Check my understanding of Time Dilation and Length Contraction

[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

 

[Ibix]

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.

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.

 

[FactChecker]

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]

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?

 

[Orodruin]

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.

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.

 

[guyvsdcsniper]

"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.

 

[Ibix]

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.

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.

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.

 

[Orodruin]

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

 

[robphy]

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.

"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.)

 

[robphy]

View attachment 295513

(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 $\gamma=\cosh\theta$ ).

 

[vanhees71]

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

 

[guyvsdcsniper]

(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