If you are really serious about this question then you would also consider what mathematicians have to say about "space". Unfortunately, this is pretty much the whole of mathematics, but I think special attention should be given to the duality between geometry and algebra. This stuff goes back to Descarte. For example, you can consider the points equidistant from a specific point, which gives a circle. Or you can consider the algebraic expression X^2+Y^2=1. Both of these viewpoints are in a sense, two sides of the same coin. What is that coin? Deep answers can be found when you start doing funky things like change your definition of numbers, to say, a finite field. Even just having two numbers 0 and 1 is quite interesting to consider. What is the corresponding geometry? Or, more confusing still, let's drop the requirement that xy = yx (commutativity). Now what are the non-commutative geometries on the other side of the coin?
Considering the wide variety of these apparently fanciful ideas that have made their way into theoretical physics fills me with wonder. I wonder if the authors of the article mention any of this stuff in their book.
Controversial, I know—but I wonder how deep that connection actually is...
'the points equidistant from a specific point' and 'X^2+Y^2=1' are both descriptions that we know how to parse and and evaluate into the same thing.
Don't get me wrong, I do think it's a super interesting property of the systems of description we formulate that it's possible to talk about the same things with different abstractions (which happens a lot in math: https://en.wikipedia.org/wiki/Duality_(mathematics)), even with very high degrees of precision—but I have a hard time seeing how this could be a property of space rather than of human conceptual structure/language.
The last bit can be said about anything. It might be relevant if the notion is intrinsically motivated by an instinctive search for closed forms. "Space" being emptiness would be isomorphic (dual) to many experiences of limits. In contrast, mystifying the unknown might inspire curiosity at best, reserving free space in the back of the mind, or philosophic arguments at infinitum at worst.
The article is somewhere in the middle with its talk around gravitational waves and einsteinian curvature of space, without directly mentioning them.
I like the better question: "What is a measurement?"
What does the measurement actually entail? If a computer reads the contents, does that mean the computer is entwined with it? What does our consciousness do to the measurement?
What does the double-slit experiment show if only computers read its result? Does the result compare when we observe it?
Crazier yet, do different human observers see the same results? Has this even been tested?
I'm simultaneously glad that someone's writing articles about these things and dismayed that too many people will read this and believe they understand astrophysics without having philosophized about it on their own. Analogies like "space goo" are useful but can be a double-edged sword(seems the author recognizes this) that can mislead the public in much the same way that the holographic universe theory leads the public to think we might be in a simulation run by space bastards, which doesn't really explain anything about the very nature of existence.
Lack of philosophizing is less of an issue than ignorance of the physics, even - especially - among philosophers. There ought to be a rule against speculating on the nature of reality in the context of quantum physics if you haven't completed the exercises in Nielsen and Chuang.
Unwarranted speculation and generalizations purely for the entertainment of those who enjoy a good mind boggle. You'd be wasting your time if you expected to gain any solid insight from the article.
Space and time are what keep everything from happening at the same time in the same place. The infinitesimal bundles of energy that make up objective reality are vastly separated in spacetime. Why is that?
Isn't the "rubber sheet" analogy better than "space goo"?
The goo analogy makes it seem like "ripples" and "bends" are something space does, where as it's (from my understanding) actually the influence of gravitational fields/aggregations of mass.
The biggest issue I see with the goo metaphor, is that it seems to suggest some sort of stationary ether that we move through as we move through space. That is to say, the mathaphor suggests that it makes sense to differentiate between stationary objects and moving objects in an objective sense. However, the core insight of relativity is that there is no such distinction.
There is currently no way to differentiate between Einsteinian relativity and Lorentzian relativity. The latter proposes an absolute reference frame. The CMB frame would be a reasonable choice for a stationary structure at the Planckian level that would host the energy bundles (quarks etc) that make up objective reality, cf. loop quantum gravity.
A one-way measurement of the speed of light is needed to differentiate between the two theories, and that has not been accomplished. In fact, it may not be possible in principle to do so. Choice then becomes a matter of taste and philosophical/physical economy.
I'm reading the whole book right now and the chapter after the one from the article is about time and goes more into spacetime according to relativity.
So far it seems to me that they sometimes provide an oversimplified analogy which they revise in a later chapter.
I'm really loving the book (half way through it!).
Part of me knows that a lot of this is being simplified down for me, but I also trust the authors to not steer the reader too far off course.
I may not have all the math and physics understanding, but I get that dark matter is real. I didn't before. That's the kind of thing the book is about, imho.
> So far it seems to me that they sometimes provide an oversimplified analogy which they revise in a later chapter.
Welcome to every high-school, undergrad and postgrad physics course. That's just how most sciences are taught. Physics especially, because all analogies lead to misunderstandings because they are an attempt to simplify the mathematics underlying the physics[1]. Such analogies will always result in certain subtleties being lost on the student, but if the student is not familiar with the subject then the mathematics would also be lost on them.
The reason why this method works is that physics operates on approximations, so an approximately accurate analogy is a step in the right direction for a more accurate mathematical model (which is still ultimately an approximation).
Some related questions that I don't know where, or how, to ask:
- Is there a “quantum” of space? Where/how is location stored?
- If electromagnetic repulsion is what makes matter “take space”, and if virtually all macroscopic phenomena are governed by electromagnetism and gravity, then could this reality be said to be “gravelectromagnetic”, and might there be other “dimensions” governed by other forces, like “cones” extending in differing “directions” from the subatomic scale? [0]
- Could gravity be the result of space trying to deflate/return to the pre-Big Bang singularity, kind of like pulling magnets apart? i.e. is gravity the “opposite” of, or a reaction to, “space?”
Could gravity be the result of space trying to deflate/return to the pre-Big Bang singularity, kind of like pulling magnets apart? i.e. is gravity the “opposite” of, or a reaction to, “space?”
I may be off the mark with what you believe, but just in case:
It's a common misconception that the big bang originated at a specific point. The big bang seems to have happened everywhere simultaneously, so it wouldn't be true to say that gravity is pulling everything back toward a point of origin.
(Ironically, the video was created because the creator was a scientist, yet they fell into the trap of believing something incorrect to the point of being publicly mistaken about it. The universe is extremely counterintuitive!)
Infinite universe can contain infinite set of objects without any of them being your doppleganger. Unless there's only limited set of objects that can exist in universe at all which doesn't seem likely.
There are a number of interesting places to start, if you want to be traditional start with reading about the Standard Model, if you want to be avant-garde start reading about String Theory :-).
I have come at the question a bit like you have, starting with Faraday and Maxwell for the electromagnetic theory, adding Lorentz and Einstein for the time and space dilation effects of general relativity. And when you start looking at light as an expanding wavefront alternating between a magnetic form and a electrostatic form and thinking about how the frequency of that oscillation relates to the other fundamental constants in the universe like the speed of light and the planck constant, you might start to wonder, as I have, whether a wavefront at the speed of light would mass appear as a side effect because it was distorting space time so hard it was dragging it around?
- The Planck units [0] are generally associated with the attempt to quantize space and time.
- Macroscopic phenomena are in turn governed by microscopic phenomena, where the strong and weak forces dominate, so I would say our dimension is equally governed by those. At high energies we know the electromagnetic and weak forces combine into the "electroweak" force, and it is commonly hypothesized that at even higher energies (such as those seen only during the very beginning of the Big Bang), all of the forces are unified. If you already knew that or were talking about something else, my apologies.
- There is the concept of the Big Crunch, where gravity would pull the universe back to a single point, perhaps in an infinite cycle. To the best of our current knowledge though, the expansion of the universe is actually accelerating, and gravity will not overtake it.
From my understanding (just a Quantum Physics I class, I could be wrong here) the Planck units quantize space or time to the extent that they define the smallest thing we can practically measure due to Heisenberg's Uncertainty Principle, but they do not preclude that things can actually be smaller than that. That is, something like length or time can be continuous, but our measurements can only ever be discrete multiples of the corresponding Planck constants.
For example, a really small object can have a length smaller than the Planck length, but we wouldn't truly know how long it was because the Planck length acts as a fundamental limit on the precision/granularity of our measuring instruments.
> For example, a really small object can have a length smaller than the Planck length, but we wouldn't truly know how long it was because the Planck length acts as a fundamental limit on the precision/granularity of our measuring instruments.
Would that be, to all intents and purposes, undetectable by us then? If so then that might be a possible explanation of "dark matter", assuming all these things were individually smaller than the Planck length.
> Would that be, to all intents and purposes, undetectable by us then?
In so far as our means for measuring particles doesn't change; namely, smashing things together at extremely high energies.
If you suppose that there are methods for measuring sub-Planck length areas then one must assume that they involve either: energies lower than those believed to be needed (which doesn't necessarily come to a solution, but pushes the problem to even higher energies and shorter lengths) OR that there is a default force that keeps space-time stable unless high energies are approached.
Note that both notions are mere speculation, the first on logic and the second on intuition about phase changes in states of matter.
> the Big Crunch, where gravity would pull the universe back to a single point
Just as the big bang didn't happen in a single place, a Big Crunch wouldn't be a contraction back to a single point. Rather, the scale factor [1] that characterises cosmic expansion would simply(!) decline back to zero.
To a first order approximation (e.g. in the FLRW perfect fluid model), a Big Crunch would resemble a time-reversal of the standard big bang cosmology.
In our universe, time reversal results in galaxies appearing at a comoving observer's horizon, and everything inside the horizon becoming denser and hotter.
Ultimately the density and heat is expected to result in beyond-the-Standard Model physics in the matter sector, and (hopefully) new physics in the gravitational sector.
We don't really know what those physics will be. Everyone hopes for something that prevents a gravitational singularity from forming, but so far what we have in terms of possible stabilizers are conjectural at best.
The time-reversals of Big Crunch and the usual-forward-time big bang cosmology with structure formation relate to the BH information loss problem. For a non-eternal BH when we time-reverse from i+ we have a gas of Hawking radiation that collapses into a time-reversed BH which eventually emits matter with much less (Boltzmann) entropy -- ions, molecules, dust, stars and even the things orbiting them. (A time-reversed stellar BH likewise will eventually spit out a white dwarf or neutron star with their respective complex layerings). How does a time-reversed BH "know" how to spit out whole stellar-mass objects when only time-reversed Hawking radiation fell into it? Most quantum gravity programmes hope that strong gravity[1] produces an environment where this sort of (time-reversed) structure formation is likely.
Flipping the arrow(s)-of-time is extremely useful for reasoning in a setting in which strong gravity is important, and extra-underlines the question of why we have the arrow(s)-of-time we do in the first place. "Boundary conditions did it" is pretty unsatisfying.
- --
[1] i.e., where the radius of curvature is on the order of the Planck length; this mostly comes from the non-renormalizability of perturbatively quantized gravity (where we quantize perturbations of a background metric) and from work in finding the effective field theory limit of semiclassical gravity; generally it's very close to a gravitational singularity and -- depending on the censorship conjecture -- always invisible to outside observers.
You may enjoy contemplating a sort of "epiphany" that I had during that usual pondering of imponderables:
That the default or base state of existence may not be nothing, not "not even nothing", but rather Everything. ...
Instead of viewing the origin of all reality/creation as things being added to a canvas of blackness/emptiness/voidness, rather consider that "Existence" may be a subtractive process: akin to holes being poked into a canvas of white, or bubbles in a boiling liquid.
(I mean even before the Big Bang, or the classic "Who Created God"/Prime Mover/First Cause question – humans are given to assuming that the start of anything must be Zero or Nothingness, that the end of everything is Oblivion, and that may not be the case.)
Our existence is a "filter", our perceptions being a very limited subset of everything that's around us, of select wavelengths and frequencies and etc. This entire universe could just be a transient bubble inside a flood of Everythingness. [0]
I've had the same thought about the starting from nothing rather than everything, but in an entirely different context.
Axiomatic Set Theory is taught starting with the empty set as an axiom and along with a small number of additional axioms, and from that you can build the integers and rationals and real numbers as well as an impressive hierarchy of different infinities. And one thing that's proved is there is no largest infinity, no set that contains all sets. There isn't an Everything set that's consistent with the Peano axioms.
However, you could build the entire system starting with the Everything set and similarly modify all the axioms to be analagously subtractive rather than additive, deriving in some sense every inverse theorem, including that there is no empty set, no Nothing.
When you do this you immediately at working with insane objects and intuition fails miserably in a way that building the other way doesn't.
I remember a mention somewhere of this kind of approach to inverse foundations for set theory, but lost track of the reference. IIRC, the approach didnt have problem with empty set, but would allow the existence as a default until some obstruction. So, 'large sets' (nowadays called proper classes) would exist.
I recently had a somewhat tangential conversation with someone, wherein the relationship between order and chaos in the universe (and specifically our case as the human race) is a function of increasing time. Humans attempt to create order from the chaotic environment, not creating more complex things in the process but simply refining what already exists (although there seem to be unavoidable patterns of "order" that recur in the universe regardless of us or any advanced organism).
This certainly fits with the idea that the universe is an attempted "ordering" bubble in a liquid of everything
This is a common theme many human societies and cultures have developed, and it makes a lot of sense when you really (really) think about it. When you take it further, you realize that also implies everything being connected fundamentally, which is an another interesting thought space to explore with a litany of deep implications, particularly around consciousness.
Plancks quantum of action says there a minimum length of space 10^-35 meters below which no experiment can measure.
Some asume this is a quantum of space, but not necessarily so. Some physicists suggest the universe is very strange at this length scale and may a sea of boiling virtual particles.
"But if you use a rigid ruler, all of its atoms would hold on to one another tightly (with electromagnetic forces), and the ruler would stay the same length, allowing you to notice that more space was created."
This is the part that I don't really understand - how does the electromagnetic force "know" the true distance?
Basically, there is an equation that determines the strength of the field that depends on the distance from the centre of the particle, or rather the "particle" creates a ripple in the field. The ripple still has a length though.
So, the question then becomes - somehow the fact that the field has a bigger differential between two spots in space, keeps from more "space" appearing between those two spots.
Yet where the field is zero (or whatever the lowest energy value is) more space can be created within the field. So, it seems that there is a "space field" and a number of other fields, that interact with each other and can influence the properties of each other.
This kind of makes sense, essentially if the "space field" can have values attached to it, that in effect would determine "distance" from our perspective, then the interactions with other fields can influence the change in distances.
IANAP, so if you are, would this be a correct line of thinking?
The electromagnetic force does not know the true distance, here the ruler is more of a theoretical construct.
Perhaps it helps, if you think about it as moving the underlying coordinates vs moving the particle. (There is no difference between the two pictures in the theory only the relation between coordinates and atoms appear. Sort of, at least.) So, if you apply a force to an atom, that means that the second derivative of its position changes. On the other hand, if we imagine for a moment that the atom is stationary and the coordinates change, then the second derivative of its position will change and it will therefore feel a force, gravity.
Usually, I enjoy articles that explain difficult concepts in math and physics, and I like to think about these concepts. But this article just rubs me the wrong way. It throws out some scientific jargon in the first paragraph that could be accurate, but instead they belittle it. Then they try to describe how some people would describe "space" but then argue as if everybody thought that way. I don't and felt talked down to. Worse, they argue as if "space" could have a simple, singular meaning, when obviously it can be defined on many levels, or at least looked at from many levels.
Then I got to the part that says: This is the part where your brain goes, “Whaaaaat ... ?” No, my brain is not so easily confused that it expresses itself in slack-jawed mono-syllables. I get it that the article is trying to simplify some explanation, but I think it's trying too hard and failing. It makes too many assumptions about what the reader thinks and then bases its arguments on these wrong assumptions.
I much preferred the discussion and links here on HN.
Fwiw, I see space as the coordinate system of our universe but with no origin because it's all inertial frames of reference. It is usually thought of as a fixed 3-d Cartesian system plus time, but as I went through life and learned about relativity and Big Bang theory and universe expansion, I understand it as a much more dynamic and complex system.
I'm trying to read through the article now, and disappointed in every paragraph. Even the illustration that are trying to be cute are blatantly inaccurate. For example the one labeled "Space Expansion" shows a grid on the floor. In the case of expansion, the number of grid lines would be the same not more, and the point is that we definitely wouldn't feel the expansion.
And then the explanation of rigid rulers and soft taffy rulers seems wrong. Both would expand because the underlying nature of matter expands along with the universe. In other words, all atoms and their distances are affected equally because the forces that determine those distances also change. It has nothing to do with soft or rigid property of an object, which is at the macro level of our perception of matter.
I really expected better of Nautilus, I thought they had a more rigorous standard.
One of the things I've thought about is relatively.
Consider a toddler strapped to his car seat in a luxurious BMW cocoon while his father speeds down the autobahn at 200km/h. He calmy drinks from his sippy cup.
You're in a passenger jet above him going 700km/hr. You're going 500km/hr faster than him.
But how fast are you really going?
Consider that the Earth is spinning around the sun at a rate of 1 billion kilometers per year or about 100,000 km/hr.
You're on Earth, so is your jet's true speed 100,700 km/hr?
Relative to the sun, yes, but everything that orbits our sun is considered our solar system which itself is orbiting our galaxy at a rate of 800,000 km/hr.
So if we add the 800k, 100k, and 700 km/hr your plane is moving, is it not fair to say you are traveling at almost a billion kilometers per hour?
I'm sure you can infer the galaxy itself is hurling through space at an ungodly speed.
I ask two questions:
1. When does this stop? What is the most supreme center in the universe?
2. Just as the child could roll down his window, and have instant access to the outside, is there a way we can do the same?
I think it's more that you have no absolute speed...? I.e.
it's an ill-defined concept. Of course we often talk about speed as if it's absolute, but as you point out it's actually always relative to some assumed background, e.g. the ground.
(It's also impossible to measure speed without some sort of external reference.)
What about angular speed, though? My physics is very rusty where it comes to rotating things, and I don't recall dealing with rotation on relativity classes in school. Since you can derive momentary linear speed from angular speed and distance from centre of rotation, I assume there is no absolute angular speed either?
No, there is absolute angular speed. Which is kind of an odd thing that rotation is like that but linear motion is not. Take the Earth for example - you can't say how fast it's moving unless it's relative to something but you can say it's doing one rotation a day.
Another odd possibly related thing is linear momentum can be any amount but angular momentum is quantized which may be why we have particles. In Maxwell's equations you can have any amount of light but in practice it arrives in chunks with one unit of angular momentum each.
Not really. If you have two bodies in hydrostatic equilibrium arranged so that you can extend the rotational axis of one such that it overlaps completely with the rotational axis of the other, how do you come up with "absolute rotation"?
You could consider the case where one is exactly spherical and the other is highly oblate. While you're free to choose a system of coordinates which keeps the highly oblate one non-rotating with respect to the coordinates, you have to appeal to fictitious forces to explain the oblateness of the coordinate-stationary body and the exact spherical symmetry of the coordinate-rotating body. Physics typically takes a simpler form if you decide the spherical body should be non-rotating against a set of coordinates that covers both bodies. (On the other hand, if these are large bodies -- planets, for example -- and you can put a lab on the surface of each, you get the Special Relativistic form of physics for practically all possible experiments wholly contained within each lab).
However, a more typical case is that neither body is exactly spherically symmetrical, in which case you might want to appeal to the view of the motions of deep sky objects observable on each body. One might be ultra-Machian and say that "absolute rotation is determined by the movement of fixed stars", but really you probably should be more interested about whether you need to resort to pseudotensors in your write-down of local physical behaviours, i.e., rely upon the principle of covariance instead, and ignore arguments motivated by less-formal arguments (sometimes only allegedly) related to any number of things Mach said.
The principle of covariance only allows a picking-out of "absolute rotation" in specific types of universe, and that picking-out is not very useful in a universe like ours.
> angular momentum is quantized
Spin is quantized in the Standard Model. Although one can call spin an intrinsic angular momentum, it's not the same thing as the angular momentum of a rotating macroscopic body like a planet. In particular, intrinsic spin survives changes of coordinates, whereas rotation does not (as discussed above).
There is a (very) technical and quite beautiful overview of the difference here:
A sibling post talked about special relativity, but you don't need special relativity to answer this question, just Galilean relativity. The answer is that you can measure velocity in any inertial reference frame you want. If you are in an inertial reference frame, you can say your own speed is 0 km/hr, or you can consider an inertial reference frame of the galaxy, which is some ungodly number, or you can measure your velocity relative to the cosmic microwave background. It's all the same -- only the relative velocity between you and another object has a real physical meaning.
Easiest way to think about it: Picture two satellites crashing into each other. It looks exactly the same if both satellites are doing 100 m/s, or one satellite is stationary and the other is doing 200 m/s.
>1. When does this stop? What is the most supreme center in the universe?
Is one of the above satellites the centre? The other? It doesn't change anything about the impact force. There's no physical difference. So we can choose either satellite to be the centre (0 km/h) or neither (100 + 100, 50 + 150, whatever)
>2. Just as the child could roll down his window, and have instant access to the outside, is there a way we can do the same?
The problem with the earth is that it's really big/heavy and gravity prevents stuff just sort of "hanging in the air" at human-height, relative to the rotation of the earth... speaking in practical terms, I mean.. so it's harder to visualise. But at the same time, sure. If you're on the earth, sitting in your chair, doing 0 m/s relative to the ground, and a satellite hanging around at head height that ISN'T rotating along with the earth hits you in the face, you just successfully accessed an intertial reference frame that's outside the earth :D
I think the true answer is that the universe is so vast, we just don't know. The answer on quore etc. when searching for the center of the universe are not really satisfactory, a frequent answer is that the question is framed wrong, as per our lack of understanding. See, the geo in geometry means the planet earth, that's our frame of reference.
there are no absolute reference frames. only relative ones! however, at least there is a fixed relationship between reference frames they all must obey with regards to the speed of light.
There is the frame of the cosmic microwave background, which allows you to measure you speed with respect to the average expansion of the universe. It's not special in terms of physics, but it is a reference.
Just thinking out loud here. If the speed of light is absolute (it's not relative right? it doesn't change in any reference frame?), then could the speed of light be considered the base axis, or to continue the metaphor in the parent comment, that the speed of light is the 'outside the car'? Also, doesn't time 'stop' when you are at C, so that the whole idea of space (speed * time) sort of collapses?
> If the speed of light is absolute (it's not relative right? it doesn't change in any reference frame?), then could the speed of light be considered the base axis, or to continue the metaphor in the parent comment, that the speed of light is the 'outside the car'?
The speed of light is the same in any (inertial) reference frame. But you can't use it as a reference to compare other speeds against, because there are more degrees of freedom than you might think: a speed is calculated from both a distance and a time. So you and I could be looking at an asteroid and you say it's stationary and I say it's going half the speed of light, and we'd both be right, even though we both agreed what the speed of light was. Special relativity works like this.
> Also, doesn't time 'stop' when you are at C, so that the whole idea of space (speed * time) sort of collapses?
If you naively plug zeroes and infinities into the equations you won't get good answers, but if you're careful and work with limits then everything works right. What specifically were you asking about when going at C?
You should spend some time doing calculations in the “hypercomplex plane”. That is, something like the complex plane, but where you’ve taken the real number line and added a a new value u such that u² = 1 instead of the value i such that i² = –1.
Try to work out what perpendicular numbers look like in this space, what “circles” look like (hint: like hyperbolae), what the tangents to those circles look like, what kind of metrical relationships arbitrary triangles or other shapes have, and so on.
If you play with this simple 2-dimensional number system for a while, you’ll come to understand the nature of special relativity much better.
* * *
The displacement between two points in spacetime can be either “spacelike” in which case there is some inertial reference frame in which the two points are simultaneous, or it can be “timelike” in which case there is some inertial reference frame where the two points are at separate times, unmoving in space, or the displacement vector can be “lightlike”, which is a boundary between the two – the two points are always in every inertial reference frame separated by some speed-of-light separation.
It's consistently relative, because the unit of speed we use is relative to our subjective experience. Hell, if you were American you would've given these values in miles/hr, so localised is the subjectivity of distance. Hours too are a relative measure of time (consider an alien who could live for thousands of years and how they would measure time, or a being that could travel near the speed of light).
One of the ones that gets me and may be central to space is the central idea in the Young's double slit experiment, the Michelson-Morley interferometer, the Fabry-Perot interferometer, etc. Indeed, the night I was studying for my final in optics and radiography, I thought of this stuff and never really studied for the exam!
So, just shine a light through a beam splitter. So, ballpark half of the light continues on essentially straight and the other half is deflected 90 degrees.
Such a beam splitter is in the M-M experiment. For the double slit, it divides the beam. For a Fabry-Perot, it ends up making many such splits.
Okay, as we heard from Feynman, we could send just one photon through any of those devices and still get the same interference effects. Feynman also explained that we'd get the same result sending one electron at a time instead of a photon.
So, here, to heck with recombining the beams and getting it to interfere with itself.
Instead, consider just the beam splitter. So, the photon (or electron, neutron, whatever) is a wave function, and after the beam splitter that wave function is in two parts traveling apart, in the case of the photon, if we add a mirror to have the two halves going in opposite directions, at the speed of light.
But such splits of the wave function happen at every window pane, no doubt in every water droplet, etc., that is happen all the time.
And such a wave function doesn't split just once but commonly many times. So, the one, poor photon as one simple wave function is soon in dozens of pieces all moving away from each other usually never to come together again. After a billion years, the pieces are still moving away from each other.
Then, presto, bingo, one part of that wave function enters our telescope and hits our detector. Then all the dozens of pieces of that wave function, scattered across a billion light years, have to disappear, instantly, since with two telescopes we can never get two detections from the one photon.
Well, that's tough to believe.
So, maybe the universe is filled with tiny pieces of wave functions condemned to go on forever. Maybe that's the dark matter?
Or perhaps the wave functions "gains a dimension" in that it spreads evenly (or weighed) in all of space, thus making it that a photon is "almost everywhere" until detection.
> And such a wave function doesn't split just once but commonly many times. So, the one, poor photon as one simple wave function is soon in dozens of pieces all moving away from each other usually never to come together again. After a billion years, the pieces are still moving away from each other.
> Then, presto, bingo, one part of that wave function enters our telescope and hits our detector. Then all the dozens of pieces of that wave function, scattered across a billion light years, have to disappear, instantly, since with two telescopes we can never get two detections from the one photon.
> Well, that's tough to believe.
There are a dozen different possibilities for what the photon has done - a dozen different universes, if you like. As long as the photon never interacts with anything else, this bundle of a dozen universes can act much the same as a single universe. Certainly if you're just looking at a telescope, all dozen versions of that telescope are behaving the same, so they behave like a single unified instance.
When the photon hits the telescope in one universe, the perspective shifts: the telescope is now "inside" the 12-way split, either the photon went one way and the telescope recorded it or the photon went another way and the telescope didn't. And when we look into the telescope, we again shift from looking at the superposition from outside to being part of the superposition on the inside.
Our language isn't great for talking about this, because it's not a binary is/isn't thing - entanglement is a continuous phenomenon. If you imagine just two photons each in one of two states, then it's easy enough to imagine: photon A is in a superposition of states 0 and 1, photon B is in an independent superposition of states 0 and 1 - each photon has two possible "local universes", but because they're distant and noncommunicating, to each one the other looks like it's in a superposition. And it's easy enough to imagine: photon A is in a superposition of states 0 and 1, photon B is in a superposition of states 0 and 1, but they're entangled such that we know the sum is 1 - here there are two possible "global universes", and we see a superposition between them, but ecah particle knows the other is in the same universe - if A is an 0 then it knows B is a 1 and vice versa. The part that's hardest to imagine is that it's also possible to be somewhere in between these two states: A and B can be partially entangled such that e.g. there's a 75% chance that the sum is 1.
> So, maybe the universe is filled with tiny pieces of wave functions condemned to go on forever. Maybe that's the dark matter?
No. The evolution of quantum systems is unitary and conserves energy.
> There are a dozen different possibilities for what the photon has done - a dozen different universes, if you like. As long as the photon never interacts with anything else, this bundle of a dozen universes can act much the same as a single universe. Certainly if you're just looking at a telescope, all dozen versions of that telescope are behaving the same, so they behave like a single unified instance.
Well that's interesting you bring it up this way.
If what you said is possibly true, then light could be a carrier of things like multi-dimensional spin, or possibly where dark matter really comes from (inter-dimensional interference).
I know Greg Egan has discussed the possibility of infinite orthogonal dimensions that energy can leak into. And by energy conservation, the result would be things like dimensional rotation and other effects we cannot yet perceive.
One theory is that the EM-Drive uses a rudimentary version of this effect. We're all still awaiting the results.
> If what you said is possibly true, then light could be a carrier of things like multi-dimensional spin, or possibly where dark matter really comes from (inter-dimensional interference).
That's a total non-sequitur. What on earth are you talking about?
> No. The evolution of quantum systems is unitary and conserves energy.
I'm guessing that all the tiny parts of the wave function basically can't interact and collapse so just continue on forever. I don't see a conflict with unitary or conservation of energy. But these tiny pieces of wave function should continue to play their role in general relativity, gravitation, etc. That's my wild guess.
To pursue wild guesses, my guess is need a solid foundation in the physics. So, I tried again with quantum mechanics. I got a famous text. It claimed that the wave functions form a Hilbert space. Tilt! No way! They can be points in a Hilbert space, but a Hilbert space is complete which from some simple examples of convergence mean that the space has to have a lot of points (wave functions) that are not differentiable and not even continuous!
Then in QM I got to where they differentiate a Fourier transform. Okay. They are doing a differentiation under the integral sign. But, can't always do that. So, I get out a book with details, right, W. Rudin, Real and Complex Analysis, that is darned, fully, careful about such things. He has a nice chapter on the Fourier transform and does differentiate it. But he also justifies the differentiation by using the dominated convergence theorem which he also proves with great care in his early chapters on measure theory. Okay, that case of differentiation under the integral sign does work. So, then, back to the physics. But the physics lectures (an MIT thing) were never clear at all about such differentiation, were not even clear about their use of the Fourier transform, and never mentioned the dominated convergence theorem. Bummer. Further, soon it became clear that physics guy was going to be sloppy: He said that a wave function is differentiable. Okay. Then, seemingly amazingly, he went on to add that it is also continuous. Of course it's continuous: Every differentiable function is continuous.
So, for the unitary stuff, okay, I studied unitary top to bottom, side to side, from Halmos, in group representation theory, for the polar decomposition, etc. I'm eager to see the role in quantum mechanics. But I suspect again I'll have to get the math from math books, not the physics books!
I want to be careful about unitary, and the claim that no information is destroyed, etc. Careful. Really careful. Much more careful than that.
Heavily physics checks itself with experiments and, then, feels free to be sloppy with the math. But for considering wild stuff such as for goofy situations for wave functions, two particles entangled, the Einstein-Podolsky-Rosen (EPR) "spooky action at a distance", symmetry giving a conservation law, across billions of years and light years, I want the math correct right down to Bourbaki and axiomatic set theory -- no more of this sloppy stuff!
The sloppy math is why I left physics and continued with math. Now I'm ready, with enough solid math, to return to parts of physics, but just out of curiosity! I'll continue with the MIT QM lectures to get out of them what is there I don't know, but often I will have to be holding my nose over how he does the math. It's old for me: My ugrad physics prof kept telling me "Let's don't get hung up on the math". Well, I did and would say "Let's get the math straight. If we are going to differentiate under the integral sign, then let's hear about the dominated convergence theorem. And, by the way, for this stuff about integrating over unbounded sets, for that mostly we have to junk the Riemann integral and use the Lebesgue integral, so, let's do that. Let's start with sigma algebras, etc., something I never heard about in physics class!"
So, I can't push my wild guesses without more physics, and there I want to be careful about the math!
While a careful review of the foundations is valuable, and there's always a chance to find something others have missed, honestly it sounds like you're missing the physical intuitions a lot more than the maths. When I read what you wrote, thinking about unitarity came later; the immediate instinctive thought below even the level of language was "wrong, the wavefunction doesn't do that". I guess it depends what you want to do, but I'd suggest getting used to working with QM in the context of physical experiments, calculating energy levels and so on, and only looking to the foundations once you've got a better sense of how the formalism is supposed to work and what problems it's trying to solve.
I know about unitary in math. Just what QM does with it I don't know yet!
I'm eager enough to further develop my intuitive understanding. My ugrad physics prof said I had "a good feeling for physics" -- that was after I blew away everyone else in his freshman physics class!! :-)
Yes, being careful can yield new results in old fields. I've published two papers that apparently did that, one paper in optimization and the Kuhn-Tucker conditions and one in mathematical statistics.
In physics I'm not really trying to publish tricky papers at the core of the foundations, but I do get the impression that quite a lot about QM is still a bit fuzzy to nearly everyone.
So, I'd like to clean that up, as much as I can, both intuitively and mathematically.
Going into the details about how to get approximations, etc. about the orbitals of the water molecule, likely relevant enough for a physics student, seems a bit of a detail I'm willing to skip over. And generally I'm willing enough to take the results of the more famous experiments at essentially face value although might try to differ on the explanations.
My ugrad physics prof pushed hard on the MM experiment, Young's double slit, and Fabry-Perot, and it's amazing how close those remain to challenging current topics.
> I do get the impression that quite a lot about QM is still a bit fuzzy to nearly everyone.
I have the opposite experience; QM is really very clean, coherent, elegant, and well-understood - far more so than GR, I found. The people who want it to work like classical physics get themselves (and anyone who listens to them) awfully confused, but that confusion goes away, and you get a much better appreciation for what QM does if you put aside the "big questions" for a while and do some concrete computation. At least that's how it worked for me.
"Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space." - Douglas Adams
This continues to be one of my favorite questions.
In high school we were creating a vacuum in a bell jar to do the 'drop a feather and drop a weight' experiment and my physics teacher asked it. "So if we didn't have our apparatus in there, and we sucked it dry, what would be in there?"
It makes a great interview question because it helps identify people who have a hard time holding an unknown concept in their head and working with it.
I asked that of one of the folks I interviewed for Google when I was there and we spiraled off into a discussion of branes and multi-dimensional manifolds and quantum wave equations[1].
I went into entrepreneurship because I hate these kinds of interviews. You think a good way to tell whether I'd be good at writing code is my opinion on philosophy outside my domain of expertise?
> You think a good way to tell whether I'd be good at
> writing code is my opinion on philosophy outside my
> domain of expertise?
It is a way (I'm not sure how to quantify it) to understand if someone can develop something that nobody has ever imagined before. My criteria for evaluating the response was whether or not the candidate could engage with the question. It is something that happened often in my experience at Google, you were presented with an 'impossible' requirements and it was up to you to figure out what you could do about it. If someone was going to say "Well I don't know anything about that, ask someone else." Then the company knew they weren't going to be as successful as we would want them to be.
In the case of the physics student it was just their passion, they had gone way beyond the course work because they were interested in interesting questions.
> If someone was going to say "Well I don't know anything about that, ask someone else." Then the company knew they weren't going to be as successful as we would want them to be.
Except that is EXACTLY the correct response -- "I don't know, but I understand that physicists have a good idea of what space-time is, and I'll review the literature and see what the scientific consensus is and we can work from there."
The exact WRONG answer, in real life if not the interview, is "Hrm, I'm not sure but how about I make something up on the spot!"
When I said (paraphrased) "I don't know, ask someone else" I meant literally that. People who are asked a question about something they don't know anything about can either, do as you suggest propose a way to research the question (win), or do as I've observed refuse to go any further (lose). People who make things up on the spot generally are weeded out before we got to that point.
I dislike the one where they ask you how would you handle a situation that is highly dependent on the organisation and the organisation goals and procedures. The only answer really I give is not to answer such silly questions.
I fail to see how someone who is not a domain expert on the nature of space-time asking someone else who is not a domain expert can result in a reliable determination of how smart either person is.
To be clear, I don't think the correct answer of "I don't know, but I'll do a review of the literature and see what the scientific consensus is" is what the interviewer was hoping for, which is my contention.
How you speculate about things you know nothing about is a far better gauge of problem solving skills than asking questions about an area where you can rely on learned facts, in my opinion.
It's not going to be accurate, but that is not the point. The point is whether you return a blank stare or start trying to reason and analyse the problem.
Sure, you might end up with any number of "I have no idea what the right value for this is - if it wasn't an interview, I'd look it up, but for the sake of argument let's say the value is X". That's fine. Your ability to make that leap and continue is more important than the right result (so is your ability to recognise and admit that you don't know and are substituting guesses)
Do you think speculation on things that are an inferential step[1](or a couple of steps) away from things you currently know could be a gauge of a person's innate intelligence?
Intelligence is required to make inferences. Assuming a common starting ground, a person who could make the most logical inferences from it to explain a result would suggest that he's smarter. I do not claim to say a person who makes 10 good points is less smart than someone who makes 11 good points. But he surely you can agree that a person who is able to make 0 inferences is likelier to be less intelligent than someone who makes a hundred.
> Do you think speculation on things that are an inferential step[1](or a couple of steps) away from things you currently know could be a gauge of a person's innate intelligence?
No, I do not. It introduces a large capacity for things to go wrong, and it is very difficult for the interviewer to separate themselves from process. Speculative development is a road marked by dozens or hundreds of failed efforts before you hit on success. Either the interviewee happens to hit upon one of the few "correct" answers in the time available -- password guessing -- or some tolerance of wrong answers is to be accepted. But it is quite difficult to differentiate bad speculation from fruitless speculation, in a way that usefully differentiates candidates based on capability.
that is correct, however that's not exactly what the person in question was looking for while interviewing (not for the other person know have knowledge about the subject) but the ability to be able to understand a concept completely once explained, and work within the rules of the concept. This of course is arbitrary, but not a completely useless question.
Obviously I don't know the specifics of the situation here. In my experience, though, hiring committees at Google want at least some interviews closer to programming (for SWE).
So don't think that this is the typical Google interview. :-)
(2) the end of the universe, (A) big expansion and cool down to nothing, (B) no more expansion and cool down to nothing, (C) contraction back to another big bang, (D) something else very different?
This question is far more philisophical than anything. Personally I subscribe to Camus' Absurdism[1] -- that our yearning for meaning and purpose is ironic given how uncaring and lacking in meaning our universe is.
> (2) the end of the universe
There are several theories[2], but from my understanding we need to better understand "dark matter" and "dark energy" (scare quotes because those names are really silly, since we know effectively nothing about either).
In particular, it appears that we live in a flat universe but the evolution of the universe becomes more complicated with the cosmological constant terms in the evolution equations (believed to correspond to dark energy). Effectively, the cosmological constant can be seen as an energy density that remains constant throughout the universe which means that the amount of dark energy increases as the universe expands. I believe we discussed the current theories in my second-year cosmology course, but I can't recall the conclusion (it wasn't taught very well).
But I don't understand how the question "what is the purpose of X" can be anything but philosophical. Science is primarily concerned with creating models of reality and testing the predictive power of those models. The "purpose" of something is not really a meaningful concept in that context.
... unless by "purpose" you mean cause? As in, what caused our universe to exist? That is also not really a meaningful question, because time began with our universe so it's not clear what the concept of "before our universe" actually would refer to. Physically, I believe the currently popular theory is that the progenitor for our universe was an anti-matter explosion caused by the spontaneous creation of a matter+anti-matter pair (which happens all the time in a perfect vacuum due to Heisenberg's uncertainty relation -- \Delta E \Delta t \ge \hbar/2). There are several unsolved problems with this theory, the biggest one being how does it explain that there is a clear imbalance between the amount of matter and anti-matter in our universe.
> But I don't understand how the question "what is the purpose of X" can be anything but philosophical.
Again, my guess is that this depends on how much we know. Or, there about has to be a purpose. And eventually as we learn more there should be some clues about what that purpose is. So I'm wondering if we know that much yet?
A first little clue is the speed of light speed limit that so far seems to say that we are quite isolated from the rest of the universe. So, somehow having us isolated was deliberate. Then, what might be the purpose of having us so isolated?
Then there's the 3 K background radiation. That's one heck of a clue. What might be the reason for giving us such data? To answer, what can we do with it? If we note what we can do with the 3 K data and that seems really special, e.g., we wouldn't be able to do that without the 3 K data, then what is so special we can do with the 3 K data might be a clue for the purpose of letting us have that data.
There's the Heisenberg uncertainty principle. So, it keeps us from being as in an 1890 view of physics, mechanistic. We are stopped at that level by some dice rolling. So, why? When we see how that stops us, we might get a clue of a purpose.
All of that is very thin stuff, but maybe we are on the way to discovering enough to start to conclude what the purpose is.
One point is our existence and our abilities: First cut, how the heck to look at the basic physics and guess the chemistry, then, especially the biology, and, astounding, how the biology developed into us. That's some amazing laws of physics that let that happen, maybe ensured that it would happen. So, what the heck is the purpose of us being here, our existing? That is, we're the most special and amazing thing we know of in the universe. So, if there is a purpose, then it looks like we are a key part of it. So, just what the heck might be what we are to do with our abilities to understand the universe? Then, do we get a hint of the purpose from what we can do? That is, is the purpose the special stuff we can, or will be able, to do? For that if we look ahead, just how much might we be able to do? Build Dyson spheres? Okay, then what would that enable?
We don't see other planets flashing light signals at us from
their Dyson spheres. So, why not? Sure: There are other, better forms of long distance communications, and every planet with a Dyson sphere knows this. So, soon we should discover this better means of communications. So, where the heck to look for those better means. Then when we find them, what would that enable us to do in the universe that would be special? Communicate only? Or both communicate and travel? Or, if long distance travel is possible, then why ever bother to travel; just send robots and have them send back the communications so we can view it. Then does that communications give us a clue about a purpose; that is, suppose we could send robots and they would communicate back; what might we discover that begins to suggest a purpose.
Or, generally, as a meta argument, if we find some things that look really, really special that finally, with our development, we can do that seem to impact, explain, discover, reveal the universe, then maybe our doing that is the purpose of the universe.
I fully agree this is very thin stuff. Still I have to suspect that as we learn more, maybe 1 million years from now, we will begin to guess at a purpose.
Or, if there is no purpose, then this is one heck of a big show for nothing!
> Or, if there is no purpose, then this is one heck of a big show for nothing!
It isn't really. The universe all falls out of a very few, very simple rules playing themselves out - and the more we study it the smaller and simpler that set of basic rules is. Physically it's pretty big, sure, but the Kolgomorov Complexity is actually pretty small, and that's the kind of measure you need to use when considering how good a given explanation is.
Kolmogorov complexity isn't directly related to physics (and I would argue it also falls into philosophy in this case), but what GP was saying is that the complexity of the universe far exceeds the complexity of the laws that govern it. So really the laws of physics are very simple if you consider how complicated the systems they produce are.
You can fit the laws that govern the entirety of particle physics on a single page. Add another quarter-page for general relativity and you have all of the laws required to run our universe (on paper).
Why does there have to be a purpose? The rest of your post is discussing philosophy, but I'll indulge anyway.
> A first little clue is the speed of light speed limit that so far seems to say that we are quite isolated from the rest of the universe. So, somehow having us isolated was deliberate.
What makes you think it was deliberate? The derivation of the speed of light comes directly from Maxwell's equations (which just describe how electric and magnetic fields interact).
Relativity further extends that idea by "simply" noticing that the propagation of light can only work if the waves travel at the speed of light relative to the observer. Thus all light must be travelling at the same speed no matter the speed of the observer, which gives you the entirety of special relativity (that predicts that no information can propagate faster than the speed of light).
I'm not sure which part of the above you could claim is deliberate. We live in a local universe (it takes time for information to travel) and thus light must have a speed. It doesn't actually matter what the speed of light is, the same derivation would apply as long as the speed is finite. Are you saying that the fact that our universe is local is deliberate?
> Then there's the 3 K background radiation. That's one heck of a clue. What might be the reason for giving us such data?
What makes you think it's data? It's literally just the echo of the big bang and comes from the random thermal motion in the "early days" of the big bang. The reason it's 3K is that it has been cooling since the big bang and that's the temperature it happens to be today. If it were any other temperature, would that also be a clue?
> There's the Heisenberg uncertainty principle. [...] We are stopped at that level by some dice rolling.
Quantum mechanics isn't dice rolling. It is true that there cannot be a local hidden-variables theory of QM, but QM still has incredible predictive power when discussing the probabilities of experiments. It is possible in the future that a non-probabilistic view of QM will emerge, it just cannot be both hidden-variables and local.
> So, what the heck is the purpose of us being here, our existing? That is, we're the most special and amazing thing we know of in the universe.
If ants could think, they would probably think they're the most amazing thing they know of in the universe. The only reason we think we're so amazing is because we have no competitor to compare to.
> Or, if there is no purpose, then this is one heck of a big show for nothing!
I don't think that life has an intrinsic purpose. In particular, it personally feels very selfish to claim that my existence is somehow meaningful to something as enormous as the universe. It just feels like unjustified hubris.
I'm trying not to be philosophical and wondering if by now we have enough data so that we can talk about purpose without being philosophical. Sure, that we have that much data now is a long shot!
> What makes you think it was deliberate?
It looks like it might be a deliberate case of our being denied information that might let us see behind the curtain, that is, see more of how the universe is working.
> (that predicts that no information can propagate faster than the speed of light).
How we get from special relativity to that, I want to check out in detail.
Also there is the EPR "spooky action at a distance". Sure, the usual statement is that this does not permit communications faster than the speed of light, but I've seen no careful, detailed argument and want to check this out.
Also, for what I started with, a photon through a beam splitter, the wave function then in two parts, and then later the wave function parts separated by some large distance, if we have photo detectors for each part of the wave function, then the usual argument/assumption is that at most one detector will get a signal from that photon. So, instantly, across light years, the other half of the wave function is destroyed. But in principle we could detect when the detector got a signal because the other half of the wave function would suddenly not exist and would not have its effect on gravity. We're talking the gravity of half a wave function of a photon; right, small. But in principle ....
> Quantum mechanics isn't dice rolling. It is true that there cannot be a local hidden-variables theory of QM, but QM still has incredible predictive power when discussing the probabilities of experiments.
Two high energy photons cross paths, there at the same
time. Maybe they generate an electron-positron pair, and maybe they don't. That's a roll of the dice.
> It is possible in the future that a non-probabilistic view of QM will emerge, it just cannot be both hidden-variables and local.
I saw the Bell's inequality part of the MIT introductory QM lectures. After that lecture, I wanted to see a much, much more careful presentation. Yes, yes, yes, I've heard what 99% of the physics community believes; I took more than enough physics to see how such beliefs are passed out. What I want to know is what the heck the truth is, including about far out possibilities, and for that at least I want the arguments, and the math, about the old stuff, solid.
> If ants could think, they would probably think they're the most amazing thing they know of in the universe. The only reason we think we're so amazing is because we have no competitor to compare to.
Not quite the "only" thing: We have axiomatic set theory as our foundation of math, and there we have pushed hard on its rough edges, e.g., what is decidable. Likely ET can't do better.
Then building on set theory, we have math, and just from the Whitehead-Russell stuff we know how that can be verified by just mechanical means, e.g., just symbol substitution. And we know that some new results can be obtained also just by mechanical means. And I have to doubt that ET can do better in the framework -- for specific math results, sure, ET can be 1 million years ahead of us.
So, basically, we seem to know how solid reasoning goes. I'm guessing that ET can't do better on the techniques of solid reasoning, that is, ET can come up with terrific theorems we have not found yet but is still limited to the same framework I just outlined.
And, ET will have seen all our basic physics and will have to agree with at least 99% of it, no matter how sloppy the MIT QM course is. ET can't disagree with that 99%. For that part of physics, we and ET are in agreement.
So, in some fundamental ways, at least the frameworks, methods, paradigms, we are about as good as there can be.
That's some of why we look special.
And it's some of why we seem to be approaching limits on what we or ET can know about the universe. So, if there is a purpose, then we are seeing about all the evidence there can be about what that purpose might be.
So far, we don't see a purpose. But I was asking if there is some more info that lets us start to guess a purpose?
> The reason it's 3K is that it has been cooling since the big bang and that's the temperature it happens to be today. If it were any other temperature, would that also be a clue?
My point about the 3 K radiation is not that it is not 2 K (as apparently eventually it will be) or 4 K (as apparently it once was) but that it is to us for photons a wall we can't see past. Also the timing is curious: 3 K is darned cold, and it took some astounding detectors to study it; in some years, the temperature will be 2 K, 1 K, etc., and need still more astounding detectors. So, at 3 K, we've come along at about the right time. When big, seemingly independent things agree in time, it looks suspicious. So, we have to suspect that the wall was deliberate. I'm willing to set that guess aside because people are talking about seeing gravitational waves from before the time of the origin of the 3 K radiation -- so the 3 K radiation is only partly a wall. And by analyzing the 3 K radiation, e.g., taking the spacial power spectrum and understanding the acoustic aspects, maybe we can get some clues about before that radiation.
Still, to me, that there is this wall of 3 K radiation, in surprising senses uniform, is one heck of a situation. I'm not, but some people got all wound up and called it the face of God! If there is a purpose, maybe from the shockingly surprising 3 K radiation we can get a clue. Uh, maybe shocking conclusions, e.g., a purpose, need shocking data so that from shocking data maybe we should look for shocking conclusions, e.g., a purpose!
Alright, I'm just going to focus on the physics in your comment.
> How we get from special relativity to that, I want to check out in detail.
It's a fairly trivial derivation once you get past the fact that Newtonian mechanics doesn't work at relativistic speeds (the big insight Einstein had was his conviction that Maxwell was correct and Newton was wrong). You do it in second-year physics courses (at least, that's when I did it). You can even do it intuitively. If light always propagates at c, no matter what speed you're travelling at, then the Lorentz transformations are the only way that different reference frames are able to agree on measurements.
> Also there is the EPR "spooky action at a distance". Sure, the usual statement is that this does not permit communications faster than the speed of light
To be fair, this is actually quite hard to wrap your head around. There are definitely papers on the topic if you want to read them, but the effective reason why you cannot communicate using entangled particles is related to the distinction between the phase and group velocities. A phase velocity can be faster than the speed of light, but it carries no information (without also knowing other properties of the wave which travel slower than the speed of light). The orientation of the two particles is (effectively) their relative phase but you can't actually communicate information using it.
> Maybe they generate an electron-positron pair, and maybe they don't. That's a roll of the dice.
Again, currently we do not have a way of predicting the outcome of an individual experiment, but there's no reason to believe that we will never be able to do so.
> We have axiomatic set theory as our foundation of math
... which gives us Godel's incompleteness theorem. Maybe ET has a far more sophisticated basis of mathematics that doesn't permit Godel. I don't know, but it's a bit odd to claim that axiomatic set theory is somehow the holy grail (it has its own problems such as the requirement of the Axiom of Choice).
> Still, to me, that there is this wall of 3 K radiation, in surprising senses uniform, is one heck of a situation.
We know why that happened though, it's because of inflation.
For EPR, as I understand it from my too crude reading, there is an event and two particles are created and fly off in different, maybe from conservation of momentum, opposite directions. So, the two particles are a QM system with one wave function which, however, is in two parts that are separating rapidly.
As I understand the usual interpretation of the wave function, there is no, say, definite spin. We don't know what the spin of either particle is, and neither does the wave function or anything else. That is, a definite value of the spin just doesn't exist yet.
Then we measure the spin of one of the particles, and that measurement gives us a spin that apparently was determined just at our measurement. Then the wave function of the two particles has to change, and the other particle has its wave function but if we measure its spin we will get what we are supposed to, say, opposite, from what we measured from the first particle. So, the fixing of the spin of the particle we measure second was somehow transmitted faster than the speed of light. Just what was transmitted faster than the speed of light we don't know about, can't detect, and is not physics in any usual sense. Still, say, if we were trying to write a computer program to simulate this, as soon as the first measurement was made, we'd have to stop the simulation clock of the universe, go the other particle, on the simulation clock, infinitely fast, fix that particle's spin, and then continue the simulation. Strange stuff.
But, sure, that doesn't tell us how to do communications with EPR "spooky action at a distance".
I don't yet know enough QM to make well informed questions about more. I should watch the MIT QM course lectures through to the end (hold my nose on how he does his math) and pick out the more important things they are saying about how wave functions behave, when there are interactions and the wave functions disappear, etc.
Yes, pretty much need to assume the axiom of choice, and some of its consequences are tough to swallow.
> Again, currently we do not have a way of predicting the outcome of an individual experiment, but there's no reason to believe that we will never be able to do so.
Right. So, if we could so predict, what surprising things could we do with that? So, we are being forbidden to do such things. Why? Does this provide a clue about purpose?
Right, this is a long way from physics at least now.
For why SR says that information cannot be transmitted faster than light, IIRC what you said about the Lorentz transformations can say that just information, of any kind, sent any way, known to current physics or not, would permit a case of time travel or seeing into the future or some such, and we don't want to believe in that.
Yes, there is physics, say, the standard model, and first cut it looks quite simple. But the consequences are astounding beyond belief. E.g., we couldn't look at the standard model and see how DNA would work and what it would do, for green plants, earth worms, ..., humans. Heck, just looking at the standard model, we might guess that the universe would be just a fog of hydrogen or something else so simple. Even if we looked at the standard model long enough to conclude that galaxies and stars would form, some stars would explode and create some of the periodic table (the rest created otherwise), condense to planets, it's still tough to see why the planets would be more than, say, just Mars. But, no, DNA happened and after a billion or so years, we happened. That looks so astounding it looks suspiciously like part of a purpose. But you are right, that's not physics yet.
The best idea I've heard about a purpose for the universe is the theory that it evolved to create black holes which contain 'child' universes inside. That would mean the purpose of the universe is the same as the purpose of life in general.
One thing about space that I didn't see mentioned in the article is that even in a complete vacuum billions of miles away from anywhere there is still inertia. If something spins around it will still experience centrifugal force, so this is an absolute property of space and the universe that isn't caused by interaction with another body.
That's because rotation is a form of acceleration, and you can measure the acceleration (or if you prefer, the gravity) of a non-intertial (accelerating) reference frame. Galilean relativity only applies to inertial reference frames.
Ether was invoked the structure of space was necessary for fields to propagate, e.g. light was a vibration of space. This is no longer necessary. And could not be detected in the M-M experiment.
The Ionian Greeks proposed most of same models of space as modern physics, but lacked experiments to select the correct model. Some model propes emptiness and others an underlying substance of matter or energy.
At the macro level, Space could expand outward infinitely, or maybe if you travel further enough and you return to where you started. Or maybe there's the multiverse thats teaming with infinite universes?
Most physicists will tell you that at the quantum level, the most fundamental level is at the Planck scale, and the "nothingness" of space is still teaming with particles popping in and out of existence. Some particles being hypothetical and have yet to be discovered.
Considering the wide variety of these apparently fanciful ideas that have made their way into theoretical physics fills me with wonder. I wonder if the authors of the article mention any of this stuff in their book.