Robert B. Laughlin (Physics Nobel Laureate, Stanford University)

[Tony Yuan]

TL;DR

The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum.

In 2005, Robert B. Laughlin (Physics Nobel Laureate, Stanford University), wrote about the nature of space: "It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed ... The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. ... Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry."

Einstein expressed himself more clearly. He gave an address on 5 May 1920 at the University of Leiden. He chose as his topic "Ether and the Theory of Relativity. " Here are the concluding remarks of his speech.
"Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense."

 

[Tony Yuan]

@jedishrfu
What do you think of these two passages?
Did Einstein fall into the vortex of ether because of his old age?
Should Robert B. Laughlin be judged as a person who is ignorant of physics?

 

[Dale]

Regardless of whether or not it is a problem in some circumstances, the luminiferous aether does have that connotation today, particularly on Internet forums.

Regarding the specific Einstein quote: “space is endowed with physical qualities”. Yes, it is endowed with some physical qualities. However, one physical quality that it is not endowed with is velocity. When aether is introduced in internet discussions it is usually used specifically to incorrectly introduce that property.

Given that all historical versions of the aether possessed velocity it is unclear what possible benefit there could be in labeling something without it as aether.

 

[Tony Yuan]

The ether around the earth is completely dragged by the earth. Therefore, with the earth as the reference system, the ether near the earth is stationary.
MMX, Fizeau experiment and Sagnac effect experiment have well verified the theory of completely dragged ether.

 

[Dale]

The ether around the earth is completely dragged by the earth. Therefore, with the earth as the reference system, the ether near the earth is stationary.
MMX, Fizeau experiment and Sagnac effect experiment have well verified the theory of completely dragged ether.

This is both factually incorrect and demonstrative of why references to the aether in internet discussions is problematic.

First, the Sagnac effect excludes a fully dragged aether. A fully dragged aether theory predicts a null result for the Sagnac effect, which is falsified by the observed existence and magnitude of the effect. So your statement is factually wrong.

Second, as I said before, the physical qualities that space does have does not include a velocity. So a dragged aether theory is not at all justified by the Einstein quote.

Comments like yours demonstrate exactly the reason that the negative connotation of aether continues. If you want to rehabilitate the aether, then start by getting your arguments correct. Once you actually have valid physics, then you can engage in a battle over the words.

 

[pervect]

My $.02, for whatever it's worth. I'll start with space, not space-time. The physical/mathematical structure of space, at it's simplest level, is that one can identify "points" in space. And one needs the idea that points can be "close" or "far" (not close). This is sometimes called the idea of neighborhoods. This is enough to give the most general notion of space, a topological space, the study of which is point-set topology.

To introduce a metric structure to space, we need the idea that points that are "close" have a unique distance, and to go to physics and not just math, we insist that this distance is somehow "physical". We can thus sidestep the innocuous but deep issues about distances between points that are not close. For instance, we don't have to insist that they are unique.

And we probably at some point need to insist that this distance squared for sufficiently nearby points can be expressed as a bilinear quadratic form. For the classical notion of space, we insist that this is a positive definite quadratic bilinear form, but for GR we will wind up relaxing this so that the quadratic form is not necessarily always positive.

[edit-add]
The cannonical examplie here is that distance^2 = dx^2 + dy^2 + dz^2. It's a quadratic. And it's always positive, so it's positive definite.

To get to the sort of space that GR uses, we further need the idea of manifolds, which informally needs a set of axioms about how we can "glue together" different charts (each chart has its own coordinates to identify points and its own associated quadratic form), so we can handle situations that aren't amenable to being covered with a single chart.

That gives us the structure of space, and sufficient foundation to develop things like the metric tensor, the Riemann curvature tensors, and the mathematical operations to make the Riemann tensor.

Nobody to my knowledge has defined what a "medium" is mathematically, but I generally think of it as having more structure than that of a space. As some other posters have observed, usually there is some concept of "velocity relative to a medium", but there isn't any such concept in the concept of space that GR uses.

Ultimately though, it's all semantics, unless and until someone gives us a precise and agreed-on mathematical definition of what a "medium" really is in terms of its mathematical properties.

"Space-time" generalizes space, replacing "points" with events, but the structure isn't really otherwise that much different, except that the quadratic bilinear forms aren't always positive when evaluated, i.e. they are not positive definite, which does complicate things a bit. These complications are not big enough to upset anything I've mentioned previously. We also have the fact that we also use a different, positive-definite quadratic form (which I have never seen named or discussed much) to define events that are "close" which is different from the Lorentzian form we use to define distance, as events with a zero Lorentz interval are not necessarily "close".

[add-expand]
The cannonical example here of the quadratic form is ds^2 = dx^2 + dy^2 + dz^2 - c^2 dt^2. It defines the Lorentz interval, which defines the structure of space-time. It's still a quadratic, but it's no longer always positive. Putting it loosely (and it's the way I think of it), space is the geometry of distance, space-time is the geometry of the Lorentz interval.

In GR, we introduce a few mathematical "children" of the Riemann curvature tensor, the Rici tensor and the Einstein tensor, via contractions. Othe than these points I don't think there is that much difference between my discussion of space and the notion of space-time. We also need the other side of the equation to do GR< the stress-energy tensor, but I don't think that's relevant to the discussion. I suppose we could talk about it if people think it is necessary.

And to repeat my point, the argument strikes me as one of semantics - what exact characteristics does something require to be considered a "medium"? The semantic issue could be resolved if there was an agreed-upon definition of what constitutes a medium. The fact that I'm not aware of any such agreed-upon definition doesn't necessarily mean it can't exist. But I can say I don't really care that much about it, the above is enough to do GR, and the rest is to my mind a distraction.

 

[robphy]

Einstein expressed himself more clearly. He gave an address on 5 May 1920 at the University of Leiden. He chose as his topic "Ether and the Theory of Relativity. " Here are the concluding remarks of his speech.
"Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense."

For completeness, here are additional quotes from "Ether and Relativity" (Einstein 1920)
( as transcribed at https://mathshistory.st-andrews.ac.uk/Extras/Einstein_ether/ )
... bolding mine for emphasis

...But this conception of the ether to which we are led by Mach's way of thinking differs essentially from the ether as conceived by Newton, by Fresnel, and by Lorentz. Mach's ether not only conditions the behaviour of inert masses, but is also conditioned in its state by them.

Mach's idea finds its full development in the ether of the general theory of relativity. According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that "empty space" in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials g_{mn}), has, I think, finally disposed of the view that space is physically empty. But therewith the conception of the ether has again acquired an intelligible content although this content differs widely from that of the ether of the mechanical undulatory theory of light. The ether of the general theory of relativity is a medium which is itself devoid of all mechanical and kinematical qualities, but helps to determine mechanical (and electromagnetic) events.

What is fundamentally new in the ether of the general theory of relativity as opposed to the ether of Lorentz consists in this, that the state of the former is at every place determined by connections with the matter and the state of the ether in neighbouring places, which are amenable to law in the form of differential equations; whereas the state of the Lorentzian ether in the absence of electromagnetic fields is conditioned by nothing outside itself, and is everywhere the same. The ether of the general theory of relativity is transmuted conceptually into the ether of Lorentz if we substitute constants for the functions of space which describe the former, disregarding the causes which condition its state. Thus we may also say, I think, that the ether of the general theory of relativity is the outcome of the Lorentzian ether, through relativation.