# Understanding Minkowski: Einstein, Relativity & Absolute Simultaneity

• B
• Joao
In summary, the conversation discusses the concept of length contraction and time dilation in the theory of relativity. It is argued that these phenomena do not involve a literal deformation of objects or a slowing down of clocks, but rather result from different coordinate systems being applied to a 4-dimensional object. The book "Einstein, relativity and absolute simultaneity" by Craig and Smith is mentioned as a source for this information. The Bell Spaceship Paradox is also brought up as an example of the consequences of treating acceleration and a Lorentz boost as the same thing. The conversation concludes by reiterating the importance of understanding Minkowski's ideas in order to fully grasp the concept of frame dependence in relativity.

#### Joao

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! =)

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
cosmik debris said:
A clock always ticks at the same rate
To be clear, an observer traveling 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! =)

Joao said:
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.

David Lewis said:
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
David Lewis said:
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).

Last edited:
nitsuj
PeterDonis said:
...the length of the thread is frame-dependent
All lengths are frame dependent.

David Lewis said:
All lengths are frame dependent.

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

I agree with both quotes, I think in agreement with Minkowski. Some people still have not caught up with Minkowski.

## 1. What is Minkowski's contribution to the understanding of Einstein's theory of relativity?

Minkowski's contribution was to introduce the concept of four-dimensional spacetime, which unified space and time into a single entity. This was a crucial step towards understanding Einstein's theory of relativity, as it allowed for a deeper understanding of the relationship between space, time, and gravity.

## 2. What is the significance of absolute simultaneity in Minkowski's theory?

In Minkowski's theory, absolute simultaneity refers to the idea that events can occur at the same time in different places in the universe. This challenges the traditional notion of simultaneity, which suggests that events can only occur at the same time in the same place. It was a revolutionary concept that helped to further our understanding of the nature of time.

## 3. How does Minkowski's theory impact our understanding of the speed of light?

Minkowski's theory states that the speed of light is constant and independent of the observer's frame of reference. This concept, known as the "invariance of the speed of light," is a fundamental principle of Einstein's theory of relativity. It has been confirmed by numerous experiments and has had a profound impact on our understanding of the laws of physics.

## 4. What is the connection between Minkowski's theory and the famous equation E=mc²?

Minkowski's theory of spacetime and Einstein's famous equation E=mc² are closely related. In Minkowski's theory, energy and mass are considered to be different components of the same four-dimensional quantity known as "energy-momentum." Einstein's equation describes the relationship between energy, mass, and the speed of light, which is a crucial concept in Minkowski's theory.

## 5. How has Minkowski's theory been proven or disproven by modern scientific research?

Minkowski's theory of spacetime has been proven to be an accurate description of the universe through numerous experimental tests and observations. For example, the famous Michelson-Morley experiment, which aimed to measure the speed of the Earth through the hypothetical "ether," provided evidence for the invariance of the speed of light and supported Minkowski's theory. Additionally, the predictions made by Minkowski's theory have been confirmed by modern technologies, such as GPS systems, which rely on the principles of relativity and spacetime.

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