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## The true nature of length contraction

I stumbled on a book that seems to throw the concept of length contraction upside down to me. Maybe someone can help me here.

All the books I've read to date, a popular example might be Elegant Universe, say that an object moving near the speed of light past an observer will appear squashed or contracted along its length. Green even had images in his book of a normal racecar at rest (as seen from the side) and one moving near light speed, which was the same exact image just squashed into a smaller size from left to right.

Now I'm reading a book called Einstein's Universe by Nigel Calder. He talks about a spaceship passing the Earth from east to west at near light speed and viewing it from a telescope:

"As you turn the telescope straight upwards, to try to see the spaceship at its moment of closest approach, you will see its tail facing you. In other words, instead of facing along its line of travel past the Earth, the spaceship appears to be turned to a point away from the Earth. Even at less extreme speeds, a passing spaceship will appear to be swivelled away from the Earth. You will see part of its tail when you would expect to see the ship from sideways-on. Again the reason is that the light entering a telescope pointing straight outwards from the Earth has been launched somewhat backwards from the spaceship, allowing for the aberration. Many accounts of relativity say, quite incorrectly, that a passing spaceship appears unnaturally squashed or contracted along its length. It DOES appear foreshortened but only in accordance with the entirely natural perspective of an object seen from an angle."

I hope you can see my confusion. I'll also add that Calder's book was written in 1979 so it can possibly be outdaded info. In previous chapters he also talks about seeing around corners as you approach light speed, which is another concept I am unfamiliar with.

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Mentor   			 				  				 				 				Blog Entries: 1  There's nothing wrong with Calder's statement.  Note that he is talking about the visual appearance of a rapidly moving object, which does not take into consideration that light from different parts of a huge object takes different times to reach your eye.  Relativity says the measured length of a passing spaceship will be contracted--but those measurements assume that you've taken into account the travel time of the light involved.  The apparent rotation of the spaceship is a famous effect called the Penrose-Terrell rotation.  It's not really rotated, it just looks that way.  Unfortunately Brian Greene was being a bit casual when he said that moving objects appear squashed.  What he meant is that the moving object will be measured as being shorter.  This sloppy terminology is common practice in popular books and is the source of some confusion.  Good for you that you caught it!

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Quote by denni89627 					 				 				I stumbled on a book that seems to throw the concept of length contraction upside down to me. Maybe someone can help me here.             All the books I've read to date, a popular example might be Elegant Universe, say that an object moving near the speed of light past an observer will appear squashed or contracted along its length. Green even had images in his book of a normal racecar at rest (as seen from the side) and one moving near light speed, which was the same exact image just squashed into a smaller size from left to right.             Now I'm reading a book called Einstein's Universe by Nigel Calder. He talks about a spaceship passing the Earth from east to west at near light speed and viewing it from a telescope:       "As you turn the telescope straight upwards, to try to see the spaceship at its moment of closest approach, you will see its tail facing you. In other words, instead of facing along its line of travel past the Earth, the spaceship appears to be turned to a point away from the Earth. Even at less extreme speeds, a passing spaceship will appear to be swivelled away from the Earth. You will see part of its tail when you would expect to see the ship from sideways-on. Again the reason is that the light entering a telescope pointing straight outwards from the Earth has been launched somewhat backwards from the spaceship, allowing for the aberration. Many accounts of relativity say, quite incorrectly, that a passing spaceship appears unnaturally squashed or contracted along its length. It DOES appear foreshortened but only in accordance with the entirely natural perspective of an object seen from an angle."            I hope you can see my confusion. I'll also add that Calder's book was written in 1979 so it can possibly be outdaded info. In previous chapters he also talks about seeing around corners as you approach light speed, which is another concept I am unfamiliar with.
Calder is right, Green wrong. That is why Green sells more books than whatsisname. I believe that Terril was the first to publish a detailed derivation of Calder's description.

## The true nature of length contraction

Thanks for the reply. You're very clear and I understand what you're saying, but doesn't that contradict the last sentance in the quote from Calder's book? From what I gather he's saying the contraction is ONLY a product of the angle the ship is seen from, not the measurable length. I guess both would have to be accounted for but I don't see why he would leave the latter out.

Also, before I get slammed for making things up, Greene may have said "measured" instead of "appeared" when talking about contraction. I lent the book to a friend so I can't confirm. I always thought of it as an appearance though, whether it was presented to me incorrectly or not. Thanks for clearing that up.
Dennis

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Quote by Meir Achuz 					 				 				Calder is right, Green wrong.  That is why Green sells more books than whatsisname.  I believe that James Trefil was the first to publish a detailed derivation of Calder's description.
Calder is wrong in his last two sentences when he says:

Many accounts of relativity say, quite incorrectly, that a passing spaceship appears unnaturally squashed or contracted along its length. It DOES appear foreshortened but only in accordance with the entirely natural perspective of an object seen from an angle.
Length contraction is not a trick of perspective, it is what's left once you account for delays due to light propogation, or measure the object's length using purely local measurements (for instance, you could use Einstein's original notion of a network of rulers and synchronized clocks, and measure the position of the front and back at a given time by noting the marks on the ruler that each were passing when clocks next to those marks both read the same time).

At worst, Greene is only guilty of a sloppy use of language, but then it is common to use the word "observed" for what someone measures in their own coordinate system, not what they actually see using light-signals.

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Quote by denni89627 					 				 				Thanks for the reply. You're very clear and I understand what you're saying, but doesn't that contradict the last sentance in the quote from Calder's book? From what I gather he's saying the contraction is ONLY a product of the angle the ship is seen from, not the measurable length. I guess both would have to be accounted for but I don't see why he would leave the latter out.
I don't have Calder's book, but if he said that length contraction is only a product of the angle the ship is seen from that would be laughably wrong. In that quoted passage, it seems clear that Calder is talking about the visual appearance of moving objects, not their actual--and quite real--relativistic contraction. If he's sophisticated enough to be aware of Penrose-Terrell rotation, it would be pretty amazing if he "forgot" to mention plain old--and quite real--length contraction.

As JesseM said, length contraction is not a trick of perception. If Calder is stating that, he's wrong. (But I don't deduce that from that quote.) Is that the only mention of length contraction that he makes?

Quote by denni89627 					 				 				 All the books I've read to date, a popular example might be Elegant Universe, say that an object moving near the speed of light past an observer will appear squashed or contracted along its length. Brian Green even had images in his book of a normal racecar at rest (as seen from the side) and one moving near light speed, which was the same exact image just squashed into a smaller size from left to right.
Well, Brian Greene knows what he's talking about, this much is certain. There are few who present abstract ideas as well as he does. That said, if you yourself accelerated up to 0.866c inertial, you'd see all planets whizzing by you squished to an ellipsoid, 50% as long as they exist in their own proper frame. Is the contraction real? Indeed. If you flew straight into a planet, you wouldn't touch it until you met its surface, and that surface is 50% contracted. It's not as though the contraction is an illusion, and you'd strike the planet before getting to it, such as say at the location where the surface would be if it were spherical. The contraction is real, but you see it only if it is moving wrt you. Technically, Brian Greene's got it right.

Quote by denni89627 					 				 				  Now I'm reading a book called Einstein's Universe by Nigel Calder. He talks about a spaceship passing the Earth from east to west at near light speed and viewing it from a telescope:       "As you turn the telescope straight upwards, to try to see the spaceship at its moment of closest approach, you will see its tail facing you. In other words, instead of facing along its line of travel past the Earth, the spaceship appears to be turned to a point away from the Earth. Even at less extreme speeds, a passing spaceship will appear to be swivelled away from the Earth. You will see part of its tail when you would expect to see the ship from sideways-on. Again the reason is that the light entering a telescope pointing straight outwards from the Earth has been launched somewhat backwards from the spaceship, allowing for the aberration.
Indeed, Penrose and Terrell revealed more about the effects of high speed than even Einstein imagined, however these effects are geometric abberation. I haven't studied this in the past in any detail, however it doesn't change the fact that Greene is also correct. Greene was just focusing his attention on relativistic effects, and not the optical effects. Here's a couple links wrt relativistic effects ...

http://math.ucr.edu/home/baez/physic...spaceship.html

http://www.fourmilab.ch/cship/lorentz.html

Quote by denni89627 					 				 				  Many accounts of relativity say, quite incorrectly, that a passing spaceship appears unnaturally squashed or contracted along its length. It DOES appear foreshortened but only in accordance with the entirely natural perspective of an object seen from an angle."            I hope you can see my confusion. I'll also add that Calder's book was written in 1979 so it can possibly be outdaded info. In previous chapters he also talks about seeing around corners as you approach light speed, which is another concept I am unfamiliar with.
Well, I don't have any idea what Nigel is talking about there. As stated, the statement is incorrect from everything I've ever learned or read on the subject. The vessel is length contracted plain and simple.

However, there is more to it than a length contraction. The vessel is also rotated in spacetime. This may be what Nigel is trying to say? Hermann Minkowski showed that if the time axis is considered as a complex spatial axis, we then have a 4-space vice a 3-space plus time. In Minkowski space, the spaceship frame is rotated wrt your frame as a stationary observer. However, we cannot see this rotation readily, as it would go somewhat hidden from us at casual glance. The spaceship is contracted in length per you, but not per it.

It's analogous to viewing an 8 inch pencil from the side. Rotate the pencil, and the pencil appears shorter. Now you'd of course know and be able to tell that the pencil is rotated in 3-space and does not really change in length, because we see depth. However, when high velocity produces this rotation, we cannot see the complex spatial axis (ie time axis) since we don't perceive time the same ways as space. We don't see the depth into the temporal dimension. So the spaceship appears contracted and not rotated (neglecting abberation).

However if the vessel had 10 windows with a clock in each window, all clocks in sync per the onboard passengers, you as the stationary observer would see those clock readouts displaying different times asynchronously. They would not be in sync per you, even though they are in sync in the vessel itself. This would be the proof of the frame rotation, and explains very elogantly why a vessel can contract per an observer while never change in its proper length per itself. This is Lorentz Symmetry.

Quote by denni89627 					 				 				I stumbled on a book that seems to throw the concept of length contraction upside down to me. Maybe someone can help me here.             All the books I've read to date, a popular example might be Elegant Universe, say that an object moving near the speed of light past an observer will appear squashed or contracted along its length. Green even had images in his book of a normal racecar at rest (as seen from the side) and one moving near light speed, which was the same exact image just squashed into a smaller size from left to right.             Now I'm reading a book called Einstein's Universe by Nigel Calder. He talks about a spaceship passing the Earth from east to west at near light speed and viewing it from a telescope:       "As you turn the telescope straight upwards, to try to see the spaceship at its moment of closest approach, you will see its tail facing you. In other words, instead of facing along its line of travel past the Earth, the spaceship appears to be turned to a point away from the Earth. Even at less extreme speeds, a passing spaceship will appear to be swivelled away from the Earth. You will see part of its tail when you would expect to see the ship from sideways-on. Again the reason is that the light entering a telescope pointing straight outwards from the Earth has been launched somewhat backwards from the spaceship, allowing for the aberration. Many accounts of relativity say, quite incorrectly, that a passing spaceship appears unnaturally squashed or contracted along its length. It DOES appear foreshortened but only in accordance with the entirely natural perspective of an object seen from an angle."            I hope you can see my confusion. I'll also add that Calder's book was written in 1979 so it can possibly be outdaded info. In previous chapters he also talks about seeing around corners as you approach light speed, which is another concept I am unfamiliar with.
have please a critical look at
Physics, abstract
physics/0507016 on arxiv

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Quote by pess5 					 				 				Well, Brian Greene knows what he's talking about, this much is certain.  There are few who present abstract ideas as well as he does.  That said, if you yourself accelerated up to 0.866c inertial, you'd see all planets whizzing by you squished to an ellipsoid, 50% as long as they exist in their own proper frame.  Is the contraction real?  Indeed.  If you flew straight into a planet, you wouldn't touch it until you met its surface, and that surface is 50% contracted.  It's not as though the contraction is an illusion, and you'd strike the planet before getting to it, such as say at the location where the surface would be if it were spherical.  The contraction is real, but you see it only if it is moving wrt you.  Technically, Brian Greene's got it right.
It is very difficult to avoid using the terms "see" and "appear" when describing Lorentz contraction (I do it myself ), but those terms can cause some confusion.

I think we are talking past each other a bit. There are two different effects being discussed:
(1) Real relativistic length contraction of rapidly moving objects.
(2) The visual appearance of rapidly moving objects.

Number 1, the relativistic Lorentz contraction, is by far the most important and is discussed in just about every book on relativity. Unfortunately, sometimes it is described as "rapidly moving objects appear contracted along their direction of motion", which may lead some to conclude that it is just appearance and not real, just an optical illusion. (Like how a pencil in a half full glass of water appears bent at the interface, but is in reality perfectly straight.) Lorentz contraction is not an optical illusion.

Number 2 is a subtle point about how rapidly moving object would appear if photographed (by a really high-speed camera) or viewed as they sped by. Oddly, it turns out that under many conditions you will not see the Lorentz contraction; instead you see the object rotated. This is an optical illusion, referred to as the Penrose-Terrell effect (after the two folks who independently figured it out in 1959). (This has nothing to do with rotation in spacetime.) Most popular books don't bring it up. But apparently there are exceptions!

Brian Greene was obviously talking about effect #1. If he used the word "appear", that is unfortunate. I forgive him! Calder, at least in that quoted passage, was obviously talking about the much less important effect #2.

Quote by Doc Al 					 				 				I don't have Calder's book, but if he said that length contraction is only a product of the angle the ship is seen from that would be laughably wrong.  In that quoted passage, it seems clear that Calder is talking about the visual appearance of moving objects, not their actual--and quite real--relativistic contraction.  If he's sophisticated enough to be aware of Penrose-Terrell rotation, it would be pretty amazing if he "forgot" to mention plain old--and quite real--length contraction.  As JesseM said, length contraction is not a trick of perception.  If Calder is stating that, he's wrong.  (But I don't deduce that from that quote.)  Is that the only mention of length contraction that he makes?

Unfortunately that is the only mention of length contraction in Calder's book. (I still have a couple chapters left but at a glance it doesn't look promising.) I don't know why he would leave the subject out but it appears he did. I'm even thinking he's just plain wrong, primarily due to his use of the word "only" in the last sentance from the quote.

It was still a really good book for laymen and I enjoyed it much. Picked it up for a buck at a second hand store in Brooklyn. It may be out of print but it's a fun read if you can find it. No math, just cool stuff to think about.

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Quote by denni89627 					 				 				Unfortunately that is the only mention of length contraction in Calder's book. (I still have a couple chapters left but at a glance it doesn't look promising.) I don't know why he would leave the subject out but it appears he did. I'm even thinking he's just plain wrong, primarily due to his use of the word "only" in the last sentance from the quote.
If that's the only mention of length contraction, then he's done a grave disservice to his readers. But, strictly speaking, I have no problem with his statement:
"Many accounts of relativity say, quite incorrectly, that a passing spaceship appears unnaturally squashed or contracted along its length. It DOES appear foreshortened but only in accordance with the entirely natural perspective of an object seen from an angle."
Assuming that he meant the word "appears" in the same sense that I discussed above. (He must mean that or why in the world would he have mentioned the apparent rotation of the object!) But if he doesn't contrast this statement of appearances, with a clear discussion of real relativistic length contraction--he should be shot!

It was still a really good book for laymen and I enjoyed it much. Picked it up for a buck at a second hand store in Brooklyn. It may be out of print but it's a fun read if you can find it. No math, just cool stuff to think about.
It's still in print. (It was reissued in 2005--in celebration of 100 years of relativity.) You got me curious--I just reserved it from the library. It will take a week to get to me, but I'll give it a quick skim when I get it.

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Quote by Doc Al 					 				 				If that's the only mention of length contraction, then he's done a grave disservice to his readers.  But, strictly speaking, I have no problem with his statement:"Many accounts of relativity say, quite incorrectly, that a passing spaceship appears unnaturally squashed or contracted along its length. It DOES appear foreshortened but only in accordance with the entirely natural perspective of an object seen from an angle."Assuming that he meant the word "appears" in the same sense that I discussed above.  (He must mean that or why in the world would he have mentioned the apparent rotation of the object!)  But if he doesn't contrast this statement of appearances, with a clear discussion of real relativistic length contraction--he should be shot!
I agree that the use of "appears" makes the statement slightly more justifiable, but I'd still say the statment "but only in accordance with with the entirely natural perspective of an object seen from an angle" is false. Correct me if I'm wrong, but an object flying by you at a very high proportion of c would appear both weirdly distorted thanks to the Penrose-Terrell effect, but also squashed significantly in its direction of motion, and at least some of the visual squashing would be due to genuine length contraction in your frame. Another way of saying this is that if you were looking at the light signals from an object moving at a high fraction of c in a purely Newtonian universe (assume you're in the rest frame of the ether so that all light signals still travel at c in your frame), you'd probably still see some distortions similar to the Penrose-Terrell effect, but you wouldn't see the same degree of visual squashing that you would in a relativistic universe.

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Quote by JesseM 					 				 				Correct me if I'm wrong, but an object flying by you at a very high proportion of c would appear both weirdly distorted thanks to the Penrose-Terrell effect, but also squashed significantly in its direction of motion, and at least some of the visual squashing would be due to genuine length contraction in your frame.
I admit that I'm a bit rusty on the details, but I think the answer is no. Terrell's 1959 paper on this was even titled "Invisibility of the Lorentz Contraction".

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Quote by Doc Al

Quote by denni89627 					 				 				It was still a really good book for laymen and I enjoyed it much. Picked it up for a buck at a second hand store in Brooklyn. It may be out of print but it's a fun read if you can find it. No math, just cool stuff to think about.
It's still in print. (It was reissued in 2005--in celebration of 100 years of relativity.) You got me curious--I just reserved it from the library. It will take a week to get to me, but I'll give it a quick skim when I get it.
Concerning Einstein's Universe by Nigel Calder...
the PBS video with Peter Ustinov (which my dad suggested I should watch when it was first shown on PBS) plus the book (which, by chance, my uncle gave to me) gave me my first glimpse of relativity... As a video and pop-book, it inspired me to seek out successively more advanced books to learn more about relativity... eventually steering the course of my education.

The video is now available on DVD http://store.corinthfilms.com/produc...productID=2467
and here is the book http://www.amazon.com/Einsteins-Univ.../dp/0517385708.
(Don't buy up all of the DVDs... I haven't ordered mine yet. )

Quote by Doc Al 					 				 				It's still in print.  (It was reissued in 2005--in celebration of 100 years of relativity.)  You got me curious--I just reserved it from the library.  It will take a week to get to me, but I'll give it a quick skim when I get it.
Good, I'm sure you'll enjoy the book regardless. In my edition it's chapter 14 : The Universal Correction, where all this is discussed.

Quote by JesseM 					 				 				I agree that the use of "appears" makes the statement slightly more justifiable, but I'd still say the statment "but only in accordance with with the entirely natural perspective of an object seen from an angle" is false.
This is what I have a problem with too. To me it's as if he's dismissing length contraction. Maybe this guy is a friggin genius and wants the reader to figure out that truth in the universe is relative too. From an abberation reference frame the statement is true, but from a relativistic one it is false. Checkmate!

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Quote by Doc Al 					 				 				I admit that I'm a bit rusty on the details, but I think the answer is no.  Terrell's 1959 paper on this was even titled "Invisibility of the Lorentz Contraction".
Interesting, I hadn't known that, thanks. Googling that paper title, I found the abstract here:

It is shown that, if the apparent directions of objects are plotted as points on a sphere surrounding the observer, the Lorentz transformation corresponds to a conformal transformation on the surface of this sphere. Thus, for sufficiently small subtended solid angle, an object will appear—optically—the same shape to all observers. A sphere will photograph with precisely the same circular outline whether stationary or in motion with respect to the camera. An object of less symmetry than a sphere, such as a meter stick, will appear, when in rapid motion with respect to an observer, to have undergone rotation, not contraction. The extent of this rotation is given by the aberration angle ($$\theta$$-$$\theta'$$), in which $$\theta$$ is the angle at which the object is seen by the observer and $$\theta'$$ is the angle at which the object would be seen by another observer at the same point stationary with respect to the object. Observers photographing the meter stick simultaneously from the same position will obtain precisely the same picture, except for a change in scale given by the Doppler shift ratio, irrespective of their velocity relative to the meter stick. Even if methods of measuring distance, such as stereoscopic photography, are used, the Lorentz contraction will not be visible, although correction for the finite velocity of light will reveal it to be present.
I assume it's still true, though, that a moving object's shape in a relativistic universe will look different than it would in the Newtonian scenario I imagined above? Perhaps in a Newtonian universe, the effect of light from different parts of the object taking different times to reach you would be to stretch the image in the direction of motion, and the Lorentz contraction is in some sense cancelling that out?

Mentor   			 				  				 				 				Blog Entries: 1  I'll have to review the paper (I'm sure I have in my pile at home) but I think you are on the right track.  The light travel time stretches out the image just enough to "cancel" the Lorentz contraction.

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