# Length contraction vs Space time

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In summary, the twin paradox is an example of differential ageing, a different phenomenon than length contraction and time dilation.

Does length contraction means the contraction of space time?

No. Length contraction can be seen as a result of viewing a 4d object at a different angle. It's closely analogous to the fact that you can slice a sausage perpendicular to its length and get a circular face, or at an angle and get an elliptical face. The sausage hasn't changed (and certainly spacetime hasn't), but the part of it you are looking at has.

Cobalt101
Does length contraction means the contraction of space time?
No. It cannot be that, because we all occupy the same spacetime yet we don't all observe the same length contraction.

Length contraction is a natural result of the relativity of simultaneity. The length of an object is the distance between where its ends are at the same time, so when things that are at the same time for one observer are not at the same time for another observer, they will find different lengths.

vanhees71
Nugatory said:
No. It cannot be that, because we all occupy the same spacetime yet we don't all observe the same length contraction.

Length contraction is a natural result of the relativity of simultaneity. The length of an object is the distance between where its ends are at the same time, so when things that are at the same time for one observer are not at the same time for another observer, they will find different lengths.
Looking at the twin paradox, the effect of the twin in acceleration is there that the twin on the spaceship does experience a time dilation. Right, I'll take some time to review this

Looking at the twin paradox, the effect of the twin in acceleration is there that the twin on the spaceship does experience a time dilation. Right, I'll take some time to review this
No, NOBODY ever "experiences" time dilation, It is something you see in objects that are moving relative to you but they see YOU as time dilated at the same time you see them as time dilated.

You, right now as you read this, are MASSIVELY time dilated according to a particle in the CERN accelerator. Has your watch slowed down?

Looking at the twin paradox, the effect of the twin in acceleration is there that the twin on the spaceship does experience a time dilation. Right, I'll take some time to review this

The twin paradox is an example of differential ageing, a different phenomenon than length contraction and time dilation. One way of seeing that it is different from time dilation is to consider teh time dilation that is present in the twin paradix: at every point in the journey, the traveling twin is at rest relative to himself while the stay-at-home twin is moving; therefore the stay-at-home clock is the time-dilated one as far as the traveller is concerned. However, traveller is still able to correctly calculate that he will age less than stay-at-home - even though stay-at-home's clock is dilated throughout the journey.

Nugatory said:
The twin paradox is an example of differential ageing, a different phenomenon than length contraction and time dilation. One way of seeing that it is different from time dilation is to consider teh time dilation that is present in the twin paradix: at every point in the journey, the traveling twin is at rest relative to himself while the stay-at-home twin is moving; therefore the stay-at-home clock is the time-dilated one as far as the traveller is concerned. However, traveller is still able to correctly calculate that he will age less than stay-at-home - even though stay-at-home's clock is dilated throughout the journey.
Hmm, the result of the twin paradox is that the person moving away from Earth experience a slower time when traveling close to the speed of light. Therefore when the twin on Earth ages 10 years, the twin traveling on the spaceship only ages 6 years by traveling toward a fraction of the speed of light. The same thing happens with gravitation time dilation as the person closer to Earth experiences a slower time passing by then the one away from Earth by a few nanosecond.

Hmm, the result of the twin paradox is that the person moving away from Earth experience a slower time when traveling close to the speed of light. Therefore when the twin on Earth ages 10 years, the twin traveling on the spaceship only ages 6 years by traveling toward a fraction of the speed of light. The same thing happens with gravitation time dilation as the person closer to Earth experiences a slower time passing by then the one away from Earth by a few nanosecond.
No, the person on the spaceship does NOT experience slower time. He/she experiences time passing at one second per second just as does the stay-at-home. What happens is that the person on the spaceship takes a different path through space-time and therefore experiences fewer ticks of his one-second-per-second clock than does the stay-at-home.

EDIT: and by the way, this is one of the most confusing things when you first start to look into special relativity so you're in good company not getting it right away.

phinds said:
No, the person on the spaceship does NOT experience slower time. He/she experiences time passing at one second per second just as does the stay-at-home. What happens is that the person on the spaceship takes a different path through space-time and therefore experiences fewer ticks of his one-second-per-second clock than does the stay-at-home.

EDIT: and by the way, this is one of the most confusing things when you first start to look into special relativity so you're in good company not getting it right away.
Well yes neither of the twins would experience a slower time, it feels shorter for one 6 years, and longer for the other one 10 years. I am thinking that speed causes space time to contract through length contraction matches the fact that the person on Earth with a more compact space time has a time dilation. If gravity increases with a more compact space time the result would be more prominent

As we have said several times, nothing happens to spacetime in the scenarios we are discussing.

Both length contraction and time dilation are effects that an observer observes happening to objects that are in motion relative to them. This is a symmetric effect - two observers in relative motion measure the same thing happening to the other. So it cannot be due to "spacetime contracting". Both observers would have to claim that spacetime was contracted for the other.

The twin paradox is showcasing a different, but related, phenomenon. There is still no spacetime contraction involved. It turns out that the elapsed time showing on your wristwatch is a measure of "distance" traveled through spacetime (it's actually called the "interval"). In other words, your wristwatch measures "distance" through spacetime in a way analogous to the way the odometer in a car measures distance through space. The different ages of the twins comes from the fact that they took different routes through spacetime. This does not involve any kind of change to spacetime. It's essentially no different from the fact that the straight line distance between two points is different from the distance between them traveling via a third - one side of a triangle is not the same length as the other two put together.

Well what Wikipedia says on time dilation is that "The laws of nature are such that time itself (i.e. spacetime) will bend due to differences in either gravity or velocity – each of which affects time in different ways." I'm still skeptical about how velocity bend time, I'm not sure if it's mass related

That kind of thing is why you should be wary of Wikipedia as a source. Velocity does nothing to spacetime or mass (old textbooks will disagree about mass, but so-called relativistic mass has been a deprecated term since the 1970s, pop sci presentations notwithstanding).

Assuming you are after a non-mathematical look at relativity, Ben Crowell's book Relativity for Poets is a good source. It's freely available from www.lightandmatter.com

Hmm, the result of the twin paradox is that the person moving away from Earth experience a slower time when traveling close to the speed of light.

This sentence makes it seem as though one person can travel closer to the speed of light than another. Instead there is relative motion between two people. Either one could claim that the other is the one moving closer to the speed of light, or just the opposite. Either one could claim that he is the one moving closer to the speed of light. It's a meaningless assertion either way because as you chase after a light beam you find you make no more progress in catching it than does the other person.

When the traveling twin moves away from the staying twin, the staying twin moves away from the traveling twin. The situation is symmetrical and each will observe the other's clock as running slow. The same is true when their relative motion causes them to get closer to each other. The only time the situation is not symmetrical is when the traveling twin changes direction, and it is this part that's responsible for the difference in proper times experienced by the twins.

It is one thing to say that each twin's proper time differs from the other's dilated time. This always involves elapses of time between events that are spatially separated in at least one their rest frames. It is quite another to say that their proper times differ from each other. This always involves elapses of time between events that are not spatially separated in either rest frame. The former has nothing to do with the difference in their ages whereas the latter has everything to do with it.

Well what Wikipedia says on time dilation is that "The laws of nature are such that time itself (i.e. spacetime) will bend due to differences in either gravity or velocity – each of which affects time in different ways." I'm still skeptical about how velocity bend time, I'm not sure if it's mass related

In terms of velocity and gravity:

If two observers are traveling with respect to each other, what does spacetime care about that? Spacetime remains flat and unchanged, but the two observers have different perspectives on it.

If a large mass is occuping space, on the other hand, spacetime itself curves and this curvature can be detected by any observer.

Well what Wikipedia says on time dilation is that "The laws of nature are such that time itself (i.e. spacetime) will bend due to differences in either gravity or velocity
The sentence is just plain flat-out wrong.

This might be a good time to remind everybody that wikipedia is not an acceptable source at Physics Forums, and stuff like this is the reason why.

Nugatory said:
Length contraction is a natural result of the relativity of simultaneity. The length of an object is the distance between where its ends are at the same time, so when things that are at the same time for one observer are not at the same time for another observer, they will find different lengths.
I thought it was both RoS and time dilation? What do you call it when you travel to Alpha Centuari at 90% of the speed of light and measure the distance traveled to be 2 LY (if I did that math right...).

russ_watters said:
I thought it was both RoS and time dilation?
It's hard to separate the two - but I can say that the distance between Earth and Alpha Centauri is pretty much by definition the distance between where the Earth is right now and where Alpha Centauri is right now. That definition works whether I'm at rest relative to them or not, and yields the appropriately contracted length if I am not.

Travel time only comes into it when we consider how long an object (not necessarily at rest relative to me) would take to traverse that distance.

russ_watters said:
I thought it was both RoS and time dilation? What do you call it when you travel to Alpha Centuari at 90% of the speed of light and measure the distance traveled to be 2 LY (if I did that math right...).
My usual example is how do you measure the length of a beetle? You just stand it on a ruler and read off the position of its head and the position of its tail. If the beetle is walking, though, that procedure will not get you its length if you don't make the measurements at the same time. In that example, failing to measure simultaneously could just be sloppy experimentalism. But the relativity of simultaneity means that there is genuine, unresolvable, disagreement over what constitutes "at the same time" in different frames (and the beetle is moving in at least one of them), and that's where length contraction comes from. Observers at rest in the two frames use the same procedure to measure length, but because they disagree about simultaneity they get different lengths.

Time dilation isn't directly relevant to this, although you can't build a symmetric picture of the world without invoking ot as well - you end up with an absolute rest frame.

Ibix said:
My usual example is how do you measure the length of a beetle? You just stand it on a ruler and read off the position of its head and the position of its tail. If the beetle is walking, though, that procedure will not get you its length if you don't make the measurements at the same time. In that example, failing to measure simultaneously could just be sloppy experimentalism. But the relativity of simultaneity means that there is genuine, unresolvable, disagreement over what constitutes "at the same time" in different frames (and the beetle is moving in at least one of them), and that's where length contraction comes from. Observers at rest in the two frames use the same procedure to measure length, but because they disagree about simultaneity they get different lengths.

Time dilation isn't directly relevant to this, although you can't build a symmetric picture of the world without invoking ot as well - you end up with an absolute rest frame.
Isn't "an absolute rest frame" by definition the measurement of "proper length" with no distortion of observation via movement relative to the object (or distance) measured? So then the distance to Alpha Centauri or the length of a beetle is not changed by "how you look at" either in relative motion. How is the above wrong?

Michael Mooney said:
Isn't "an absolute rest frame" by definition the measurement of "proper length" with no distortion of observation via movement relative to the object (or distance) measured? So then the distance to Alpha Centauri or the length of a beetle is not changed by "how you look at" either in relative motion. How is the above wrong?
"absolute rest frame" is an ambiguous term. Do you simply mean a frame of reference in which is an object is at rest? If so, then leave out the "absolute" since it adds nothing but confusion. If on the other hand, you mean an absolute frame of reference against which anything's motion can be measured, then that is an incorrect concept as there is no such thing.

Michael Mooney said:
Isn't "an absolute rest frame" by definition the measurement of "proper length" with no distortion of observation via movement relative to the object (or distance) measured? So then the distance to Alpha Centauri or the length of a beetle is not changed by "how you look at" either in relative motion. How is the above wrong?

That's not an "absolute" rest frame, it's the rest frame of the beetle and the ruler, which is to say a frame in which the beetle and the ruler are not moving. That's a very convenient frame to use if the beetle and the ruler are sitting on a lab bench and the lab bench is bolted to the same concrete floor upon which I am standing... But I would find it very difficult to convince an observer watching with a telescope from Mars that the beetle, ruler, lab bench, and concrete floor were not moving - they're attached to the earth, which is going around the sun at a very different speed than Mars.

For that matter, if I had a good enough telescope and he had a beetle and a ruler, I would find that his beetle and ruler were contracted relative to mine. Who is to say why my perspective (my beetle is uncontracted, his beetle is contracted) has any more natural significance than his perspective (my beetle is contracted, his beetle is not)? We can imagine consulting an independent authority, such as an alien from the Andromeda galaxy (moving at about 300 km/sec relative to both of us) who is right, but the only answer we'd get is that we're both wrong.

phinds said:
"absolute rest frame" is an ambiguous term. Do you simply mean a frame of reference in which is an object is at rest? If so, then leave out the "absolute" since it adds nothing but confusion. If on the other hand, you mean an absolute frame of reference against which anything's motion can be measured, then that is an incorrect concept as there is no such thing.
The phrase, "absolute rest frame" quotes Ibix above. Of course all motion is "relative to what?," so there is no absolute frame of reference for velocity. But "proper length" always refers to length as measured from at rest with the object or distance in question. That leaves the question, "Is length variable with how you measure it or do "things" and distances have objective lengths independent of "how you look at them." (Objective vs subjective, the latter meaning frame dependent.) Measurement does not change lengths or distances. They exist objectively prior to varieties of frames of reference from which they are measured. Something to consider besides repeating the rules of orthodox special relativity/ subjectivity.

Michael Mooney said:
The phrase, "absolute rest frame" quotes Ibix above. Of course all motion is "relative to what?," so there is no absolute frame of reference for velocity. But "proper length" always refers to length as measured from at rest with the object or distance in question. That leaves the question, "Is length variable with how you measure it or do "things" and distances have objective lengths independent of "how you look at them." (Objective vs subjective, the latter meaning frame dependent.) Measurement does not change lengths or distances. They exist objectively prior to varieties of frames of reference from which they are measured. Something to consider besides repeating the rules of orthodox special relativity/ subjectivity.
PROPER length has an absolute value but measured/calculated length is frame dependent so yes, length is variable depending on how you measure it.

Michael Mooney said:
The phrase, "absolute rest frame" quotes Ibix above
and you misunderstand, apparently, the way in which he used it, which was to say somewhat indirectly what I said specifically in post #20 which is that there IS no such thing as an absolute frame of reference.

@Ibix, jump in if I have misrepresented what you meant.

Michael Mooney said:
Isn't "an absolute rest frame" by definition the measurement of "proper length" with no distortion of observation via movement relative to the object (or distance) measured? So then the distance to Alpha Centauri or the length of a beetle is not changed by "how you look at" either in relative motion. How is the above wrong?
You are correct that there is one frame in which the beetle is at rest, and all observers agree what that frame is and what length the beetle is in that frame. As Nugatory and phinds have said, though, that is only a special frame for that one beetle, not for beetles in general nor for the laws of physics.

If you start with Einstein's two postulates you derive the Lorentz transforms, which can be interpreted as length contraction, time dilation and the relativity of simultaneity. So insisting that one of these doesn't happen implies that at least one of the two postulates is wrong. My memory of a long ago argument is that denying time dilation forces you to abandon the principle of relativity. I didn't mean to kick off a long discussion - I was only meaning to note that my claim that you get length contraction from the relativity of simultaneity didn't mean to imply that you could forget about time dilation entirely.

phinds said:
@Ibix, jump in if I have misrepresented what you meant.
Sorry - I was sleeping on duty. You've interpreted me as I intended.

I just thought of something, anything traveling at the speed of light has a distance close to zero. So if I have a stick of 1cm moving close to the speed of light it gets close to zero, but if I also have a stick of 10000000000000000cm moving close to the speed of light it also gets close to zero. So at the speed of light you can't really tell how long the stick is but only when you slow it down

Depends how precise your measurements are. The longer stick is still sixteen orders of magnitude longer than the shorter one, as long as they move at the same speed with respect to you. Certainly, the faster they move with respect to you the more precise your measurements will have to be to separate the two sizes, but this is always possible in principle because no massive object can reach light speed.

phinds said:
PROPER length has an absolute value but measured/calculated length is frame dependent so yes, length is variable depending on how you measure it.
If that were true then the distance to Alpha Centauri (or to the Sun) and the length of Earth's diameter would vary with how you measure it. However, in fact astronomy and Earth science have determined those distances and that length very precisely. The actual distance between stars (astronomically speaking) does not change with all possible varieties of measurement frames, nor does the nearly spherical shape of earth.

Michael Mooney said:
If that were true then the distance to Alpha Centauri (or to the Sun) and the length of Earth's diameter would vary with how you measure it. However, in fact astronomy and Earth science have determined those distances and that length very precisely. The actual distance between stars (astronomically speaking) does not change with all possible varieties of measurement frames, nor does the nearly spherical shape of earth.
All those things are different when measured in different frames of reference. Proper length is invariant, but it isn't always what it is "natural" to measure.

We seldom need to worry about this kind of thing for distances to nearby stars, since stellar velocities around here are fairly low relative to us. Distances will be measured in something like the sun centered frame, but any sensible frame will yield very nearly the same answer.

Michael Mooney said:
If that were true then the distance to Alpha Centauri (or to the Sun) and the length of Earth's diameter would vary with how you measure it. However, in fact astronomy and Earth science have determined those distances and that length very precisely. The actual distance between stars (astronomically speaking) does not change with all possible varieties of measurement frames, nor does the nearly spherical shape of earth.

Now you are misunderstanding what proper length is. It is the length that would be measured in a frame in which both ends of the object are at rest, but it is no more "actual" or "real" than the length measured in any other frame. It's tempting to to dismiss the contracted lengths as less real or even some sort of illusion - but before you succumb to that temptation you should work carefully through Bell's spaceship paradox and Purcell's derivation of magnetic forces.

Doc Al
My 2 cents would add that there are levels of reality (measurement) which are "good enough" for what we are measuring at the moment. I would certainly agree that there is really no such thing as precise measurement. But there is measurement that is 'good enough' for our purposes at the moment we need them. Like I wouldn't need to know anything about quantum distances if I was sending a payload to the ISS. There are measurements available that are good enough. More than good enough, actually, because out standards are usually double or triple what we really need for accuracy or safety. But I wouldn't use my metre-stick (just doesn't sound as good as yard-stick) to measure the wavelength of a red light, or whatever. That's why it's called 'relativity' I guess.
It's also got to do a bit with attitude. For example some of us are just more subjective than we are objective (I find engineers tend to be more objective, but that's me). Then, of course, we start to approach uncomfortable areas like, dare I say it, meta-physics.
Jump in anytime to correct me, folks. Have a good one.

ebos said:
My 2 cents would add that there are levels of reality (measurement) which are "good enough" for what we are measuring at the moment. I would certainly agree that there is really no such thing as precise measurement. But there is measurement that is 'good enough' for our purposes at the moment we need them. Like I wouldn't need to know anything about quantum distances if I was sending a payload to the ISS. There are measurements available that are good enough. More than good enough, actually, because out standards are usually double or triple what we really need for accuracy or safety. But I wouldn't use my metre-stick (just doesn't sound as good as yard-stick) to measure the wavelength of a red light, or whatever. That's why it's called 'relativity' I guess.
It's also got to do a bit with attitude. For example some of us are just more subjective than we are objective (I find engineers tend to be more objective, but that's me). Then, of course, we start to approach uncomfortable areas like, dare I say it, meta-physics.
Jump in anytime to correct me, folks. Have a good one.
I think you are misunderstanding the entire topic of this thread, which has nothing to do with the accuracy of measurements but rather the differences in what is seen from different frames of reference.

That is, your post is perfectly reasonable, it's just completely irrelevant to the topic at hand.

vanhees71
phinds said:
I think you are misunderstanding the entire topic of this thread, which has nothing to do with the accuracy of measurements but rather the differences in what is seen from different frames of reference.

That is, your post is perfectly reasonable, it's just completely irrelevant to the topic at hand.
Yeah, well I thought it looked pretty easy, peasy. Must be that new BP med.

My head always tries to go to the practical end, because that's how I understand stuff, and I think I was trying to give an example to the OP that they might understand too. However, I may have got off track.
Like now: Those damn meds! Hate getting old.
Anyways, thanks for being so 'nice'. Hope that doesn't that make you cringe? Because I do like the 'new' phinds. Don't ever feel you need to modify your replies to me. OK, let's quickly get back to physics and/or football.