# Check my understanding of Time Dilation and Length Contraction

• B
• guyvsdcsniper
In summary, the conversation discusses the concepts of Time Dilation and Length Contraction in the context of Special Relativity. The speakers clarify that these phenomena are not experienced by oneself, but rather measured in relation to another observer's frame of reference. It is also mentioned that the terms "proper time" and "proper length" refer to the time and length measured by clocks and rulers at rest with respect to the object being measured. The conversation concludes with a recommendation to look into Minkowski diagrams for a better understanding of these concepts.
guyvsdcsniper
TL;DR Summary
You either experience Time Dilation and Proper Length or Proper Time and Length Contraction. Is this correct?
I just started learning about Special Relativity and have come upon the topics of Time dilation and Length contraction. Its a bit abstract for me and I just want to cross ref my knowledge here and see if someone can tell me if I am understanding this correctly. I've attached an excerpt of a passage in my textbook just for reference.

So if I am at rest and a particle passes by my at the speed of light, I am witnessing the particle with time dilation. If I was the particle, I would be witnessing proper time.

In the second instance, If I am at rest and measure the creation and decay of the particle then I am measuring Proper Length. This is because I am at rest wrt to the particle. But if I am the particle, moving at the speed of light, everything passing by me appears shorter because of how fast I am going?

So you either experience Time Dilation and Proper Length or Proper Time and Length Contraction.

Thats what i got from reading. Maybe there is other combinations of these 4 properties but for right now, is this correct?

S

quittingthecult said:
So if I am at rest and a particle passes by my at the speed of light I am witnessing the particle with time dilation. If I was the particle, I would be witnessing proper time.
Time isn't defined for things traveling at the speed of light. Assuming you mean something traveling near the speed of light relative to you then yes, you will see its clocks ticking slowly and your own ticking normally.
quittingthecult said:
So you either experience Time Dilation and Proper Length or Proper Time and Length Contraction.
No. Nobody ever experiences time dilation or length contraction - it's always something that happens to somebody else. It's always something or somebody else's clocks ticking slowly, and their rulers that are length contracted.

Proper time and proper length and the times and lengths measured by clocks and rulers at rest with respect to whatever it is they are measuring. The word "proper" here is taken in the Latin sense of "its own" (it's the root word from which is derived "property" in English). The proper time I experience is the time my clocks measure; the proper time you experience is the time your clocks measure. The proper length of my arm is the length I measure with my own ruler, and the proper length of your arm is the length you measure with your ruler.

Now, if I am moving with respect to you and you measure the length of my arm then you will measure my arm to be shorter than I do (assuming I'm pointing my arm in my direction of travel, Superman style). If you measure the tick rate of my watch it will be slow compared to your clocks. And if I measure your arm length and your watch tick rate I will find the same thing - your arm is short and your watch ticks slowly.

I strongly recommend looking up Minkowski diagrams. They're very much the simplest way to understand how this all fits together. They're just displacement-time graphs, but you can also draw my frame's axes on them and begin to see why all this happens.

vanhees71, guyvsdcsniper, robphy and 2 others
quittingthecult said:
Summary:: You either experience Time Dilation and Proper Length or Proper Time and Length Contraction. Is this correct?
In SR, if you are in a non-accelerating inertial reference frame, then you are perfectly justified to say that you are stationary and experience nothing strange. If others are moving with respect to you, in a non-accelerating inertial reference frame, then they are equally justified to say that they are stationary and experience nothing strange. But you will observe both time dilation and length contraction in them and they will observe both time dilation and length contraction in you.

guyvsdcsniper and Ibix
Ibix said:
Time isn't defined for things traveling at the speed of light. Assuming you mean something traveling near the speed of light relative to you then yes, you will see its clocks ticking slowly and your own ticking normally.

No. Nobody ever experiences time dilation or length contraction - it's always something that happens to somebody else. It's always something or somebody else's clocks ticking slowly, and their rulers that are length contracted.

Proper time and proper length and the times and lengths measured by clocks and rulers at rest with respect to whatever it is they are measuring. The word "proper" here is taken in the Latin sense of "its own" (it's the root word from which is derived "property" in English). The proper time I experience is the time my clocks measure; the proper time you experience is the time your clocks measure. The proper length of my arm is the length I measure with my own ruler, and the proper length of your arm is the length you measure with your ruler.

Now, if I am moving with respect to you and you measure the length of my arm then you will measure my arm to be shorter than I do (assuming I'm pointing my arm in my direction of travel, Superman style). If you measure the tick rate of my watch it will be slow compared to your clocks. And if I measure your arm length and your watch tick rate I will find the same thing - your arm is short and your watch ticks slowly.

I strongly recommend looking up Minkowski diagrams. They're very much the simplest way to understand how this all fits together. They're just displacement-time graphs, but you can also draw my frame's axes on them and begin to see why all this happens.
I believe you are correct as the book does mention speeds near the speed of light. I should have been more precise with my wording.

So it all comes down to perspective? In a non- accelerating inertial frame, I would experience my own proper length and time and someone in there own frame would experience their own proper length and time?

Dilation and contraction is something you measure, not experience? And it acts upon things moving wrt to you?

Is that correct?

quittingthecult said:
In a non- accelerating inertial frame, I would experience my own proper length and time and someone in there own frame would experience their own proper length and time?
"Measure" would be a better verb than experience here.

quittingthecult said:
Dilation and contraction is something you measure, not experience? And it acts upon things moving wrt to you?
They are effects that apply to measurements performed in another inertial frame with the conventions of that inertial frame being used (in particular, the simultaneity of that frame). It would be more accurate to say that they affect measurements of objects moving (rectilinearly) relative to you.

vanhees71, guyvsdcsniper, robphy and 1 other person
Orodruin said:
"Measure" would be a better verb than experience here.They are effects that apply to measurements performed in another inertial frame with the conventions of that inertial frame being used (in particular, the simultaneity of that frame). It would be more accurate to say that they affect measurements of objects moving (rectilinearly) relative to you.
I meant to say measure in that first paragraph, thank you for catching that.

Ok its starting to make sense now. Still reading the chapter but everyone's explanation has helped tremendously. Thank you so much.

quittingthecult said:
I believe you are correct as the book does mention speeds near the speed of light. I should have been more precise with my wording.
Yeah - usually you can let a bit of imprecision slide, but not here. There are very important distinctions between things traveling at lightspeed and things traveling near lightspeed. Things traveling at lightspeed are massless, cannot travel at any other speed (so there's no transform into their rest frame because they don't have one), and can't have clocks and rulers nor truly "experience" anything.
quittingthecult said:
I would experience my own proper length and time
Yes. In fact, that is a tautology. Your own proper time is the time measured by your own clock - your own heartbeat, your own sense of the passage of time. You can't experience anything else.
quittingthecult said:
So it all comes down to perspective?
I think that depends what you mean by perspective. It turns out to be quite closely analogous to asking how wide a cylinder is, where we would get different answers if we measured at different angles to the cylinder axis. In spacetime, the long axis is the timelike extent of an object and the cross-section is what we call "the object now". Depending on the "angle" between the object's axis (which is the direction in spacetime it calls "time") and the axis you have chosen to call time, you get a different cross section. The different lengths of the different cross-sections are "length contraction", and the projection of clock ticks along a moving object's time direction onto yours becomes time dilation.

I don't know if that'll make sense. As I say, I strongly recommend learning to draw Minkowski diagrams. They were the thing that made relativity "click" into place for me, and then the stuff about angles and projections will make more sense.

vanhees71 and guyvsdcsniper
Ibix said:
I think that depends what you mean by perspective. It turns out to be quite closely analogous to asking how wide a cylinder sausage is
FTFY - it will forever be a sausage in my world

vanhees71, guyvsdcsniper, Nugatory and 1 other person
Ibix said:
I strongly recommend looking up Minkowski diagrams. They're very much the simplest way to understand how this all fits together. They're just displacement-time graphs, but you can also draw my frame's axes on them and begin to see why all this happens.

Orodruin said:
"Measure" would be a better verb than experience here.

And then connect the two with
• an "operational definition" of "measure", "see", etc ... (e.g. using light signals and radar measurements) and
• geometric constructions and its associated algebraic calculations with dot-products (and tensors).
That's when it really clicked for me.

Then the spacetime diagram becomes a geometric way of thinking
beyond being a catalog of events and a plot of values one gets from an algebraic calculation.(I much prefer "radar measurements" over "lattices of clocks and rods".
I think "radar" is more along the relativistic viewpoint.
The two are pretty much equivalent for inertial observers in special relativity.)

vanhees71 and guyvsdcsniper
quittingthecult said:

(Typos referring to the diagram are corrected)

The first sentence is misleading. (What book is this?)

Time-dilation and Length-contraction are different geometric constructions on a spacetime diagram, despite the visual similarity of the associated algebraic equations when viewed through blurry glasses.

What is more correct to say is that
an observer in one frame may use "time-dilation" as an explanation of what was observed,
whereas another would use "length-contraction" in their explanation.

It's akin to finding an unknown feature (like a triangle side or angle or coordinate of an event)
using one triangle in approach A, and
then using a different (but geometrically similar) triangle in approach B.

For instance, see my answer (discussing the muon problem) in
https://physics.stackexchange.com/q...-distance-traveled-and-the-times-it-takes-why

From that answer (for a simplified muon),
and not using standard textbook methods (so hopefully this isn't giving the expected "answer" away)

Time-dilation according to the lab involves timelike edge BP and timelike hypotenuse BD in Minkowski-right triangle BPD.
Time-dilation according to the muon involves timelike hypotenuse BX and timelike edge BD in Minkowski-right triangle BDX.
Length-contraction according to the muon involves spacelike edge PD and spacelike hypotenuse DX in Minkowski-right triangle DPX.
All three are Minkowski-similar right-triangles.

Details are in the link above...
for the simplified muon (using the diamonds)
and for the real muon (using hyperbolic trigonometry, where $v=\tanh\theta$ and $\gamma=\cosh\theta$ ).

Last edited:
Ibix
robphy said:
And then connect the two with
• an "operational definition" of "measure", "see", etc ... (e.g. using light signals and radar measurements) and
• geometric constructions and its associated algebraic calculations with dot-products (and tensors).
That's when it really clicked for me.

Then the spacetime diagram becomes a geometric way of thinking
beyond being a catalog of events and a plot of values one gets from an algebraic calculation.(I much prefer "radar measurements" over "lattices of clocks and rods".
I think "radar" is more along the relativistic viewpoint.
The two are pretty much equivalent for inertial observers in special relativity.)
It's also important to note that you never "see" length contraction. The reason is that what you see is determined by the light, origin from all parts of an object, reaching your eye simultaneously (in your own momentaneous rest frame):

https://en.wikipedia.org/wiki/Terrell_rotation

robphy, FactChecker and Ibix
robphy said:
(Typos referring to the diagram are corrected)

The first sentence is misleading. (What book is this?)

Time-dilation and Length-contraction are different geometric constructions on a spacetime diagram, despite the visual similarity of the associated algebraic equations when viewed through blurry glasses.

What is more correct to say is that
an observer in one frame may use "time-dilation" as an explanation of what was observed,
whereas another would use "length-contraction" in their explanation.

It's akin to finding an unknown feature (like a triangle side or angle or coordinate of an event)
using one triangle in approach A, and
then using a different (but geometrically similar) triangle in approach B.

For instance, see my answer (discussing the muon problem) in
https://physics.stackexchange.com/q...-distance-traveled-and-the-times-it-takes-why

From that answer (for a simplified muon),
and not using standard textbook methods (so hopefully this isn't giving the expected "answer" away)

View attachment 295530

Time-dilation according to the lab involves timelike edge BP and timelike hypotenuse BD in Minkowski-right triangle BPD.
Time-dilation according to the muon involves timelike hypotenuse BX and timelike edge BD in Minkowski-right triangle BDX.
Length-contraction according to the muon involves spacelike edge PD and spacelike hypotenuse DX in Minkowski-right triangle DPX.
All three are Minkowski-similar right-triangles.

Details are in the link above...
for the simplified muon (using the diamonds)
and for the real muon (using hyperbolic trigonometry, where $v=\tanh\theta$ and $\gamma=\cosh\theta$ ).

View attachment 295531
The book is kenneth krane, modern physics, 4e

## 1. What is time dilation?

Time dilation is a phenomenon in which time appears to pass slower for an object in motion compared to an object at rest. This is a consequence of Einstein's theory of relativity and is caused by the difference in velocity between the two objects.

## 2. How does time dilation affect the measurement of time?

Time dilation causes time to appear to pass slower for an object in motion compared to an object at rest. This means that the measurement of time will be different for the two objects, with the object in motion experiencing time at a slower rate.

## 3. What is length contraction?

Length contraction is a phenomenon in which an object in motion appears to be shorter in the direction of motion compared to the same object at rest. This is also a consequence of Einstein's theory of relativity and is caused by the difference in velocity between the two objects.

## 4. How does length contraction affect the measurement of length?

Length contraction causes an object in motion to appear shorter in the direction of motion compared to the same object at rest. This means that the measurement of length will be different for the two objects, with the object in motion appearing shorter.

## 5. What are some real-life examples of time dilation and length contraction?

Some real-life examples of time dilation and length contraction include the effects of high-speed travel on astronauts, the operation of particle accelerators, and the accuracy of GPS systems. These phenomena have been observed and measured in various experiments and are an important part of understanding the universe and its behavior.

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