Sorry for the delay, busy with the family at Christmas.
Explain to me in a nutshell the prevailing theories on the concept of multiverses.
So in a nutshell, there's really only two. They're not competing in any way, both could be true, as they deal with separate issues.
The First: In Quantum Mechanics we have the Many-Worlds interpretation. In brief, unlike most theories of physics, the maths of quantum mechanics doesn't come with a clear mental picture of what is going on. So there are several "narratives" people use to picture the maths mentally. Many-Worlds is one such.
It basically says the universe has several parallel timelines. In one timeline an atom decayed, in another it didn't. Two separate histories. Now in science fiction this is usually presented as "every possibility" occurs, but that isn't true, only a small range of histories are possible and most don't differ all that much. I can say more about this, but it becomes a bit technical, keeping in mind having a nutshell answer.
The Second: Genuinely different universes with totally different laws. Maybe a world with ten dimensions and nine forces, rather than four dimensions and four forces like ours. Worlds where gravity works differently so that things spin when they fall. Places where relativity isn't true. Totally different worlds. Some theories of particle physics suggest this. In most models of this conjecture there are a lot of such different universes.
Again, both could be true. Our universe might have several timelines and there could be separate universes as well.
Are they realistically plausible?
The first type (multiple timelines) has no evidence against it yet, despite some attempts to falsify it. However all the evidence can still be explained by orthodox versions of Quantum Mechanics, so the jury is out. In other words, it makes predictions we can verify and those predictions hold up, but other ways of looking at Quantum Mechanics also make those predictions, so hard to know.
The second type has no strong evidence in its favour, but we're not advanced enough to perform the necessary experiments. It's the kind of thing that may need to wait until we colonise space.
Could we hypothetically exist in multiple dimensions?
I'm taking this to mean "does the universe we live in possibly have more than four dimensions?" So far the evidence is strongly against this, we seem to exist in a four dimensional reality. Predictions of theories with more than four dimensions have been shown to be wrong.
How does a mathematician connect the hypothetical to reality?
For the different universes or multiple dimensions theories the connection takes one of two forms.
They predict something about particles, e.g. an extra species or maybe a change in how they collide with each other. For example if we live in four dimensions photons flying toward each other bounce off each other 0.00012% of the time, but if there is a hidden fifth dimension they bounce off each other 0.00027% of the time.
Or they predict something about the heat signature of the big bang, e.g. if there are other universes out there, the should have affected the big bang and the cold patches in the big bangs after glow should be 0.0045% cooler than they would be otherwise.
For the multiple timeline theories, going into the way you connect it to reality would go outside the nutshell scope, it's a technical enough topic.
I've been thinking over the past few months how to express the essential mystery of quantum mechanics. As a result here is the briefest simplest version I can give. I've decided to cut all technical minutia and focus on the core issues in three short posts. This one is about the main issue with understanding Quantum Mechanics.
The Main Issue: The basic problem with Quantum Mechanics is that it doesn't really seem to be "about" anything.
In the mathematics of Newtonian Physics you can point to terms in the equations and say, oh that's a force, that's momentum, that's the position of the particle, etc Even the solutions of equations have an obvious meaning, i.e. this is the path the object will take.
In General Relativity it's the same. Yes it might discuss spacetime and four-dimensional curvature, these are abstract and strange. However it is still a narrative about entities changing and developing, they just happen to be very abstract entities.
Quantum Mechanics on the other hand is only "about" probabilities to see results. It just says "in such and such a circumstance when you have equipment set up in a particular way, you have the following chance of seeing this value for that quantity". However it doesn't say how things get those values. It's sometimes not even clear that the values are really a property of the object in question, an atom let's say, or just something you get when your equipment interacts with an atom.
It's not even really clear if an electron is actually an object in quantum mechanics, or just a bunch of probabilities arranged in a certain way, i.e. in certain experiments with equipment arranged a certain way you have a high chance of detecting charge concentrated around a point. However it's not clear that's actually due to you finding a small object with a charge, or is it just something that happens to your equipment in those situations.
This is not just philosophical musing, quantum mechanics itself is genuinely unclear about which is the case.
The following is additional and provided because I have noticed it helps some, but others find it confusing. If it is the latter for you, just ignore: Julian Schwinger in his book "The symbolism of atomic measurement" and Giacomo Mauro D’Ariano in "Quantum Theory from First Principles: An Informational Approach" both derive Quantum Mechanics from first principles as a theory of how a rational agent might assign chances to experimental outcomes, without basically any insight from physics. D'Ariano in particular essentially derives it as the most general mathematical theory of "learning", i.e. updating your knowledge of the world. This provides a clearer picture of the problem to some. What are you learning about? Just experimental results and how "bet on them", or something genuine about the world?
So continuing on, what is difficult when you try to make sense of QM? What aspects make it difficult to see what QM is about?
I realised three posts wasn't going to cut it, but I'm still trying to keep things brief! Apologies!
A brief sketch of QM mathematically will help.
Quantum Mechanics describes the current state of the world as a set of amplitudes. Amplitudes are numbers that when you square them, they give the probability of some event occurring. Right now, since I'm not giving anything an interpretation, that's all they are.
So there's an amplitude for anything of the form: Amplitude to see quantity A in region R have value V at time period T .
A concrete case would be: Amplitude to see the Voltage in this wire be 4.5V between 10:40 and 10:50.
QM might give this an amplitude of -0.2, squaring makes it 0.04. So that's a 4% chance of this happening.
Just note that the amplitudes can be negative, however since we square them to get the probabilities, the probabilities won't be.
The final component is the uncertainty principle. Most quantities come in pairs, like position and moment, voltage and electric potential. When the amplitudes for one are concentrated around one value, meaning that outcome is very likely, the probabilities for the other become more spread out and uniform. Or put another way, as one element of the pair becomes more certain, the other becomes more random. Such pairs are called conjugate variables.
With this in place, I'll begin a list of problems, spread over some posts, before ending with interpretations.
1. What's a particle?
So QM presents a very detached and almost totally observation based picture of a particle. It is simply the case that there are certain "states of the world", that is lists of amplitudes, where a set of quantities co-occur (abstract, but just wait).
So an electron is just a case where the amplitudes say certain equipment will always detect a bit of spin with a bit of electric charge. To then conclude that there is an object, like a little ball, that travels around holding those properties is a mental picture that QM doesn't give any particular support to. This will get more extreme in the two cases below.
The silver oven: Let's say I've set up an oven that burns silver and I build a piece of equipment that can detect spin and charge. I then notice the oven makes the detector click every 30 seconds. So I say I have detected an electron, which the oven produces at a rate of one every 30 seconds. My detector is sensitive enough to narrow the location of the clicks down to the nanometer.
Now, without touching the oven, I go off and get a new detector that can narrow the clicks down to the femtometer and position it outside the oven. So I will continue to get clicks every thirty seconds, but sometimes it will be three clicks. Two with negative electric charge and one with positive. In a particle based view, I have seen two electrons and one positron.
Why though? The oven creating the particles hasn't changed, I've just made the equipment finer in resolution. Now the normal intuitive explanation is that the equipment, by probing so deeply, provided the energy to create the particles, but QM is silent on this. In fact it always presents there being a nonzero amplitude to detect three clicks in a femtometer sized region. The previous equipment just didn't have access to regions of that size, but QM always said the possibility was there.
So what is the oven actually emitting. It's hard not to conclude that its just "some charge and some spin" which will be packaged as single or multiple clicks depending on your equipment.
The beam of light: Take a beam of light. The conjugate variables in the case of light is colour(frequency) and photon number. Hence the higher the probability for the light to be a single colour, the more spread out its probabilities are for photon number. This can be tested with Laser light. Lasers are states of the electromagnetic field that are highly likely to be observed having only one consistent colour. Consequently when you place a photon detector in front of them they have an equal likelihood of producing several values. The exact same beam of laser light could be measured as containing 10 photons one minute and 1000 the next.
Again how many particles are there? Is the possible conclusion that there is no such thing, simply probabilities for clicks?
Similar "uncertain particle count" occurs in all quantum mechanical system of sufficient complexity, for example most atomic nuclei have an indeterminate number of pions inside them. So to what extend can we say what anything is "made of", if particle count isn't fixed?
Ending on a brief point, even Hydrogen in QM is just a state with a set of amplitudes that "often" act like those of a proton combined with those of an electron. However some of the amplitudes for hydrogen events can't be parsed as a combination of those for a proton or an electron. So to what extend is it made of a proton and electron?
In Quantum Mechanics possibilities can interfere. (If the mathematics below is tedious, skip to the bolded point)
Consider betting on a horse to come in various positions in a race, say 1st, 2nd, 3rd in a three horse race. The horse can be fed either Smithson horse food or Johnson horse food.
In the first case his chances of coming in the various positions are: (0.1,0.4,0.5)
i.e. 10% chance of coming first.
In the second case: (0.2,0.4,0.4)
If you don't know which of the brands of food the horse takes, you can combine the above to get: (0.15,0.4,0.45)
So a 15% chance of winning when you aren't sure of which brand he took.
However in the QM case, since amplitudes can be negative, we could have for the first case: (0.316,-0.632,0.707)
and for the second: (0.447,0.632,0.632)
I won't go into how these are combined when the horse could eat either brand of food, but the main point is that the second possibility would cancel out due to the minus signs.
Hence a quantum horse has a chance of coming second if he eats one brand, a different chance of coming second when he eats another brand, but if he could eat either brand he has no chance of coming second at all. It is possible for an outcome to cancel out from two different sets of possibilities,even though it is possible in each of them alone.
This is why the double slit experiment is confusing. There are points on the detection screen that have a chance of being lit up when either slit is open, but not when both are open, because the two events of "particle goes through right slit and hits point A" and "particle goes through left slit and hits point A" have their probabilities cancel out.
If you see the probabilities as purely a reflection of your knowledge, it is very hard to see how this is possible. How by not knowing a binary outcome (Horse food A or B) do I remove something that can happen under either outcome?
The basic problem with Quantum Mechanics is that it doesn't really seem to be "about" anything.
One question which I have regarding the motivation to study and research this stuff is what motivates you to do it? (Thank God that you do, because we wouldn't be where we are as a species without folks such as you!)
Chance as a real force is a myth. It has no basis in reality and no place in scientific inquiry. For science and philosophy to continue to advance in knowledge, chance must be demythologized once and for all. –RC Sproul "A lie can travel half way around the world while the truth is putting on its shoes." –Mark Twain " ~"If that's not sufficient for you go soak your head."~Faith Paul was probably SO soaked in prayer nobody else has ever equaled him.~Faith :)
I've nothing profound to offer on that point unfortunately. I'm motivated to study it the same way I'm motivated to play sports, swim or read fantasy. I just like it. When I hear something from it I just want to know more.
quote:No More Dark Matter? A New Theory of Gravity Could Explain Away Dark Matter and Energy
A New Theory
A new gravitational theory formulated by Erik Verlinde, renowned string theory expert at the University of Amsterdam and the Delta Institute for Theoretical Physics, might just do away with the roles of dark matter and dark energy in explaining the physics of the universe.
Modern physicists haven’t been able to explain why outer regions of galaxies rotate much faster than they should based on the mass and energy of the stars, planets, interstellar gasses, and other matter within them. The best explanation thus far for this strange gravitational behavior has been dark matter, a type of matter that we can’t see and that we haven’t really discovered yet.
Verlinde has a different explanation for these deviations in motion, and he calls his new theory emergent gravity. In his theory, gravity is an emergent phenomenon and not a fundamental force. As such, it’s a product of fundamental bits of information that are stored with the structure of spacetime itself. When those fundamental bits change, gravity emerges.
“We have evidence that this new view of gravity actually agrees with the observations,”says Verlinde in a Delta ITP press release. Indeed, using his theory, he has produced accurate predictions of the velocities of stars rotating around the core of the Milky Way and stars in other galaxies without any need for dark matter. By including an adaptation of the holographic principle within his theory, Verlinde is also able to account for dark energy, the unseen force causing the universe to expand.
A New Paradigm
Our current understanding of gravity is largely based on Einstein’s theory of general relativity. While that theory can explain a lot of the behavior of our universe, it doesn’t hold up when applied to quantum physics, which becomes evident in extreme situations like near a black hole or during the Big Bang. Therefore, Verlinde and many other physicists think that our theory of gravity needs to be updated.
“Many theoretical physicists like me are working on a revision of the theory, and some major advancements have been made,” says Verlinde. “We might be standing on the brink of a new scientific revolution that will radically change our views on the very nature of space, time and gravity.”
Of course, Verlinde’s theory is still just that — theoretical — and it does have its limitations, including an inability to explain large-scale effects like galaxies clustering together. However, it is a plausible path toward reconciling the two pillars of modern physics, Einstein’s theory of general relativity and quantum mechanics, and therefore worth thinking about…even if it might make your brain hurt.
Like many modified gravity theories, recent observations of galaxies like NGC1052-DF2, which obeys General Relativity without Dark Matter, make them less likely to be true.
It's easier to explain them as the presence or absence of Dark Matter, rather than some Galaxies obey General Relativity and others don't.
The theory also has internal problems related to energy-momentum conservation and how realistic it is that quantum systems would have the properties it requires.
EDIT: I should add that there are hints gravity and thermodynamics are related in some way, which this theory is attempting to use. However in its particular case there are the problems I mentioned above.
Okay back to the short posts, since the grunt work was done in the last.
Superposition is just when more than one of the probabilities is non-zero.
So let's say there is a particle that could be spin up or down. Definitely up is (1,0), definitely down is (0,1), a superposition is then something where the amplitudes are like:
If you square the amplitudes you get the chance of each (1/2 for both). So superposition is a case where various outcomes might be measured, i.e. If A,B,C,etc are outcomes it's just the case where the possibilities are
A or B or C or....
However the problem is that unlike "or" in normal probability, the separate outcomes can affect each other (interference above) or create new behaviour not possible in either.
For example in some atoms, there is a special frequency of light that when the outer shell of electrons has spin up the light is passes through, when it is spin down the light the light passes through, but when it is spin up or spin down the light is reflected. So "or" can create totally new behaviour.
Think about this if it were applied to everyday objects. Drug A doesn't cure a certain disease, Drug B doesn't cure it either. However if the drug was put in a box where nobody knew which one it was, i.e. it was "Drug A or Drug B", that did cure the disease.
It would mean double blind studies couldn't be done, because they'd create new effects (and indeed you can't do the equivalent of double blind tests on quantum objects)
If you combine 2. and 3. together, we can see that although QM describes things probabilistically, it is very hard to attribute this probability purely to lack of knowledge, since altering probabilities can destroy behaviour present in two of the outcomes, or create behvaiour present in neither.
And here ends the difficulties, probably the major one. It is really just superposition applied to states of more than one object.
If I have two electrons, I can have four possible states for their spin:
Up, Up Up, Down Down, Up Down, Down
An entangled state is one like (using the order above):
(0.707, 0, 0, 0.707)
A half chance for both to be up and a half for both to be down.
States like this are a complex subject, but the essential point about them is that they are highly correlated. Many explanations of these types of states assume an interpretation, so I am going to give a completely interpretation neutral description.
Imagine a pair of gloves are made in a machine. One is the left hand glove, one is the right hand glove and one is red and one is green. They are each locked in a box and shipped to China and Chile. A scientist in Chile lowers a spectroscopy unit into the box and discovers his glove is red. Obviously he knows the one in China is green. However it's still 50:50 as to whether the Chinese glove is left or right handed.
Pairs of quantum particles are more strongly correlated than this. In the "Quantum Glove" case learning your glove is red not only tells you the other is green, but gives you a 75:25 chance that the other is left vs right handed, i.e. you learn a little about the properties you didn't measure.
The really confusing thing is that this only works for two gloves, not one on its own. If you had just made one quantum glove, finding out that it was red would still leave handedness 50:50
So learning one of a set of 50:50 binary options for one of the objects actually improves the odds for an unmeasured aspect of the other object. It is very difficult to understand how this could be the case. How do I affect and improve the probabilities for something I didn't even measure? In QM two objects can be so correlated that separate properties get linked. Learning about one means you learn a bit about the other, but only when you have two objects.
With this done, there is one more post. The interpretations.