# Trying to understand length contraction

1. Feb 16, 2016

### Jmundi

I have a very basic question about the relativity of simultaneity (damn that's a mouth full).

So basically rule no. 1 would be that it's all relative right? In the example of the ladder thought experiment it's shown that because of "Lorentz length contraction" a ladder which is bigger than a garage can from one viewpoint fit into said garage and from another viewpoint not fit. Am i understanding it so far?

And all of this is because there are two separate references of observation, the aforementioned frames in this thread. In the first reference frame the observer is together with the ladder moving through the garage and the other reference is a dude looking at them from the other opposite house. Right?

OK first of all i'm a bit confused about the "Lorentz length contraction". Is this an actual literal contraction or is it just an illusionary one? If it's a literal one, how does that happen on purely physical basis? What does speed have to do with how long something is? I would think that the length of an object has an absolute value, no matter how it is perceived from different observers. If it's not a literal contraction and it just depends on the observer then the whole argument becomes useless so i'm just going to assume that physics claims an actual contraction.

So how does that happen physically? And why is the contraction experienced differently by different observers?

Last edited by a moderator: Feb 16, 2016
2. Feb 16, 2016

### Staff: Mentor

What's the difference?

Before relativity was worked out, this is what everybody thought. But it turns out not to agree with experiment; experiment says that the length of an object depends on the speed of the object relative to whoever or whatever is measuring its length.

The best way I know of to understand length contraction is to view it as a spacetime analogue of viewing an object from a different angle in ordinary Euclidean space. The "size" of an object in your visual field can depend on the angle from which you view it. Changing your speed relative to an object is the spacetime analogue of changing the angle from which you view it; the object's length in your frame is the spacetime analogue of the object's size in your visual field in ordinary space.

Note that changing "viewing angle" in ordinary space has physical consequences--for example, if I have an object that is too wide in one dimension to fit through a doorway, I might still be able to fit it by changing the relative angle of the object and the doorway. The ladder/garage scenario is just the spacetime analogue of this: changing the speed of the ladder relative to the garage changes the relative "spacetime angle" and can allow the ladder to fit into the garage. (Note that, since this is spacetime, the length of time the garage doors are open is part of the definition of the "opening" that the ladder has to fit into--and this length of time also changes from frame to frame, so time dilation is also part of the effects of spacetime "angle".)

3. Feb 16, 2016

### peety

As I understand it the Lorentz contraction is not the solution of the paradox but its cause. The garage sees the long ladder contracted (by 'sees' I mean that the ladder really is contracted from the garage frame) and consequently it can fit. But the ladder (which thinks it is at rest) sees the already small garage contracted even further, so how could it fit? The fact that it would still fit seems paradoxical, but the solution is that because of the relativity of simultaneity the two ends of the ladder are within the garage at different times.
I think it is important to realise that relativity is not about appearances but about observations and calculations in the physical sense.

4. Feb 16, 2016

### Staff: Mentor

Yes, this is true. In the terms I used in my previous post, relativity of simultaneity is part of the effect of changing the "angle in spacetime": the two "doorways" that the ladder has to fit through can be offset in time as well as in space, depending on the "angle in spacetime" from which they are viewed.

The invariants are about observations and calculations in the physical sense, yes; either the ladder passes through the garage or it doesn't, independent of which frame you choose (which "angle in spacetime" you view it from).

But things like length contraction, time dilation, and relativity of simultaneity are not invariants--they depend on your choice of frame ("spacetime viewing angle"), so in a sense they are "about appearances", because changing your "viewing angle" in spacetime can change them without changing any physical invariants. From a purely logical standpoint, there is actually no need to even use these frame-dependent concepts at all; everything can be done purely in terms of four-dimensional geometric objects independent of any choice of frame. But the frame-dependent concepts happen to match up with things that are pre-relativistic intuition says ought to be absolute, not frame-dependent, so we find ourselves compelled to talk about them, even though it's not really logically necessary; if we could re-train our intuitions appropriately, we could discard all of the frame-dependent concepts and just talk about invariants.

5. Feb 16, 2016

### Jmundi

Thank you! I said i prefer simple words and examples and you gave me those.

So from what i understand, the 3 dimensional value of the ladder itself has not changed (its contraction in this sense is illusionary), but adding time dilation makes its size change depending on the observable angle?

And how are we supposed to re-train ourselves without asking those that are already re-trained? It's like asking a child to know the multiplication table without learning it because it's just basic addition and it's logical and he ought to just know it.

In my head, things (3 dimensional objects) have absolute values. Values that can be measured not only with "sight", but by actually touching them and seeing that they end where we observe them to end. All those experiments to me (the uneducated, but curious one) seem to only take into account the "observing" part without the actual "let's go and touch it and see whether it really is that size or it's just an illusion" part. That's why i'm asking. Adding a 4th dimension in the form of time and saying that that dimension affects the other 3 (and on top of that it's a different effect depending on the location of the observer from the object) is mind boggling. I don't have the years to go back to school and start learning physics just so i can understand this, but i would really like to, hence me asking :)

6. Feb 16, 2016

### Staff: Mentor

Where did I say you couldn't ask? Isn't that exactly what you're doing in this thread? The responses I'm giving you are the responses of someone whose intuition is already re-trained. That's what we're here for.

And if you replace "3 dimensional objects" with "4 dimensional objects", that statement is still true. Spacetime intervals work the same in SR as ordinary lengths work in your intuitive 3-dimensional geometry (except for the fact that timelike intervals have opposite signs to spacelike intervals--i.e., the geometry of spacetime is Minkowskian instead of Euclidean).

The "lengths" that are talked about in length contraction are actually measured lengths; but they're measured by observers in relative motion, and in SR, observers in relative motion will measure different lengths for the same object. But this is just spacetime geometry; it's no different, conceptually, from the fact that if I measure a cube along one of its sides, and you measure it along a diagonal, we will get different numbers. We are measuring the cube at different angles. Similarly, if you and I are in relative motion, we are measuring objects in spacetime at different angles, so we measure them to have different lengths; changing your speed relative to something is the spacetime equivalent of changing the angle at which you measure it. (And because time is involved, changing the angle in spacetime also changes the length of time we measure between two particular states of the object--which is just time dilation.)

Yes, but it works; it agrees with experiment. That's why we have to go through all this. If experiments had come out differently, we might have been able to stick with Newtonian physics and absolute space and time. But it didn't happen that way.

As far as the effect being different depending on location, again, this is no different, conceptually, from the fact that your measurements of an object, such as the angle it subtends in your visual field, can depend on how far away you are from it. It's just geometry.

7. Feb 16, 2016

### Jmundi

That simple explanation was enough, but thank you for the rest nonetheless. :)

Cheers.

8. Feb 16, 2016

### pixel

"I would think that the length of an object has an absolute value, no matter how it is perceived from different observers."

In the rest frame of the object, i.e. the frame that is moving along with the ladder, its length is always the same no matter the speed of that frame with respect to another frame. That's as close to an "absolute value of length" as you can get - observers moving at different relative speeds to the objects's rest frame will measure different lengths.

9. Feb 17, 2016

### Mister T

I don't understand the distinction. The "observing" part is the "let's go touch it and see whether it really is that size or it's just an illusion". The purpose of experimental science is to establish the validity of an explanation through observation. One of the conclusions reached from that process is length contraction. It's measurable through observations that indicate it's not an illusion.

The four-dimensional explanation is just that, a way of explaining the results of observations. There are other ways to do it. You don't need to spend years to begin to understand it and you don't have to go back to school to begin to understand. You do need the intellectual curiosity, though. There's no substitute for cracking a book.

10. Feb 17, 2016

### jartsa

Let's consider the length contraction of the range of an electric car. We measure the range in a frame where the road is moving fast.

1: Car drives transverse to the motion of the road. Batteries last the normal time multiplied by time dilation factor. Car gains distance to the start line painted on the road at normal rate divided by the time dilation factor. Range is unchanged, because batteries drain slowly, and the car gains distance to the start line painted on the road equally slowly.

2: Car drives parallel to the motion of the road. Batteries last the normal time multiplied by the time dilation factor. Car gains distance to the start line painted on the road at normal rate divided by the time dilation factor squared. Range is contracted, because batteries drain slowly and car gains distance to to start line painted on the road super slowly.

Why does this happen? Well, in order to avoid exceeding the speed of light, the car must not gain distance to the start line painted on the road at normal rate, particularly in case 2.

If I had any idea about the mechanisms going on inside a rope, I might be able to tell why a moving rope is contracted.

11. Feb 17, 2016

### Jmundi

There are a few senses that come into play when making an observation about something. Firstly you would see it. Then to make sure that what you see is what you get, you could also trace your fingers along the outlines of said object to make sure that the outlines ARE in fact what you see. For the sake of what i meant i will use only those two senses. What i asked was whether the observations everyone is talking about are only from the first sense, namely "seeing". Did the tool that did the observing only observe the visual distortion that the "ladder" did or did it use some other ways of measuring which could account for the actual "tracing along the outlines" of the object?

Take a pencil between your two fingers and start moving it rapidly to the left and right. Is the image you are observing the actual form and size of the pencil or is it just an illusion? Basically that's what i was asking.

12. Feb 17, 2016

### Staff: Mentor

We've been tossing the word "length" around rather freely without being clear on exactly what it is: If one end of an object is at point A and at the same time the other end of the object is at point B, then the length of the object is |B-A|, the distance between those two points.

We have many different ways of determining this distance, and they certainly do not all rely on visual observation. For example, in the pole-barn paradox, someone at rest relative to the barn might conclude that both ends of the pole are inside the barn at the same time - this is sufficient to conclude that the length of the pole is less than the length of the barn using a reference frame in which the barn is at rest. Someone at rest relative to the pole might find that the leading edge of the pole hits the far wall of the barn at the same time that the trailing edge of the pole is still outside the barn, and just as correctly conclude that length of the pole is greater than the length of the barn using reference frame in which the pole is at rest. These position measurements can be made by having observers with wristwatches ride along at the two ends of the pole (their job is to record the time when they pass the barn doors) and sit at the barn doors (their job is to record the time when the ends of the pole pass); this is essentially a way of tracing along the outlines of the pole to find where it starts and ends.

I have bolded that all-important phrase "at the same time" above. Events, such as the end of the pole being in a particular place at a particular time, that are simultaneous (that is, happen at the same time) using one reference frame are not necessarily simultaneous using another reference frame. Google for "relativity of simultaneity" - it underlies both time dilation and length contraction, and is essential for resolving most of the common/popular "paradoxes" of special relativity.

13. Feb 17, 2016

### alw34

No implied disagreement here: The 'fly in the ointment' in my personal view trying to understand relativity here is that one cannot bring different observers and rulers together in a stationary setting, a common point in space and time, and compare length measurements locally 'see' the different lengths, as Nugatory emphasizes is required.

But what verifies the theory for me, what helps me gain an insight, is that the flip side of the length contraction part of the theory is reciprocal time dilation: Clocks, thank heaven, DO record the actual differences in elapsed time due to relative motion when brought together at a common point in space and time.

14. Feb 17, 2016

### Mister T

To observe means to use any of your senses to draw a conclusion. Once could, for example, use only the sense of sight. But that doesn't mean that what you see is the same as what you observe. To draw a valid conclusion you would have to allow for things such as the time it takes for the light you see to travel from the object you're looking at. Only then can you draw a valid conclusion about properties, such as the length, of an object.