# Differences between different simultaneity conventions

• analyst5
In summary: Huh? You can't synchronize ideal inertial clocks that are in relative motion. Whichever ##\epsilon##-synchronization convention you choose relative to a given inertial world-line, the clock synchronization is between all spatially separated clocks at rest with respect to the clock described by said...
analyst5
Hi guys, I'm reading a text regarding different possible ways of synchronizing clocks in an inertial frame, so maybe somebody could help me with some details. The standard ways, the Einstein synchronisation, is characterized by the synchronisation parameter which is 1/2.

Since I've red that basically we can put any number between 0 and 1 instead of 1/2 as a paremeter, can somebody explain to me what kinds of differences arise in simultaneity while using different synchronisation methods, compared to the Einstein method, maybe with a space time diagram so I can figure out what is really meant by the oftenly used sentence 'we may synchronise the clocks the way we like'.

analyst5 said:
Since I've red that basically we can put any number between 0 and 1 instead of 1/2 as a paremeter, can somebody explain to me what kinds of differences arise in simultaneity while using different synchronisation methods, compared to the Einstein method, maybe with a space time diagram so I can figure out what is really meant by the oftenly used sentence 'we may synchronise the clocks the way we like'.

The differences lie in the geometry and topology of the simultaneity hypersurfaces defined by the synchronization or simultaneity convention. This results, in particular, in the Lorentz transformations having different forms, and in general much more complicated when compared to ##\epsilon = \frac{1}{2}## synchrony, relative to different synchronization conventions.

See here for more details and see the references therein: http://www.mcps.umn.edu/assets/pdf/8.13_friedman.pdf

I would also recommend checking out: https://www.amazon.com/dp/0691020396/?tag=pfamazon01-20
as it goes into much more explicit, calculational detail on non-standard simultaneity conventions for inertial frames.

Last edited by a moderator:
WannabeNewton said:
See here for more details and see the references therein: http://www.mcps.umn.edu/assets/pdf/8.13_friedman.pdf

Friedman makes a couple of points:

- Only the $\epsilon=1/2$ definition of simultaneity is consistent with defining simultaneity according to the slow transport of clocks.

- Picking $\epsilon\ne 1/2$ is equivalent to defining simultaneity in a noninertial frame.

Last edited by a moderator:
@ WBN, thanks for the link, I quickly looked it up and the description of what happens seems a little complicated, but I guess I'll invest more time. I found this on the net: http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/significance_3/index.html#Conventionality.

In one of the chapters, there is a good example what happens when the parameter is 1/4 and not 1/2, but unfortunately I don't understand what do surfaces of simultaneity look like from the perspective of the other clock (the right one) and how would the surfaces differ if we used a smaller, or bigger number than 1/2 as our parameter. I hope somebody could give me an explanation.

analyst5 said:
In one of the chapters, there is a good example what happens when the parameter is 1/4 and not 1/2, but unfortunately I don't understand what do surfaces of simultaneity look like from the perspective of the other clock (the right one)...

The same exact thing that happens when regarding ##\epsilon = \frac{1}{2}## synchrony will happen for the ##\epsilon = \frac{1}{4}## synchrony: the simultaneity surface at an angle ##\theta## to the 4-velocity of one inertial time-like curve at some event will be rotated through some angle ##\Delta \theta## to the 4-velocity of a different, time-like curve passing through the same event. The only difference in the case of ##\epsilon = \frac{1}{4}## is ##\theta \neq \frac{\pi}{2}## but is rather some oblique angle. ##\Delta \theta## is determined by the Lorentz transformations as usual, with the latter being expressed in terms of the chosen synchronization convention. See the Friedman paper for more details on how to calculate this angle explicitly.

analyst5 said:
and how would the surfaces differ if we used a smaller, or bigger number than 1/2 as our parameter. I hope somebody could give me an explanation.

If ##\epsilon \in (0,1)## and ##\epsilon = \text{const}## then different values of ##\epsilon## simply yield space-like hyperplanes of different angles ##\theta## to the 4-velocity of a given inertial time-like curve.

If we allow ##\epsilon = \epsilon(x)## then the simultaneity surfaces will look a lot more interesting i.e. they can be arbitrarily curved embeddings into Minkowski space-time, so long as ##\epsilon(x)\in (0,1)##. Friedman gives an example of such a simultaneity surface.

Does this angle dramatically differ between different simultaneity parameters from 0 to 1, and what about trying to synchronize other way round, I mean from the perspective of the other clock?

analyst5 said:
Does this angle dramatically differ between different simultaneity parameters from 0 to 1...

No it varies smoothly. Again see the Friedman article.

analyst5 said:
...and what about trying to synchronize other way round, I mean from the perspective of the other clock?

Huh? You can't synchronize ideal inertial clocks that are in relative motion. Whichever ##\epsilon##-synchronization convention you choose relative to a given inertial world-line, the clock synchronization is between all spatially separated clocks at rest with respect to the clock described by said world-line.

analyst5 said:
Does this angle dramatically differ between different simultaneity parameters from 0 to 1
The angle is probably not the thing to think about. What you probably should focus on is the speed of light. With the value of 1/2 the speed of light is isotropic, c in both directions. At the extremes the speed of light is infinite in one direction and c/2 in the other direction. The difference between 0 and 1 is just which direction is infinite.

## What is the concept of simultaneity?

The concept of simultaneity refers to the idea that two events happening at the same time can be perceived differently by different observers, depending on their relative position and motion.

## What are simultaneity conventions?

Simultaneity conventions are different ways of defining and measuring simultaneity in different frames of reference. These conventions are used to reconcile the differences in perception of simultaneity between observers.

## What are some examples of simultaneity conventions?

Some examples of simultaneity conventions include Einstein synchronization, Lorentz synchronization, and Reichenbach synchronization. These conventions differ in their assumptions and methods for measuring simultaneity.

## What is the difference between these simultaneity conventions?

The main difference between these conventions lies in their treatment of the speed of light and the concept of time. Einstein synchronization assumes that the speed of light is constant and that time is relative, while Lorentz synchronization assumes that time is absolute and the speed of light is not constant.

## How do simultaneity conventions impact our understanding of time and space?

The differences between simultaneity conventions can have a significant impact on our understanding of time and space, as they affect how we perceive and measure these concepts. They also play a crucial role in the theory of relativity and have implications for other areas of physics, such as quantum mechanics.

• Special and General Relativity
Replies
51
Views
2K
• Special and General Relativity
Replies
17
Views
710
• Special and General Relativity
Replies
20
Views
1K
• Special and General Relativity
Replies
127
Views
6K
• Special and General Relativity
Replies
51
Views
3K
• Special and General Relativity
Replies
84
Views
4K
• Special and General Relativity
Replies
16
Views
901
• Special and General Relativity
Replies
35
Views
1K
• Special and General Relativity
Replies
47
Views
1K
• Special and General Relativity
Replies
27
Views
1K