Relativistic contraction happens which way?

[IAN STINE]

When I accelerate my object it shrinks lengthwise: 1.nose moves back closer to tail OR 2.tail moves forward closer to nose OR 3.both ends move closer to middle OR 4.none of the above ?

 

[mitchellmckain]

Both ends, the leading edge in the direction of motion and the trailing edge in the direction of motion, move closer to the point on the path of motion which is closest to your position. So if one edge is at the point closest to your position then it does not move at all and it is only the other edge which moves closer to it.

 

[IAN STINE]

A respected scientist once wisely advised us to make something as simple as possible but not more so. My original posted question went several simples too far. My goal is to contemplate on a theoretical basis the relation of an object's "gross" velocity and the velocity of its constituents as they move when the object's length changes relativistically due to acceleration of the whole object. Intimately related also is analysis of conservation of momentum under the same circumstance. I anticipate special excitement in the general field of interaction of a fast object's time dilation and the rate of progression of its shrinkage. During a half century of studying relativistic field physics I do not recall even one comment by a century of scientists explaining the specific manner of the shrinkage hence my poorly presented question. Obvious now should be my absolute disinterest in optical illusion length change caused by nonsimultaneous lines of sight or any relatively practical observation concern. My interest lies solely in theoretical contemplation of the real physical shrinkage necessary to justify MM. Surely work has been done along these lines already but I am ignorant of it.

 

[Janus]

The reason that you have never found anything on this subject is that it is a non-issue. "How" the object contracts depends on the arbitrary choice of what point of the object you choose as the reference point.

 

[DrGreg]

Your object doesn't really shrink in any physically measurable sense. From a "static" observer's point of view, his or her calculation of the length has shrunk.

The calculation is made from observations and must account for the fact that it takes time for light to travel from the object to the observer. Different observers perform the calculation using different assumptions and so they get different answers.

If, instead, your object remains "static" and the observer accelerates, the observer will still calculate that the length of the object has shrunk, even though nothing has happened to the object at all.


Here's an analogy: calculating the length of an object in relativity is a bit like slicing a loaf of bread and measuring a slice. If you slice the bread diagonally, you get bigger slices. But the loaf hasn't really got any bigger. To get a diagonal slice you can either keep the knife fixed and rotate the loaf, or keep the loaf fixed and rotate the knife. (But in the geometry of relativity, diagonal slices are smaller rather than bigger.)

 

[mitchellmckain]

Your object doesn't really shrink in any physically measurable sense. From a "static" observer's point of view, his or her calculation of the length has shrunk.

This is not true. The shrinking of the object is part of the squashing of space in the direction of motion which allows you to travel large distances in as short a time as you like even though you never exceed the relative speed of light.

The calculation is made from observations and must account for the fact that it takes time for light to travel from the object to the observer.

Absolutely incorrect. The phenomena you are talking about (which accounts for the time it takes light to reach the observer) is called the aberration of light. This is a completely different distortion of what you see, and the effect is to make things appear to be stretched out, rotated and far in front of you. See http://www.fourmilab.ch/cship/aberration.html or my simulator at http://www.relspace.astahost.com

Different observers perform the calculation using different assumptions and so they get different answers.
If, instead, your object remains "static" and the observer accelerates, the observer will still calculate that the length of the object has shrunk, even though nothing has happened to the object at all.

It is true that the shrinking of the object must be calculated because the aberration of light means that you see something completely different. But this calculation represents where things really are in relationship to you, rather than just what you see. It is the truth behind the illusion. But it is a relative truth because from the objects point of view (to an observer residing on the object) it is you who are squashed not it. This seems like a contradiction but it isn't because of the relativity of simultaneity. Both you and the (observer on the) object "see" (in an interpretive sense) different parts of each other at different times. If there are clocks on the object, which to the (observer on the) object are sychronized, then you "see"
(after you account for the time it takes light from the clocks to get to you) the clocks reading different times. In conclusion, the object is shorter because its rear end is from a time when it has already moved forward (a later time) relative to the front end which you see from an earlier time before it has moved.

For another example. Suppose you travel to a star 10 light years away at 99.5% of the speed of light. Then from your perspective it is Earth and your destination which is traveling in the opposite direction at 99.5% of the speed of light. The trailing edge of the Earth - destination combination (which are now only 1 light year apart) is your destination and the clocks at the destination show a much later time by about nine years than the clocks on earth. Your trip takes slightly more than a year since you only have 1 light year to travel, during which the time on the clocks at your destination advance to just over 10 years past the time you left earth. When you slow to a stop the distance between Earth and your destination stretches back to the 10 light year distance and clocks on Earth spin forward to match the clocks at your current location. So according to observers on Earth and at your destination, your trip took 10 years rather than only the 1 year which you experienced.

 

[DrGreg]

To mitchellmckain:

Your disagreement with me is a question of semantics over what I mean by "physically measurable". If you regard all coordinate distance and time values within the theories of Relativity as "physical measurements", then there is nothing wrong with anything you said.

I was trying to make a distinction between quantities that can be measured directly and unambiguously, such as proper length and proper time, and other quantities which might be regarded as derived variables within the mathematical model of Relativity, such as coordinate distance and coordinate time relative to an inertial frame. Such derived quantities are defined by convention and, for a moving object, can only be calculated from observations.

When I say an "observation" I mean what you actually see with your eyes (or detect with a radio), which has already undergone aberration; the "calculation" is to remove the aberration. However, the calculation can be performed only in the context of a theoretical model. To calculate coordinates of events in 4-dimensional Minkowski space you have to make an assumption about the synchronisation of clocks (which amounts to assuming that the one-way speed of light is constant). This is an excellent assumption to make - the basis for all Relativity theory. Under that assumption you can successfully predict the results of any meaningful and relevant experiment you may care to do (in the context of this thread, at least). Nevertheless, it is an assumption and not a fact. (If you believe it is a fact, see this thread: Einstein's Clock Synchronization Convention. It is possible - but painful - to make alternative assumptions and still get the right answer.)



To come back to the original post in this thread, the reason IAN STINE's object shrinks isn't because the object itself has undergone some physical change, it is because the convention for measuring distance differs between the object's rest frame and some external observer. (You can call that "squashing of space" if you like, although I prefer not to.)

 

[selfAdjoint]

To come back to the original post in this thread, the reason IAN STINE's object shrinks isn't because the object itself has undergone some physical change, it is because the convention for measuring distance differs between the object's rest frame and some external observer. (You can call that "squashing of space" if you like, although I prefer not to.)

This argument that Lorentz dilation is just a "convention for measurement" ignores that the muon's relativistically extended lifetime really does permit it to reach the surface and be detected from where it is produced in the upper atmosphere, where as its proper lifetime (which you somehow regard as more real) would have it decay before it had moved a few feet in the Earth frame. Lorentz dilation is real, it is physical and it is different for differently moving observers. You cannot apply your intuitions gained from the slow moving conditions of human life to physics at relativistic speeds.

 

[mitchellmckain]

To mitchellmckain:
This is an excellent assumption to make - the basis for all Relativity theory. Under that assumption you can successfully predict the results of any meaningful and relevant experiment you may care to do (in the context of this thread, at least). Nevertheless, it is an assumption and not a fact. (If you believe it is a fact, see this thread: Einstein's Clock Synchronization Convention. It is possible - but painful - to make alternative assumptions and still get the right answer.)

To come back to the original post in this thread, the reason IAN STINE's object shrinks isn't because the object itself has undergone some physical change, it is because the convention for measuring distance differs between the object's rest frame and some external observer. (You can call that "squashing of space" if you like, although I prefer not to.)

I think I get what you are saying. In fact I think you are approaching this from the standpoint of general relativity as compared to my very exclusively special relativity oriented explanation.

I have not really gone beyond the introductory level in General relativity as represented by Robert Wald's book, Schutz' first course and a superficial reading of Hawking & Ellis' book "The large scale structure of space time". As far as research goes, I have only had cause to apply some of the ideas in a theoretical mechanics project (Barbour Bertotti theories) and in my personal studies of optics near a black hole for my simulator (webpage mentioned earlier). Anyway I never felt prepared to take on an educators role in any serious explication of General relativity.

 

[DrGreg]

This argument that Lorentz dilation is just a "convention for measurement" ignores that the muon's relativistically extended lifetime really does permit it to reach the surface and be detected from where it is produced in the upper atmosphere, where as its proper lifetime (which you somehow regard as more real) would have it decay before it had moved a few feet in the Earth frame. Lorentz dilation is real, it is physical and it is different for differently moving observers.

I am perhaps guilty of being pedantic in my choice of language over what is "real" or "physical".

To argue my point: to measure the lifetime of a muon in the Earth's frame you require two clocks at the beginning and end of the muon's journey that have been synchronised (or you have to perform some calculation that is equivalent to doing so). The lifetime you measure depends on how you perform the synchronisation. Relativity theory decrees the correct way to perform such synchronisation and you get the result you described. My point is that it is possible -- though not a good idea in my view and most others' -- to synchronise the clocks a different way and get a different answer. The lifetime in the Earth frame is an internal feature of Relativity theory and not something that could be measured unambiguously by anyone who didn't believe that the speed of light was independent of direction.

My argument above applies when both the muon and the observer are inertial. If somehow the muon could be forced to change direction, so that it returns to its starting point in the Earth frame, the earth-frame time can be measured unambiguously as the observer's proper time, and you would get a "real" discrepancy between the observer's proper time and the muon's proper time. But this is more than simple Lorenz dilation, this is the standard twins "paradox".

You cannot apply your intuitions gained from the slow moving conditions of human life to physics at relativistic speeds.

I agree wholeheartedly.

 

[DrGreg]

I think I get what you are saying. In fact I think you are approaching this from the standpoint of general relativity as compared to my very exclusively special relativity oriented explanation.

Actually I wasn't thinking of GR -- my knowledge in that area isn't very deep either.

I was thinking of Lorenz ether theory. In my opinion this isn't a very good theory but, if properly formulated, it isn't actually wrong, in the sense that the results it predicts are identical to those of SR. I believe (correct me if I'm wrong, anybody) you can justify the theory using the mathematics of GR -- you have to use a non-orthogonal coordinate system with a non-diagonal metric tensor.

 

[Sojourner01]

The Lorenz contraction in a way is similar to universal spacetime expansion. The object isn't contracting as such, the space it occupies is.

 

[mitchellmckain]

Actually I wasn't thinking of GR -- my knowledge in that area isn't very deep either.

I was thinking of Lorenz ether theory. In my opinion this isn't a very good theory but, if properly formulated, it isn't actually wrong, in the sense that the results it predicts are identical to those of SR. I believe (correct me if I'm wrong, anybody) you can justify the theory using the mathematics of GR -- you have to use a non-orthogonal coordinate system with a non-diagonal metric tensor.

I don't know, but I would not be surprised. GR is such a broad theoretical framework that it can used describe practically anything. Which is why we have to rely on experimental results to tell us what is correct. This is the problem with the hypothetical EPR bridges sci fi writers use for stories to create ftl travel. Just because GR can describe them doesn't mean they exist or ever could. So they are just a fantasy.

 

[IAN STINE]

As is so frequent on this forum, responses provide a great amount of insight and intellectual provocation and this has been no exception, relatively speaking. I absolutely should have been more definitive; I was especially intending to distinguish between what I see as two poles of meaning when generally describing Relativity effects: the "ground state" whereby I leisurely walk over to a circumstance and lazily put my tape measure on things and obtain lengths which I and any bystanders would agree are the "real physical" information about sizes versus the "extreme state" wherein very rapid motion causes optical illusions because different lengths of lines of sight make photons originating from an object's real physical front and real physical rear reach my eye at substantially different times. Analysis of simple thought experiments which try to resolve observations made by both a "stationary" observer and a "moving" observer to a common denominator so that both calculate c as unvarying chronically force me to conclude that there must be BOTH a real physical time dilation AND a real physical length contraction, within the frame of reference that ELECTRODYNAMICS is a functional theory. Consequently I found my thoughts wandering to pondering the relative onset of the contraction.

 

[DrGreg]

... the "ground state" whereby I leisurely walk over to a circumstance and lazily put my tape measure on things and obtain lengths which I and any bystanders would agree are the "real physical" information about sizes versus the "extreme state" wherein very rapid motion causes optical illusions because different lengths of lines of sight make photons originating from an object's real physical front and real physical rear reach my eye at substantially different times.

The point is you can "leisurely walk over" only if you are traveling at the same speed as the object you are measuring. If the object is moving at high speed relative to you, or you are moving at high speed relative to object (which means the same), you cannot measure both ends of the object at the same time yourself -- you cannot be in two places at once -- so you need an assistant to measure the other end. Both of you need to have a way of synchronising your clocks so you can agree what is "at the same time".

This procedure gives the Lorentz contraction. It doesn't matter if you stay still and the object accelerates, or the object stays still and you accelerate, you still measure that the object is shorter. It isn't something that actually happens to the object.

Does that help?