## Can Einstein-Rosen bridges – if they exist – link two points of which one lies outside of the observable…

So there’s stuff very far away that is, due to expansion, accelerating away faster than the speed of light, so fast that its light will never reach us even with infinite time – and we can’t reach that point even if we travel at the speed of light for all eternity. The comoving distance of where the universe becomes fundamentally unexploreable is, afaik, some 46.5 billion light years or so.

Theoretical Einstein-Rosen bridges could connect any two points of space-time. What I wonder though is whether this could also apply to points that are farther than these 46.5 billion light years apart, or whether this is a theoretical maximum distance for wormholes as well?

Whether the answer is yes or no – an explanation would be great 🙂

Edit: maybe I’m mixing up observable universe and hubble volume here – I mean the one relevant to the question of course 🙂

## Did Ludwig Boltzmann read Albert Einstein’s publication published on Brownian motion one year before…

Apparently there was some negative reception of Boltzmann’s idea of an “atom”. I assume the mathematics used by Einstein in his publication did not use any of Boltzmann’s statistical mathematics otherwise Boltzmann would have know about it.

Einstein calculated the size of the atom as well as it’s existence in his publication of Brownian motion.

Boltzmann apparently passed away a year after he had been vindicated by Albert Einstein. Was Boltzmann aware of this at the time that he passed away?

## Wave Analytics (Einstein Analytics) Conditional Formatting on Table

I am looking for a way (I haven’t found one, and I don’t think it is possible) to have conditional formatting on Pivot Table or just any Table within Wave Analytics. E.g. Ability to conditionally color any cell. For example, if a value is lower than a static value or another column’s value by specific percentage, then set one color, if lower by another percentage, then set another color.

I tried manipulating the JSON behind a Pivot table, but it was not working. SAQL conditional color is only possible for Number widget.

If anyone had any experience in successfully producing conditional formatting for Wave table-type charts, please let me know.

## What is the geometric interpretation of the Einstein tensor \$R_{mu nu} – frac{1}{2} g_{mu nu} R\$

The Riemann curvature tensor $$R_{mu nu rho sigma}$$ has the geometric interpretation of giving how much parallel transport fails to close around tiny loops. The Ricci tensor $$R_{mu nu}$$ the Riemann curvature averaged over all directions, as in, if there is negative curvature in some direction there must be positive curvature in another if $$R_{mu nu} = 0$$.

What is the geometric interpretation of the Einstein tensor
$$G_{mu nu} = R_{mu nu} – frac{1}{2} g_{mu nu} R?$$
Is there a way to understand
$$nabla^mu G_{mu nu} = 0$$
Intuitively?

## Did Ludwig Boltzmann read Albert Einstein’s publication published on Brownian motion one year before…

Apparently there was some negative reception of Boltzmann’s idea of an “atom”. I assume the mathematics used by Einstein in his publication did not use any of Boltzmann’s statistical mathematics otherwise Boltzmann would have know about it.

Einstein calculated the size of the atom as well as it’s existence in his publication of Brownian motion.

Boltzmann apparently passed away a year after he had been vindicated by Albert Einstein. Was Boltzmann aware of this at the time that he passed away?

## Did Ludwig Boltzmann read Albert Einstein’s publication published one year before Boltzmann passed away?

Apparently there was some negative reception of Boltzmann’s idea of an “atom”. I assume the mathematics used by Einstein in his publication did not use any of Boltzmann’s statistical mathematics otherwise Boltzmann would have know about it.

Einstein calculated the size of the atom as well as it’s existence in his publication of Brownian motion.

Boltzmann apparently passed away a year after he had been vindicated by Albert Einstein. Was Boltzmann aware of this at the time that he passed away?

## The action of Einstein Maxwell system for arbitrary dimensions

The question is as mentioned in the title. To write the action for the Einstein-Maxwell system in arbitrary dimension.

Is it possible just to add them (The Lagrangian for gravity and for electromagnetism) linearly to the Lagrangian in order to get the action?

I have not been able to find a lot of resources regarding this on the internet, if you have something relevant please comment.

## Not getting response from apex action einstein bot

Below is configuration screenshot –

``````public with sharing class ChatBotTime {

public class ChatBotTimeAndTempOutput {
@InvocableVariable(required=true)
public String city;
@InvocableVariable(required=true)
public Decimal temperature;
@InvocableVariable(required=true)
public String dateStamp;
}

public class ChatBotTimeAndTempInput {
@InvocableVariable(required=true)
public String city;
}

@InvocableMethod(label='Get System Time' description='Returns the current system time and temperature for the given cities')
public static List getSystemTimeAndTemp(List inputs) {
List results = new List();
for(ChatBotTimeAndTempInput i:inputs){
ChatBotTimeAndTempOutput item = new ChatBotTimeAndTempOutput();
item.city = i.city;
item.temperature = Math.floor(Math.random() * (1000 - 100) + 100) / 100;
item.dateStamp = String.valueOf(dateTime.now());
}
return results;
}
``````

}

## Varying the Einstein-Hilbert action without reference to a chart

In most treatments of General Relativity, when the the Einstein-Hilbert action over some manifold $$mathcal{M}$$ (plus Gibbons-Hawking-York term if $$mathcal{M}$$ has a boundary), given by

$$S=frac{1}{2kappa}int_{mathcal{M}}star,mathcal{R}+frac{1}{kappa}int_{partialmathcal{M}}star,K$$

(with $$8pi G=kappa$$) is varied, it is done so by an implicit choice of chart. Namely, one writes the action (locally) as

$$S=frac{1}{2kappa}intmathrm{d}^dx,sqrt{det(g)},mathcal{R}+frac{1}{kappa}intmathrm{d}^{d-1}y,sqrt{det(h)},K$$

From this, one uses the coordinate equations for $$mathcal{R}$$ and vary it with the components of the metric tensor in this particular chart to derive the Einstein field equations, which is a very long and tedious process, prone to mistakes from misplaced indices.

However, it is generally possible to derive equations of motion for field theories without referencing a coordinate chart. In fact, such methods are typically very generalizable and very powerful for calculating conserved quantities. Consider, for instance, (Euclidean) Maxwell theory of a $$U(1)$$ gauge field $$A$$. The action is simply

$$S=frac{1}{2e^2}int_{mathcal{M}}Fwedgestar,F+int_{mathcal{M}} Awedgestar,j,$$

where $$F=mathrm{d}A$$ and $$j$$ is some matter current. Under a general transformation $$Ato A+delta A$$, we have

$$delta S=frac{1}{e^2}int_{mathcal{M}}mathrm{d}delta Awedgestar,F+int_{mathcal{M}}delta Awedgestar,j\=int_{mathcal{M}}delta Awedgeleft(frac{1}{e^2}mathrm{d}star F+star,jright)+int_{partialmathcal{M}}delta Awedgestar,F,$$

from which the equations of motion are immediately $$mathrm{d}F=0$$
and $$mathrm{d}star F=-e^2star,j$$, assuming $$delta A$$ has no support on $$partialmathcal{M}$$.

Does there exist a similar completely covariant and coordinate-independent derivation of the Einstein field equations from the Einstein-Hilbert action?