referring to 'real' I am referring to the measurements taken by an observer that is at rest with the body measured.
Any measurement that is taken by an observer in motion with respect to the measured is altered by a function of that velocity. So which would one consider real if any? what I am saying is that as any one else's measurement is a function of their velocity (with respect to me and my desk) it will be different due to that velocity.

Please, everyone, understand that I am not suggesting that there is any 'absolute' space but that from all the possible frames with their own measurements, it does not seem unreasonable to consider the measurement that is not changed as a function of the velocity, is the 'standard' which all the others are a function of.

Does the body have one existence, but different measurements due to the conditions under which it is measured, or does it have different existences in each reference frame?

Maybe this is merely a philosophical point...

But it would seem quite simple to me, to say it has one existence and, that due to the conditions (relative velocity), it is measured differently by the moving observers. As I said in my original post
much as the pitch, of the sound of a passing car, being higher as it approaches and lower as it recedes, is real to an observer, whilst the actual pitch of the sound produced does not vary. It is once again an effect (albeit entirely different in nature) due to the relative velocity.

Grimble:)

loglo
2009-Dec-11, 12:38 PM
Absolutely! I have no problem whatsoever with that!

But in this post: what I am saying is that as any one else's measurement is a function of their velocity (with respect to me and my desk) it will be different due to that velocity.

Please, everyone, understand that I am not suggesting that there is any 'absolute' space but that from all the possible frames with their own measurements, it does not seem unreasonable to consider the measurement that is not changed as a function of the velocity, is the 'standard' which all the others are a function of.

Does the body have one existence, but different measurements due to the conditions under which it is measured, or does it have different existences in each reference frame?

Maybe this is merely a philosophical point...

But it would seem quite simple to me, to say it has one existence and, that due to the conditions (relative velocity), it is measured differently by the moving observers. As I said in my original post

Grimble:)

I don't see your beef, there are invariants in SR, why not use them as your "real" things if you must consider something real?

NorthernBoy
2009-Dec-11, 05:38 PM
it does not seem unreasonable to consider the measurement that is not changed as a function of the velocity, is the 'standard' which all the others are a function of.

Yes, you are perfectly entitled to do that. Relativity, though, tells you that there is nothing special, or preferred, about this frame. If someone else chooses that their "standard" frame is one in which the object is always receding at 0.5c, then their standard is every bit as valid as yours. You might argue that yours helps calculations, or just feels right, but that is not the same as saying that your frame is "preferred" in terms of the science.

You need to separate the question of your own personal, human preferences, from whether the laws of physics are any different in that frame from others, and we know that they are not.

Grimble
2009-Dec-11, 09:51 PM
Yes, you are perfectly entitled to do that. Relativity, though, tells you that there is nothing special, or preferred, about this frame. If someone else chooses that their "standard" frame is one in which the object is always receding at 0.5c, then their standard is every bit as valid as yours. You might argue that yours helps calculations, or just feels right, but that is not the same as saying that your frame is "preferred" in terms of the science.

You need to separate the question of your own personal, human preferences, from whether the laws of physics are any different in that frame from others, and we know that they are not.

OK, I'm sorry but I will answer points raised in others posts and lose the thread of what I am trying to determine.

Let me try another way of asking: is length contraction a physical change to the length contracted or a change to the scale by which it is measured? (from proper to coordinate units)

Grimble

Strange
2009-Dec-11, 10:39 PM
is length contraction a physical change to the length contracted or a change to the scale by which it is measured? (from proper to coordinate units)

I will be interested to see what the experts say, but my answer would be: yes.

You drew an analogy with doppler shift earlier. Does that actually change the pitch or is it just an effect of the speed the sound travels at?

Again, the answer is yes: they are both valid ways of describing or thinking about what is happening.

If the scale you measure something by changes (really changes, not like choosing to use feet instead of metres) then the size of the thing measured has changed.

sirius0
2009-Dec-12, 02:42 AM
If you are at A, then you measure a real contraction to the length. The realness is due to the validity of your inertial frame. If you had placed a ruler along the train when it was at the station and you used this to measure the train as it rushes by then you will conclude the train hasn't changed it's measurement but that the ruler has shortened relative to a ruler you have with you. This is also real. In fact the example in the OP is more like this last idea as it deals with one unit, two units. Remember too that time dilates as the train progressess. Meaning that while A,B,C may agree about A' meeting A but they wont agree with where each other see B' and C' relative to their selves. Because the points are the same rest lengths apart they can only line up in a frame where they are at rest with respect to each other. The term 'rest length' or 'proper length' might be the one you are after. Anyone in any inertial frame can calculate the rest length of an object in any other inertial frame (and they will all agree). This is quite easy to prove mathematicaly from the same assumptions that derive the Lorentz. Rest length is that length you measure when you are at rest with respect to the object you are measuring.

sirius0
2009-Dec-12, 05:19 AM
basically once you accept that light travels at C for all frames then the rest follows from there. There really isn't another way once C is invariant. Even LET had to do a lot of patch work in order to cater for this. The proofs (subject to C= const) are very firm.

Grimble
2009-Dec-12, 11:56 AM
If you are at A, then you measure a real contraction to the length. The realness is due to the validity of your inertial frame. If you had placed a ruler along the train when it was at the station and you used this to measure the train as it rushes by then you will conclude the train hasn't changed it's measurement but that the ruler has shortened relative to a ruler you have with you. This is also real.


So, if the primed system is the moving system and v=0.866, γ=2, then as L' = L/γ we can say that; 2 units measured in the moving system, that is 2 coordinate units, are transformed into 2/γ = 2/2 = 1 unit measured in the rest system, that is proper units. i.e. length contraction.

All simple and straight forward but that is not what we are looking for.

No, what we want to know is what is the length, 2 proper units, when converted into coordinate units i.e. we need to convert the units the other way round: L=γL' that is 2 proper units = 2*2 = 4 cordinate units.

So the unit size has halved but the unit quantity has doubled, so yes we have length contraction of the scale we measure with but the overall length stays the same...?

Now I feel even more confused:confused:

Grimble

Sam5
2009-Dec-12, 04:33 PM
So the unit size has halved but the unit quantity has doubled, so yes we have length contraction of the scale we measure with but the overall length stays the same...?

Now I feel even more confused:confused:

Grimble


It’s due to the relative motion in the theory itself, and it involves visual measurements from a distance while your system and the other system are moving relatively.

Will your desk shrivel up or shrink in length just because someone is looking at it from a distant redshifted receding galaxy, a galaxy that you and your desk are moving relative to at .6 the speed of light? No it won’t, not as long as you are measuring your desk while you are stationary relative to it. But according to the theory, your desk is supposed to be seen and measured as being contracted, as seen from that other galaxy, while you will see (at a distance and while the relative motion takes place) the other guy’s desk (the same kind of desk as yours) as being length contracted.

See Einstein, “Theory of Relativity”, 1915. See the sentences I have marked:

http://i50.tinypic.com/vzgaow.jpg

This situation is visual and temporary, while the relative motion takes place. See his footnote #1 in his paper “The Relativity Principle and Conclusions Drawn From it”, 1907:

http://i46.tinypic.com/29wpt6v.jpg

NorthernBoy
2009-Dec-12, 06:39 PM
Let me try another way of asking: is length contraction a physical change to the length contracted or a change to the scale by which it is measured? (from proper to coordinate units)

Grimble

Physical change. A moving object is shorter than when it is stationary.

Grimble
2009-Dec-12, 07:21 PM
Physical change. A moving object is shorter than when it is stationary.

Yes, that is its length comprises less units, but everyone seems to say it as if those units are the same size, but they are not, are they? So if one were to calculate its length in terms of # of units x size of units in each case how would they compare then?

sirius0
2009-Dec-13, 12:05 AM
Yes, that is its length comprises less units, Less units in A
but everyone seems to say it as if those units are the same size, but they are not, are they? The units in A are the same size if we are observing from A, the units in A' are shorter if we observe them from A.
So if one were to calculate its length in terms of # of units x size of units in each case how would they compare then?

They compare in the same way that length dilation compares. If we measure the length of the train from A with units from A the length is shorter and this is as real as the length of my nose. If we measure the length using a unit we know to be valid in A' then we get the rest length, but this is not our experience of the length (we being in A) but it is the experience of a passenger in A'. I am quite sure if you worked your way through the steps in your text instead of just applying some 'formulas' to some 'problems' you would begin to understand this. Of course I don't know that this has been your approach, but I think these sorts of questions often arise from these sorts of inadequate study strategies.

RussT
2009-Dec-13, 09:13 AM
It depends on which observer you ask.

There is no way that they "really" line up. Differently moving observers will have different views about how they line up, and each of those views is equally valid. It's true that those different observers will disagree about when things happen (like the various observers passing each other), but you need to remember that simultaneity is different for different observers, too. For example, C and C' will not agree on when exactly it is that A and A' meet. So if you ask the two of them where they are relative to each other at "that moment", it's not surprising that you'll get different answers, because they are talking about different moments.

No. There may be other reference frames where they align observer to observer at some moment in time, but that will not be the case from either the reference frame of the train or of the embankment, and none of those reference frames should be viewed as being any more "what really happens" than any other.

In one of Grimble's other thread you showed this...
http://www.bautforum.com/1591400-post4.htmls


And there's a fairly simple thought experiment that demonstrates why there can't be length contraction in a direction perpendicular to travel. Imagine you have two meter sticks moving relative to each other, perpendicular to their length. So:

| |

At each end of both meter sticks is a piece of chalk, set to draw a line on the other meter stick as they pass. Now, if the principle of relativity holds, an observer moving along with either meter stick is perfectly justified in deciding that his meter stick is at rest, and it's the other meter stick that is moving. If there were length contraction perpendicular to the direction of the motion, the observer on the left would see the meter stick on the right as shorter, and so would expect the chalk lines from that meterstick to be drawn on his own at, say, 10 cm and 90 cm, and the chalk on his own meter stick would miss the other one entirely. So he'd expect only his own meter stick to have chalk lines on it.

However, the observer on the right would expect the opposite, that his meter stick would be the one that would end up with chalk lines on it. If we actually did this experiment, and one or the other meter sticks contracted, we'd be able to determine which was "really" moving, and that would violate the principle of relativity. For the principle of relativity to hold, there cannot be any changes in length along the directions perpendicular to the direction of motion.

SO, which "Observer" should be considered the "Right One"...the one that see's "Reality"???

One is saying it "Can't Happen" and one is saying that it must...

sirius0
2009-Dec-13, 10:41 AM
In one of Grimble's other thread you showed this...
http://www.bautforum.com/1591400-post4.htmls


SO, which "Observer" should be considered the "Right One"...the one that see's "Reality"???

One is saying it "Can't Happen" and one is saying that it must...

No there is no problem or contradiction of with what Grey has said. He was talking about perpendicular length. No one in this thread has suggested that the train's roof height has become shorter. If we say that the train's travel is along the x axis then only those measurements of the train that have a component in x will have any contraction. A length 'normal' (aka 'sticking straight up') to the direction of travel will not undergo contraction, veiwed from A. Indeed considering the length if it was 'normal' is another way of arriving at the rest length. Perhaps another name for Rest Length could be Normal Length (with appropiate explanation).

sirius0
2009-Dec-13, 10:42 AM
I would think that contraction only occurring in the direction of the velocity not too hard to accept though. Imagine a marching girl (or boy) twirling her baton on the deck of the train. As it spins through the horizontal it will get narrower. As it approaches the normal it will get longer. Not a very realistic sight but real nevertheless.

Surely this train is going to go through a tunnel. What if the tunnel is, from the point of view of A, just long enough for the shortened train? What if as soon as it enters gates at either end of the tunnel slam shut simultaneously. This will work from the A veiw point. The train was 'really' shortened after all. It is now up to us to consider what the passengers think about this and here lies the length contraction counterpart to the twins paradox. The reason I raise this paradox is to point out that the length in each frame is absolutely real for that frame.

Grimble
2009-Dec-13, 11:47 AM
Less units in A
Of course

The units in A are the same size if we are observing from A, the units in A' are shorter if we observe them from A.
Yes, absolutely. No problem with that.

They compare in the same way that length dilation compares. If we measure the length of the train from A with units from A the length is shorter and this is as real as the length of my nose.
Yes

If we measure the length using a unit we know to be valid in A' then we get the rest length, but this is not our experience of the length (we being in A) but it is the experience of a passenger in A'.
Of course

I am quite sure if you worked your way through the steps in your text instead of just applying some 'formulas' to some 'problems' you would begin to understand this.
Oh, I do understand it, it is the very basics of SR

Of course I don't know that this has been your approach, but I think these sorts of questions often arise from these sorts of inadequate study strategies.
Quite possibly so, but those are not the questions I am asking!

Let me try again...

In Chapter 12: (http://www.bartleby.com/173/12.html)The Behaviour of Measuring-Rods and Clocks in Motion he takes the length of the metre measuring rod and using LT transforms it into coordinate units, then calculates how long a metre coordinate unit is in rest (proper?) units in his system K, and it is shorter by a factor of gamma.

But when he transforms the length of the rod into coordinate units he doesn't look to see how many coordinate units are the result - that is what I was referring to in my calculations in post #23.

Now it is interesting that you compare this with time dilation for, in that same chapter, Einstein takes the opposite approach and takes the duration of one one-second tick of the moving clock, transforms that into coordinate units and then compares, not the one coordinate second with the proper time in the rest frame, no, he compares the proper units in system K with the whole of the transformed coordinate units and finds that the time is dilated not contracted.
The following diagram demonstates this.
Two frames of reference A and B, moving with v = 0.6c, the horizontal scale in blue is proper units and may represent either ct or x as the diagram is for a single axis in each of the two frames to shew how they are related by Minkowski's rotation.
http://img41.imageshack.us/img41/287/specialrelativitydiagrar.jpg (http://img41.imageshack.us/i/specialrelativitydiagrar.jpg/)
We can see length contraction and time dilation shewn here in the same drawing and see how they are related.
For length contraction take the blue figure 1 for frame A. LT rotates this (drawn to scale) and it becomes the pink 1 on the diagonal line. Now projected down onto B's axis and it becomes the green 1 coordinate unit.
1 coordinate length unit = 0.8 proper units - length contraction.
However, for time dilation he again transforms the blue proper unit, by rotation, into the pink rotated (diagonal) unit, but then takes the blue proper unit once again and projects that (normally) back onto the pink diagonal and finds that 1 blue unit = 1.25 pink units - time dilation.

So both contraction and dilation are seen for the same units, depending on which comparison is made. The coordinate units that result from Lorentz transformations have smaller units (contraction) but more units (dilation) and that this is exactly what has to happen to satisfy Einstein's two postulates.

Grimble

sirius0
2009-Dec-13, 09:03 PM
Yes understood so what is the issue for you?

sirius0
2009-Dec-13, 11:08 PM
Hmm I think we are having trouble with our respective ways of explaining things. I have looked at post 23 and your last one. You do realise that if we say A is at rest then the proper length and coordinates for that train length are actually in A' ? We in A see a contracted length. That frame chosen to be at rest does not necessarily have the proper length or proper time. Often the proper time is in a different frame to the proper length. This IS reality.

Grey
2009-Dec-14, 04:15 PM
SO, which "Observer" should be considered the "Right One"...the one that see's "Reality"???

One is saying it "Can't Happen" and one is saying that it must...Sirius0 has the right of it. The quote from me was talking about whether there could be length contraction perpendicular to the direction of motion (as it says in the very first sentence), while Grimble is clearly asking about length contraction parallel to the direction of motion. So, no contradiction at all to suggest that those two cases are different. No observer should be considered the "right one" any more than any other. All frames of reference are equally valid.

Grimble
2009-Dec-15, 09:08 AM
Hmm I think we are having trouble with our respective ways of explaining things. I have looked at post 23 and your last one. You do realise that if we say A is at rest then the proper length and coordinates for that train length are actually in A' ? We in A see a contracted length. That frame chosen to be at rest does not necessarily have the proper length or proper time. Often the proper time is in a different frame to the proper length. This IS reality.

So, let's try that. Let us say that A in my diagram is the x axis of the embankment, and that B (that is your A') is that of the train, moving at 0.6c.
Then the proper length of the train is shewn in the blue, proper units, scale, 5 in this case, which being rotated (the green diagonal line) gives the projected red, coordinate scale, along the x axis of A, so that, just as you say, "we in A see a contracted length" - 5 coordinate units which is equal to 4 proper units as expected from the values of v and γ.

Do you agree?

Grimble:)

RussT
2009-Dec-15, 11:30 AM
Sirius0 has the right of it. The quote from me was talking about whether there could be length contraction perpendicular to the direction of motion (as it says in the very first sentence), while Grimble is clearly asking about length contraction parallel to the direction of motion. So, no contradiction at all to suggest that those two cases are different. No observer should be considered the "right one" any more than any other. All frames of reference are equally valid.

Yes thanks...I see that now...;)

I read that "Looking perpendicular" to the direction of motion.

sirius0
2009-Dec-16, 08:57 AM
Hmm, thinking. by the way the bartleby link has a typo. Should be v=c not v=0

sirius0
2009-Dec-16, 12:04 PM
I think I agree with your last post but not with the direction you are sending that plot. You seem to be trying to develop a transcendental metric with your proper units, trying to mesh two different frames as if the time dilation somehow cancels out the length contraction. This just isn't true you seem to be double dipping you're relativistic effects by jumping between frames. But I am not sure. Why are the increasing directions of your plot in the same direction?

sirius0
2009-Dec-18, 05:58 AM
I don’t agree that your plot is about time dilation. Of course, implicitly, length contraction and time dilation are two expressions of the same thing. That is what the derivation of the Lorentz is all about. That is because for C to be constant in all frames then all different inertial frames will not agree on lengths (with a component parallel to the velocity between the frames) or time elapses.

I think your plot is about length contraction in both the view of B from A and the view of A from B. However the angled lines readily represent the hypotenuse used to derive the Lorentz often. They are effectively transforms, even rotations, but I am not up to Minkowski as yet. The two angled lines are effectively reciprocal functions of each other as any general study of Cartesian functions will demonstrate. So it is not surprising that you can find the time dilation from these. L’/L = gamma=delta t is to be expected (for the case Einstein is discussing in your link).

I don’t like the blue proper coordinates as this is just wrong. You still seem to be after something global but in the wrong place. Just at least don’t join them from one end to the other. In your OP you had six points Those at rest on the bank were A,B,C and though at rest WRT each other will not agree on the timing of their respective primed counterparts. I.e. A will not agree with B on which point of time B’ aligns with B so you can’t be drawing global coordinates in sorry.

Grimble
2009-Dec-24, 10:46 AM
Many apologies for the delay in responding to you, Sirius0, but it is a busy time of year!


I don’t agree that your plot is about time dilation. Of course, implicitly, length contraction and time dilation are two expressions of the same thing. That is what the derivation of the Lorentz is all about. That is because for C to be constant in all frames then all different inertial frames will not agree on lengths (with a component parallel to the velocity between the frames) or time elapses.

Time dilation can be seen in my plot, if one takes the units to refer to time, then 5 units of proper time (depicted in blue for either frame A or frame B), rotated to the corresponding diagonal and shewn by the red or green figure 5, will be dilated, along the diagonal, to the value 6.25, which is what the dilation will be.


I think your plot is about length contraction in both the view of B from A and the view of A from B. However the angled lines readily represent the hypotenuse used to derive the Lorentz often. They are effectively transforms, even rotations, but I am not up to Minkowski as yet. The two angled lines are effectively reciprocal functions of each other as any general study of Cartesian functions will demonstrate. So it is not surprising that you can find the time dilation from these. L’/L = gamma=delta t is to be expected (for the case Einstein is discussing in your link).

Exactly so.


I don’t like the blue proper coordinates as this is just wrong.
What I have drawn is a diagram shewing two frames each with just one axis drawn horizintally. Each axis may represent either time or length.
Observers in either frame will consider themselves, and their frame of reference, to be at rest. They will, therefore, each be seeing proper units.
Now, I have been told, that proper time is not necessarily the same in different frames, but I cannot see how such a claim can be justified.
If two frames are at rest with respect to one another they will, in effect, be in one reference frame and their proper units will be common between the two of them. If one has a constant velocity with respect to the other then that changes nothing, for each will still consider itself to be at rest, and the other moving and it must surely still have the same proper units. If not then a third (possibly virtual frame), permanently situated at the mid point between them, will still be able to compare their coordinate units and from them calculate the proper units and if they were different that would lead to the possibility of differentiating a preferred frame - Einstein's K0


You still seem to be after something global but in the wrong place. Just at least don’t join them from one end to the other. In your OP you had six points Those at rest on the bank were A,B,C and though at rest WRT each other will not agree on the timing of their respective primed counterparts. I.e. A will not agree with B on which point of time B’ aligns with B so you can’t be drawing global coordinates in sorry.
I can see what you are saying, however my diagram shews that time dilation and length contraction, mean the scales change, not the overall length or time just the way they are measured.