Aren't Planck constants all about that ?
Spacetime is a sort of cartesian representation of space and time, with probably 4 axes (x, y, z, time).
Many relativity concepts obey this, for example stuff moving in space at the speed of light, move literally zero on the time axis. And you can calculate the relationship between time and speed by rotating vectors.
So back to quanta: we don't know if time is discrete. We don't even know if time actually exists, or its properties, because the math right now has results that are quite weird (like implying moving backwards in time should be normal and common as moving forward...), also there are arguments over the shape of "spacetime" with most people assuming it is a 4d cube, but maybe it ins't.
No, on a Minkowski diagram with the x axis as a one space-like dimension coordinate (e.g. radius in metres) and the y axis as the time-like coordinate (e.g. -ct, where t is in seconds and c is the speed of light; - because of the sign convention[0]), something travelling at the speed of light traces out a 45 degree angle.[1]
This is a fundamental property of Minkowski spacetime, the spacetime of Special Relativity (and the spacetime in local sections of the fibre bundle in General Relativity).
Indeed, in a hyperbolic solution in General Relativity, everything moves at one second per second on the timelike axis measuring each object's proper time. This is one of many properties of time we do know very well; what's unclear is whether the property is emergent in the behaviour of systems of small objects, or whether it is fundamental to physics and applies to every object everywhere.
General Relativity requires that the manifold be infinitely differentiable, and thus continuous, rather than discrete. Anything that seeks to explain gravitation and the observables from tests of relativity will have tremendous trouble introducing discretization on the background while retaining compatibility with those tests. For all practical purposes, that's true for everything outside the event horizon of a black hole and more recent than the first 1e-38 seconds after the big bang.
[0] https://en.wikipedia.org/wiki/Sign_convention [1] https://en.wikipedia.org/wiki/File:Minkowski_diagram_-_photo...
Thus you don't have a "full dimensional vector {x,y,z}" but you have a bunch of particles each keeping a list of variables with distances to other particles around them.
Maybe I'm not explaining it right, but no one has proposed anything like this as far as I know.
In the standard cosmology, we use quantum fields that permeate the whole of spacetime and carry values at each point in spacetime. Some of the fields have values at each point that correspond to the presence of absence of a particle at that point (e.g. the electron field), while other fields provide a mechanism for one field to influence the state of another. In General Relativity we have the metric tensor, which is a field that carries information relevant to the causal structure of spacetime, and is determined by the values of the other fields (roughly, matter determines curvature, which in this case is a component of the distance in space and time from one configuration of matter to the next).
So, rather than saying spacetime doesn't exist, we say instead that spacetime is only relevant when there is a configuration of matter within it that can be used to established one or more systems of coordinates (e.g. the matter states converge, diverge or oscillate).
However, in Special Relativity there is no spacetime curvature (by definition) and so we do not need to use a metric tensor (we could naturally use the Minkowski tensor to describe the Minkowski spacetime, which is the spacetime of Special Relativity), but commonly attach a 4-vector to particles or bound collections of them. As with any spacetime in General Relativity, there is nothing special about a Minkowski spacetime that has nothing in it, or that has any other always-unchanging configuration of mass-energy.
The Standard Model of Particle Physics is a group theory with the Poincaré group as a subgroup; the Poincaré group is the isometry group of Minkowski spacetime, or in other words, in Special Relativity, when you move something following the rules of the Poincaré group, you do not change the fundamental states of the thing you are moving. The Poincaré group in 3+1 spacetime has 3 (bidirectional) linear spacelike translation components, 3 components of (bidirectional) rotation, 3 components of Lorentz boost, and one timelike translation. So if you do a particle-smashing experiment today and the same experiment tomorrow (or in a lab across campus), you will get the same result.
One can represent the action of the Poincaré group in several different ways. There is no harm in either approach in your second paragraph, as long as one is careful about how one manipulates either representation (especially, for example, swapping one representation for the other).
First let us observe that even in the classical universe there are discrete quantities. Atoms, for example, are discrete. You can't have half a uranium atom because that's not a uranium atom any more, it's some other kind of atom. But aside from these discrete quantities most of the things that describe the state of the classical world seem to be continuous: you can position an atom anywhere, you can move it at any speed (including zero), etc. and hence the atom can have any value for its total energy.
This turns out to be only an approximation to the truth. It turns out that classical systems in fact can only have energies that are discrete multiples of some very small number. This number is not Planck's constant, but it's derived from Planck's constant in a way that depends on the physical setup. This is why, for example, to see quantum effects you have to control the setup very carefully, which generally means making things very cold so they don't jiggle around too much. This is one of the complications that I can't get into here. But the details don't really matter. What matters is that it turns out that some of the quantities we thought were continuous are in fact discrete, it's just that the units are so small that it's not apparent until things are very small and/or very cold. And in particular, energy is discrete.
But the underlying math of QM is not discrete, it's continuous. So how do we get from the continuous math of the quantum wave function to the discrete behavior we observe in reality? We don't really know. If we really understood that we could explain why Planck's constant has the value that it does, and we can't do that (yet). One possibility is that space and time are discrete just like energy it, but it's just not apparent because the units into which nature slices up space and time are too small for us to access experimentally. If space and time do turn out to be discrete, then the continuous math of QM will turn out to be merely a very (very!) good approximation.
But the distinction that really matters between the quantum and the classical is that states in the quantum universe are described by complex numbers and states in the classical universe are described by real numbers. That is the thing that makes quantum and classical fundamentally different, and it's the thing that makes the quantum world "weird" to us, because that's how you get things like entanglement and destructive interference. The quantization part is, ironically, a relatively unimportant detail, at least when it comes to talking about things like time crystals. (It's incredibly important for other things, like semiconductors.)
Seriously though, I don't actually know much about QM, I only know the One Thing that makes the rest of QM easy to understand (kind of like knowing Lisp makes the rest of computer programming easy to understand).
In case you want to know that One Thing, it's written up here: http://www.flownet.com/ron/QM.pdf
There's also a movie version: https://www.youtube.com/watch?v=dEaecUuEqfc
When I first wrote the paper 15 years ago I submitted it to Physics Today. It was rejected, not because it was wrong, but because the reviewers thought that it was nothing new, that everyone already knew this stuff. Since then the physics community has bifurcated rather neatly into two camps: the ones who agree with the PT reviewers, and the ones who think I'm a "category 5 loon" (that was Lubos Motl's term). Personally, I think the existence of people like Motl and your anonymous "dismissive" QFT experts -- and the fact that I can still stump card-carrying physicists with the EPRG paradox -- falsifies the hypothesis that "everyone already knows this stuff."
I will also say, because I'm feeling rather annoying by all this, that in 15 years no one has ever pointed out any actual mistakes in the paper (except for a few typos).
So I just wanted to ask in respect of "no one has ever pointed out any actual mistakes" - have you seen the stackexchange discussion at http://physics.stackexchange.com/questions/208609/does-the-f... , and do you have any comment on the assertion there that your statement of EPRG misses the point that "even if Alice does let her system produce interference, the other system will not produce interference either"?
The thing that people who critique my work generally miss is that it is not about physics, it's about pedagogy. It's about how the physics is explained. Everyone agrees on the physics. It's the explanation that is at issue. The whole first half of the talk is the problem statement.
(God damn this is annoying: "I'm afraid I won't have time to critique whatever it is he says in the second half of the video." Well, the second half is where I explain why the EPRG paradox doesn't actually work. By the time I gave that talk I already knew that people got this wrong, so I went to great lengths to highlight the fact that EPRG was a straw man. And then people jump into the middle of the video, see the story out of context, and say "This is wrong." Well, duh, of course it's wrong. That's the whole fucking point!)
I did suspect that "Garret then claims that this can be used for superluminal communication" missed that you were using this as a kind of reductio, but I then took it to mean that your reductio was not working how you expected it to. Probably I should re-watch the video - it's been a couple of years.
> your reductio was not working how you expected it to
Actually, it pretty much works exactly how I expected, and has for 25 years (I started down this road in 1990 when the EPRG paradox first occurred to me. It took me ten years to find someone who knew the answer.)
The problem is when people look at EPRG out of context and think that my thesis is that I've invented FTL and therefore I am the World's Greatest Physicist. (And now some moron is probably going to cite this very comment and say that I've claimed to be the Worlds Greatest Physicist because they saw that I wrote "... I am the World's Greatest Physicist" and they don't have time to read the part that they elided.)
Edit: downvote me all you like, but at least be accurate. I'm referring to the title of the tech talk video linked several times in this thread: "The Quantum Conspiracy: What Popularizers of QM Don't Want You to Know"
But I think you give too short a shrift to Many-Worlds because it's not intuitive to you. Plenty of things about QM are not intuitive; I don't think that's sufficient reason to reject it.
[UPDATE] Yes, my recollection is correct. Go watch it again starting at the 58 minute mark or a little earlier.
just to confirm my interpretation, its saying that:
- fundamentally the universe is governed by quantum mechanics
- classical physics doesn't truly exist
- the classical physics we see and intuit can be explained by entropy (information theory) of the quantum state
- measurement and entanglement are the same in the sense that both imparts "information" into the system. this in effect acts as a "filter", an example of which is the double-slit experiment where the waves are "filtered" to particles when being measured
- our conscious mind is a classical construct so its naturally difficult to intuit quantum laws
is that mostly correct? also, how popular is this theory in the physics community?
Mostly.
> also, how popular is this theory in the physics community?
Not very. The fashionable way to think about this stuff is something called "decoherence" which really amounts to the same thing but phrased in different terms.
so if i were to do further research into this, I would use the keyword "decoherence"?
also not being a physicist, could I naively think this would be a good candidate for the "theory of everything"?
Decoherence, relational quantum mechanics, quantum information theory, the Von Neuman measurement model -- all of these turn out to be the same thing.
> also not being a physicist, could I naively think this would be a good candidate for the "theory of everything"?
No, the "theory of everything" refers to the unification of quantum mechanics and relativity. Completely different topic.
Also, when you say there are not discrete things, do you mean in the QFT sense of field excitations?
Yes.
> If so, how can we talk about discrete systems.
That is an excellent question! And the answer is that when you do the math, the result of taking a subset of the wave function (the mathematical operation is called a "trace") is something that looks like a classical system. If you want the details, see this paper:
http://www.flownet.com/ron/QM.pdf
Or this video
https://www.youtube.com/watch?v=dEaecUuEqfc
which covers the same material.
Your statement just connected to unrelated subjects in my head that might mean something. As I studied hardware, I found that underneath these nice, mathematical blocks that we build digital with are analog components that appear to operate on messy, kind-of-chaotic waves of electricity they hand-tune into the digital cells. Then, you say the clean building blocks of classical systems are composed of messy waves in quantum. Worded like that, it makes me wonder if analog vs digital could teach us something about quantum vs classical. Or some universal principle at work. Reason I wonder is some of the math keeps showing up in different disciplines.
What you think? Is my brain overreaching on this?
But the ability of classical math to model all this is truly extraordinary.
https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.htm...