Retarded time and advanced time (and binning)

In summary, "Retarded time and advanced time (and binning)" explores the concepts of retarded and advanced time in the context of physics, particularly in wave propagation and causality. Retarded time refers to the time it takes for a signal to travel from a source to an observer, while advanced time pertains to the hypothetical scenario where signals travel backward in time. Binning is introduced as a method to categorize or group data points within specific time intervals, facilitating analysis in both theoretical and experimental frameworks. The discussion emphasizes the implications of these concepts in understanding temporal relationships and the flow of information.
  • #1
complexconjugate
3
0
TL;DR Summary
How to calculate electromagnetic radiation contributions for a given observer
Hi!

I am dealing with the propagation of electromagnetic emissions through the atmosphere. To quickly outline:
Imagine some charge distribution flying at relativistic speeds and inducing a four-potential A. We define some retarded time at which the charges are at some positions, and calculate the observer time (the advanved time for the emission time) by integrating over the refractive index of the atmosphere. So far so good.

If you plot the retarded time t* over observer time t, you get these multi-branch functions, like in this plot:
zotero_3OPqowuHet.png

t is the observer time, t* is the emission time, t_B is just some plot relevant parameter. The different line styles correspond to different refractive indices (solid = realistic, dashed = 1, dotted = 1.0003).

If I want to calculate the contribution for an observer at time t, t* gives multiple possible solutions. If I want to go the other way and want to calculate where the emission for a given t* ends up, I feel like I can in essence just iterate over all my possible t* and tally up when in time it arrives.

As you can see in the plot, many retarded times are compressed into very short observer times and I am not sure how to deal with that properly. If I had infinite precision it would be fine, but my data will be binned in time, and (for the solid line) emissions from t* = 10³ to t* = 10² end up in the same t bin. Do I add all of these? That was my first instinct but then the bin values depend on my sampling rate of t*. Do I scale the contributions to each bin with dt*/dt or something similar? This feels both trivial and somehow just beyond my grasp...

Further, does someone have experience with taming these multibranch functions? Again, would I just add the different t* contributions into their shared t bin?

I hope my question is clear (and belongs here), let me know if you need more info.

PS, I didn't want to open several threads in a short time, but if anyone has Jefimenko's equations for non-vacuum media or literature in that direction, I'd be very grateful.

Cheers!
 
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  • #2
complexconjugate said:
TL;DR Summary: How to calculate electromagnetic radiation contributions for a given observer
https://byjus.com/physics/propagation-of-electromagnetic-waves/#:~:text=The propagation of electromagnetic waves through the vacuum happens at,the speed in the vacuum.

This should definitely help with the basic understanding of it.

Also if you have some more time


This is a lecture that was given and it is just incredibly explained. Explaining stuff is not where I shine at, in order to explain something good you have to know it cold. As I have a basic understanding of it I don't know it cold so someone else will chime in shortly will a way better explanation also.
 
  • #3
I'll also keep my eye out for a better explanation as I will be reviewing some materials.
 
  • #4
My hint
Parametric equations
x=f(t), y=g(t)

Think about it,
I= is the interval of the perimeter in this case T
T= is the time

You've got to find the important points which are the ones at both ends of the line

X=__ •t•10³, Y=__•t•10²


Hope that helped some and again soon some smarter people should start to arrive and chime in.
 

FAQ: Retarded time and advanced time (and binning)

What is retarded time in the context of physics?

Retarded time refers to the time at which an event is observed, taking into account the time it takes for light (or another signal) to travel from the source of the event to the observer. It is often used in the context of electromagnetic radiation and wave propagation, where the effects of the finite speed of light must be considered.

What is advanced time, and how does it differ from retarded time?

Advanced time is a concept used in theoretical physics to describe the time at which an effect is felt at a source, assuming that signals or influences can propagate backward in time. Unlike retarded time, which accounts for the delay in observing an event, advanced time considers the hypothetical scenario where effects can precede their causes, leading to discussions about causality and time symmetry.

What is the significance of binning in data analysis?

Binning is a data preprocessing technique used to group a range of values into discrete intervals or "bins." This is significant in data analysis because it helps to simplify datasets, reduce noise, and make patterns more apparent. Binning is commonly used in histograms and other graphical representations to facilitate the understanding of distributions and trends.

How are retarded time and advanced time related to binning in data analysis?

Retarded and advanced time concepts can be relevant in binning when analyzing time-series data, especially in fields like astrophysics or signal processing. When binning data that is influenced by time delays or advanced effects, it is essential to account for these time shifts to ensure accurate representation and interpretation of the data. Properly implementing retarded and advanced time can lead to more meaningful insights from binned data.

Can retarded and advanced time be applied in practical scenarios?

Yes, retarded and advanced time concepts are applied in various practical scenarios, such as in electromagnetic theory, quantum mechanics, and signal processing. For instance, in telecommunications, understanding retarded time is crucial for synchronizing signals across distances. Advanced time is more theoretical but can influence discussions on causality and time travel in physics, impacting how we understand the universe and its laws.

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