# Is this way of understanding Minkowski correct?

• B
Hi all! Sorry for the bad English! =)

I'm reading a book about the interpretations of the findings of Einstein and others and i came across a statement that sounded very nice, but since it's its author is more tendentious to the Lorentz interpretation, I'm not sure if it's right. As I understood it, the point is like:

Length contraction and time dilation aren't really the object being deformed or time doing funny things. Everything is just 4 dimensional things that appears funny when looked from different perspectives, just like a snake may appear to be very small if it's perfectly straight and looked directly in its face (we would only see it's face and have no idea of its length) , and very big if looked from above.

In a direct citation:

Similarly, time dilation does not involve a literal slowing down of relatively moving clocks as they endure through time, but rather results from the application of different coordinate systems to the changeless 4-dimensional object and calculating the difference between the temporal coordinates of two events. P. 25.

The book is "Einstein, relativity and absolute simultaneity" from Craig and Smith.

Thanks! =)

Ibix
2020 Award
Yes, that's correct.

You could regard an idealised ruler as a 1d line in space - but it is extended in time as well, so it's actually 2d, one spatial length and one time-like length. All different frames do is pick a different slice across that 2d sheet to call "the ruler, now". The odd thing about Minkowski geometry is that the perpendicular cross-section gives the longest length, which is why we get length contraction.

Joao
The quote seems OK to me. A clock always ticks at the same rate but can appear slowed or sped up depending on reference frame of the observer.

Cheers

Joao
Ibix
2020 Award
A clock always ticks at the same rate
To be clear, an observer travelling with an ideal clock will always regard it as ticking at the same rate. Observers not moving with it may disagree, as you note.

Joao
Thanks a lot everyone! It's much more clear now! =)

Length contraction and time dilation aren't really the object being deformed or time doing funny things.
We need to rigorously define the term "really". The Bell Spaceship Paradox says the thread connecting two moving ships gets shorter, will build up internal stress and eventually break.

PeterDonis
Mentor
2020 Award
The Bell Spaceship Paradox says the thread connecting two moving ships gets shorter, will build up internal stress and eventually break.

The "gets shorter" here is not correct. The "build up internal stress and eventually break" are correct.

The "gets shorter" is problematic for two reasons. First, the length of the thread is frame-dependent (while the internal stresses and the thread eventually breaking are not). Second, in the initial rest frame of the two ships (which is the usual frame in which the thread is said to "get shorter"), what "gets shorter" is not the actual length of the thread (that stays the same in this frame), but the unstressed length of the thread (which contracts according to "length contraction" in this frame).

More in this Insights article:

nitsuj
Ibix
2020 Award
We need to rigorously define the term "really". The Bell Spaceship Paradox says the thread connecting two moving ships gets shorter, will build up internal stress and eventually break.
The problem isn't the definition of "really". Rather, it's distinguishing clearly between an acceleration and a boost. Bell's spaceship paradox is designed to smack you in the face with the implications of naively treating them the same.

A Lorentz boost is simply a change in perspective. All (non-null) worldtubes have their slope altered all the way along them. An acceleration is a bend in a particular worldtube, that of the accelerated object. The former always includes length (de-)contraction of all objects and has no physical consequences. The latter may or may not include length contraction, depending on how the acceleration happens and how the internal structure of the accelerated object works. There are physical consequences.

So I don't think you've got an argument here. You are free to analyse any problem (length contracted or otherwise) in any frame you like and there are no physical consequences. But you have to analyse the actual problem and not fall for Bell's inviting trap (or anything similar).

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nitsuj
...the length of the thread is frame-dependent
All lengths are frame dependent.

PeterDonis
Mentor
2020 Award
All lengths are frame dependent.

Yes. Which doesn't change the point I was making at all.

Meir Achuz