# Why isn't length contraction permanent even though time dilation is?

• Ganesh Ujwal
In summary, I think the main difference between time dilation and aging is that time dilation is only a characteristic of remote observations, while aging is a function of your world line through space-time. Proper length is not affected by acceleration, it is a measure of how long an object is in its rest frame as measured by light signals.

#### Ganesh Ujwal

Why isn't length contraction permanent even though time dilation is?
It's my understanding that when something is going near the speed of light in reference to an observer, time dilation occurs and time goes slower for that fast-moving object. However, when that object goes back to "rest", it has genuinely aged compared to the observer. It's not like time goes slow for a while, and then speeds back to "normal," so that the age of the observer once again matches the object. The time dilation is permanent. Why wouldn't the same thing happen with length contraction? Since the two are so related, you'd think if one is permanent, the other would be also. And from everything I've read so far, length contraction is not permanent. An object will be at rest touching an observer, go far away near light speed, return to touching the observer, and be the same length it was at the beginning. It shortens, and then grows long again, as if its shrinkage was an illusion the whole time. Did I just not read the right things or what? Were my facts gathered incorrectly?

Last edited:
Ganesh Ujwal said:
Why isn't length contraction permanent even though time dilation is?
Time dilation is not permanent. If you bring a moving clock to rest then it is no longer time dilated.

Age is a different thing than time dilation. Age involves an integration along a world line. If you integrated contracted lengths then those would also be permanent.

PeterDonis
Ganesh Ujwal said:
It's my understanding that when something is going near the speed of light in reference to an observer, time dilation occurs and time goes slower for that fast-moving object.

ONLY from a different frame of reference. No one actually "experiences" time dilation, it is a characteristic of remote observations. As Dale pointed out, AGING on the other hand is a function of your world line through space-time. You, right now as you read this, are MASSIVELY time dilated relative to an accelerated particle at CERN. Does knowing that make you feel any older or that things have slowed down for you?

The real lesson of the twin paradox is that different paths through spacetime can have different amounts of elapsed time, even though they start and end at the same point (a point in spacetime is an event, with a unique time and location), just like two different curves through space can have different lengths, even though they start and end at the point.

vanhees71
Ganesh Ujwal said:
Why isn't length contraction permanent even though time dilation is?
It's my understanding that when something is going near the speed of light in reference to an observer, time dilation occurs and time goes slower for that fast-moving object. However, when that object goes back to "rest", it has genuinely aged compared to the observer. It's not like time goes slow for a while, and then speeds back to "normal," so that the age of the observer once again matches the object. The time dilation is permanent. Why wouldn't the same thing happen with length contraction? Since the two are so related, you'd think if one is permanent, the other would be also. And from everything I've read so far, length contraction is not permanent. An object will be at rest touching an observer, go far away near light speed, return to touching the observer, and be the same length it was at the beginning. It shortens, and then grows long again, as if its shrinkage was an illusion the whole time. Did I just not read the right things or what? Were my facts gathered incorrectly?
As has been pointed out, there are two different things with regard to time, one is Time Dilation and the other is Aging. Time Dilation is not permanent whereas Aging is permanent.

The same is true for length. There are two different things with regard to length. One is Length Contraction and the other is Proper Length. In a similar way to time, Length Contraction is not permanent whereas Proper Length is permanent. You have to know the difference between these two concepts. Proper Length is a measure of how long an object is in its rest frame as measured by light signals, not by a ruler. Length Contraction is the ratio of the length of an object as measured in a particular way by light signals in a frame in which the object is moving divided by its Proper Length. That particular way requires a simultaneity convention.

Special Relativity has nothing to say about how the Proper Length of an object is affected by accelerating it. That depends on how it is accelerated and what it is made out of, among other factors. When people gloss over these factors and say that an object is Length Contracted when going from rest to a high speed, they assume that its Proper Length remains the same. This is the same assumption you are making when you said,

"An object will be at rest touching an observer, go far away near light speed, return to touching the observer, and be the same length it was at the beginning."

But that assumption is not warranted. It is possible for an object accelerated from the trailing edge, like a rocket, to experience a permanent compression so that its Proper Length is shorter after it reaches its final speed. Then when it turns around and is accelerated in the same way to get back, it experiences another permanent compression and finally when it turns around again to "decelerate" to a stop, it experiences a third permanent compression so that its measured length is shorter than before it took its trip.

Or, if the object was accelerated by its leading edge, it could experience a stretching during all three firings of the rocket and end up longer than before it took its trip.

So we can't tell by Special Relativity what will happen to the Proper Length of an object as it takes its round trip. But what we can tell is that after it has reached its final speed on the way out or on the way back, whatever its Proper Length is, the object will be Length Contracted according to the observer who remained at rest and it will not be Length Contracted after it gets back.

ghwellsjr said:
You have discovered a defect in PF's feature that finds "similar threads" as it linked to itself!
Yes indeed! Regretfully I was interrupted when replying..
I now deleted that post, but I can't find back the appropriate recent thread. Perhaps you also remember, maybe one month ago we had a similar thread about the difference between time and space in the Lorentz transformations.

ghwellsjr said:
You have discovered a defect in PF's feature to find similar threads that links to itself.
Oh oh, you commented that to a different post! This seems to be another bug...

harrylin said:
Yes indeed! Regretfully I was interrupted when replying..
I now deleted that post, but I can't find back the appropriate recent thread. Perhaps you also remember, maybe one month ago we had a similar thread about the difference between time and space in the Lorentz transformations.
After you deleted your post and before you made this one, I deleted my post as I thought it was no longer relevant but then when I saw this post but before I read it, I thought it was your original post so I re-entered mine but when I read your post, I again deleted my re-entered post.

Anyway, is the post that you were remembering this one:

DaleSpam said:
Time dilation is not permanent. If you bring a moving clock to rest then it is no longer time dilated.

Age is a different thing than time dilation. Age involves an integration along a world line.
Building a device to measure age is simple. Just get a ticker (which is the part that is subject to Time Dilation) and a counter to count the ticks and you're done. I've just described a clock.

DaleSpam said:
If you integrated contracted lengths then those would also be permanent.
I have no idea either mathematically or in a hardware realization what you mean here. A clock integrates Proper Time with respect to Coordinate Time. With respect to what do you integrate Contracted Lengths and how would you implement such a device in hardware and what would you call the final result?

There is no close analogy between length contraction and time dilation. Time dilation involves a clock, which has a one-dimensional world-line. Length contraction involves a ruler, which has a two-dimensional world-sheet. It is not true that time dilation is to time as length contraction is to distance.

phinds
ghwellsjr said:
Building a device to measure age is simple. Just get a ticker (which is the part that is subject to Time Dilation) and a counter to count the ticks and you're done. I've just described a clock.?
The thing you call a ticker is what defines a clock. It measures ##d\tau##. The counter does the integration to give age ##\tau=\int d\tau##.

ghwellsjr said:
I have no idea either mathematically or in a hardware realization what you mean here.
I was thinking of an odometer. Each turn of the odometer is analogous to a tick of the clock, and you can equip it with a counter to do the integration.

Of course, the analogy is inexact for the reason mentioned by bcrowell and a bunch of complications due to rotation etc. But the basic idea of ticks and integration is there.

John goes off on a rocket while Jill stays on earth. When John returns, he has aged less due the accumulation of relativistic time dilation.
What if John carries a ruler with him and holds it permanently in the direction of motion during his trip? If Jill was somehow watching with a telescope, his ruler would appear shorter. When he stops and returns, Jill would again see his ruler shorter.

Once John gets back to Earth and shows Jill his ruler, why isn't it now in reality shorter than Jill's ruler? If age accumulates, why doesn't length contraction?

John REALLY aged slower while he was travelling. His heart beat slower, his cell division slowed, etc.
But did John's ruler REALLY get shorter? (Krane in Modern Physics explicitly says no, it only "appears" so to the other observer)

luxor99 said:

John goes off on a rocket while Jill stays on earth. When John returns, he has aged less due the accumulation of relativistic time dilation.
No, he experiences ZERO time dilation. What has happened is that he has taken a different path through space-time.

John REALLY aged slower while he was travelling. His heart beat slower, his cell division slowed, etc.
Absolutely not. He did no such thing, he just took a different path through spacetime and so experienced a smaller number of seconds than the stay at home did.

m4r35n357
luxor99 said:
But did John's ruler REALLY get shorter?
I am not sure what you mean by "REALLY" here. Do you have some sort of experiment in mind that you would consider to be evidence of a ruler really getting shorter?

luxor99 said:
Once John gets back to Earth and shows Jill his ruler, why isn't it now in reality shorter than Jill's ruler? If age accumulates, why doesn't length contraction?

The differential aging that we see in the twin paradox is not time dilation. We can see this because time dilation is symmetrical (John's clock is slow according to Jill's clock, and Jill's is slow according to John's) whereas the differential aging is not.

Time dilation is the statement that one tick of the moving clock covers less time than one tick of the stationary clock, and this does indeed work like length contraction: The moving meter stick covers less distance then the stationary meter stick, and both effects disappear when the relative motion ends. (Be aware that there is some sloppiness in this "covers less" language - for more precision you'll want to go back and derive the time dilation and length contraction formulas starting from the relativity of simultaneity).

Differential aging is the result of John's path through spacetime being shorter than Jill's. A car driving on a shorter path through space travels a shorter distance and its odometer turns fewer times and accumulates fewer miles than that of a car driving on a longer path through space. Likewise, a human body moving on a shorter path through spacetime travels through less time and accumulates fewer heartbeats and gray hairs than one traveling on the longer path.

Thus, you don't want to be comparing differential aging with length contraction. The appropriate comparison would be if John used his length-contracted ruler to lay out two objects a given distance apart. That distance would be shorter according to Jill, and it would remain that way even after John matched speeds with Jill and his rulers and clocks both agreed with Jill's again.

luxor99 said:

John travels with speed v=3/5 c from planet A, where Jill lives, to planet B, where Jill's sister lives. The two planets are separated by a distance of 3.0 light years according to Jill and her sister. As he travels, he "sees" the women's rulers are length-contracted, while the women see his clock running slower due to time dilation.

When he reaches planet B, his spaceship's odometer will read 2.4 light years, so he concludes that their rulers really were shorter than his during the trip. Similarly, they see he has only aged 4 years while they have aged 5 years, so they conclude that his clock really did run slower than theirs. Nevertheless, if they were to compare rulers and clocks once they're again at rest relative to each other, they don't find any differences.

vela said:
...
if they were to compare rulers and clocks once they're again at rest relative to each other, they don't find any differences.
For the clocks, that's true only in the sense that they are both ticking at the same rate. They would not show the same elapsed time.

luxor99 said:
What if John carries a ruler with him and holds it permanently in the direction of motion during his trip? If Jill was somehow watching with a telescope, his ruler would appear shorter. When he stops and returns, Jill would again see his ruler shorter.

Likewise, Jill would observe John's clock running slow. During his return, Jill would again observe his clock running slow

Once John gets back to Earth and shows Jill his ruler, why isn't it now in reality shorter than Jill's ruler?

Once John gets back to Earth and shows Jill his clock, it's ticking at the same rate as hers.

If age accumulates, why doesn't length contraction?

Rulers don't accumulate measurements of distance traveled. But odometers do. The odometer that John carried with him will forever show that the distance he traveled is less than the distance measured by Jill. Just as the clock he carried with him will forever show that the time he spent traveling is less than the time measured by Jill.

John REALLY aged slower while he was travelling. His heart beat slower, his cell division slowed, etc.
But did John's ruler REALLY get shorter? (Krane in Modern Physics explicitly says no, it only "appears" so to the other observer)

Which part of that is Krane's? All of it or just the word "appears"? Time dilation and length contraction are not just matters of appearance. They are real.

phinds said:
For the clocks, that's true only in the sense that they are both ticking at the same rate. They would not show the same elapsed time.
Right. I should have been a bit clearer on what I meant there.

Mister T said:
Time dilation and length contraction are not just matters of appearance. They are real.
You have to be careful when saying that "time dilation is real" to be sure you specify that it is ONLY real to the observer. It is not anything experience by the traveler being observed and that distinction is the root of many misunderstandings of time dilation.

So, @luxor99, has any of this clarified things for you?

Even though Bcrowell's #10 establishes why length contraction is not conceptually comparable to either time dilation (not permanent) or differential aging (permanent), one can formalize Dalespam's odometer suggestion to arrive an accumulated "road traversed" quantity that has many similarities with differential aging. See the following thread, esp. posts #1 and #40:

## 1. Why does length contraction only occur when an object is moving at high speeds?

The concept of length contraction is based on the theory of relativity, which states that the laws of physics are the same for all observers, regardless of their relative motion. When an object is moving at high speeds, its relative motion causes the distance between its endpoints to appear shorter to an observer. However, at lower speeds, the effects of length contraction are negligible and cannot be observed.

## 2. How does time dilation relate to length contraction?

Time dilation and length contraction are two sides of the same coin in the theory of relativity. Time dilation refers to the slowing down of time for an object in motion, while length contraction refers to the shortening of an object's length in the direction of its motion. Both phenomena occur due to the relative motion of an object and are a result of the same underlying principle.

## 3. Can length contraction be observed in everyday life?

Length contraction can only be observed at extremely high speeds, close to the speed of light. In everyday life, the effects of length contraction are too small to be noticeable. For example, if a person were to travel at 99% of the speed of light, their length would only contract by about 14%. This level of speed is not attainable by any known means of transportation.

## 4. Why is time dilation permanent while length contraction is not?

Time dilation is a permanent effect because it is based on the fundamental concept that the speed of light is constant in all reference frames. This means that time will always appear to move slower for objects in motion. On the other hand, length contraction is not a permanent effect because it is based on the relative motion of an object. Once an object returns to a stationary state, its length will return to its original value.

## 5. Are there any real-life applications of length contraction?

While length contraction is not observable in everyday life, it has significant implications in modern physics, particularly in the fields of particle accelerators and space travel. In particle accelerators, particles are accelerated to extremely high speeds, which results in their length contracting. This allows scientists to study the behavior of particles at energies that would not be possible at slower speeds. In space travel, the concept of length contraction is essential for understanding the effects of relativity on spacecraft and their journeys through the universe.