Here is an experiment.
Say you have a photon, a particle of light, and it decays into a positron and an electron. The electron spins in one direction and the positron spins in the opposite direction. You know that the spins are opposite because the photon had zero spin, so to preserve angular momentum, their spins have to be the same value and in opposite directions.
And here is the Quantum Probability Mechanics >>
Without looking, there is no way to know if the electron is spin up or down, or whether the positron is spin up or down, since a photon decay can lead to either of these two alternatives:
Possibility: A. Electron is up and positron is down ... or
B. Electron is down and positron is up.
They have to be opposite. That is the only requirement. Quantum Theory does not violate the Law of the preservation of angular momentum.
We label A as Quantum state A, and B as Quantum state B. We can regard the electron-positron system as ONE physical system. And we can then say that this system is either in Quantum State A or Quantum State B. Remember that this ONLY means what I stated above. Mainly, that there are two possibilities:
Possibility: A. Electron is up and positron is down ... or
B. Electron is down and positron is up.
Because both quantum state A or B are possible, you cannot know which one happened until you look. Definitely, one or the other one did happen, in reality. You just don't know which because either thing could have happened. This is a very important point. Observation does not create reality. The only reason that you cannot know which until you look is because the law of Physics that describes the decay of a photon does not make a unique prediction, since nature is probabilistic and not deterministic.
Looking lets you either verify or not the predictions of the quantum theory, by doing the experiment over and over again and building up an empirical statistical table of results.
In Quantum Theory, even though you have not looked at the electron or positron, a physical system is still described. A mathematical object is still used to stand for the electron-positron system even though we don't know if it is in state A or B.
Again: State A >> The electron has spin up and the positron has spin down.
State B >>>>>>> The electron is spin down and the positron is spin up.
When we are in a state of "ignorance" like this, due to the probabilistic nature of Reality, we describe the state of the system when it is not being measured as State a plus State B = some State S.
Or Quantum State S = quantum state A + Quantum State B.
or just
S = aA + bB, . . equation 1
where small a and small b are numbers that are calculated from a formula in Quantum Theory. These small numbers are calculated from the application of the Quantum Theory to the specific physical situation and tells us the probability that, since measure, the electron will either be spin u or down.
Summary:
We are trying to find out if either electron is spin up or spin down. Once we know that, we know that the positron is the opposite, by the law of the conservation of angular momentum. The mathematical object S is defined by equation 1. You do not need to know what it is. You just need to know what I have written so far.
The photon has disintegrated, and one electron has flown off in one direction, and the positron has flown off in the other direction. For clarity, assume that they are now a few million miles away from each other.
By solving a Quantum Field equation, we can derive S as a mathematical function from which we can deduce the probability that the electron-positron system is in state A or B.
From the form of the equation, we can derive the probability that it is in state A from the small a, and the chance that it is in state B by the small b.
Step 1: measure the spin of either particle.
Step 2: repeat this experiment over and over again and tabulate the results.
Step 3: compare the predictions (a and b) with the empirical data.
Then conclude whether, as the number of experiments increases, the data converges to the probability predictions a and b.
Note that you only have to measure the spin of either the electron or positron. You can assume that the other particle will have the opposite spin. If it doesn't, then you have done the experiment wrong.
So now the question is: Where is this mysterious "quantum entanglement"? There is none. It only shows up if you interpret the above procedure within a weird modern context: mainly, that the S function represents a real physical quantity that exist in space.
So ....
Before you observe either the electron or the positron, the system is in a state (or mathematical object) S that is mathematically in a combination (what mathematically is called a "superposition" ) of both states, given by equation 1. The mathematical object A describes electron-up-and-positron-down, and B is (like I said above) the state of the system when you have electron-down-and-positron-up. I am just repeating and summarizing what I have already written.
The popular interpretation of a superposition of States (eq.1) is that, before you observe a system like S, the system is in a physically undefined physical state. The electron and the positron are both up and down at the same time. This is the equivalent of saying that the Schrodinger cat is both alive and dead before you open the box and take a look.
This contradicts the Probability Interpretation (proposed by Born and Von Neuman 100 years ago but ignored today) that S describes a probability prediction. Why was this view discarded? Because they did not know what I have proposed as the basis of why Probability is needed. This is my contribution: That since the cat can be both dead and alive, you can't know which until you open the box. The key word is "can." The cat is either alive or dead, not both, before you open the box. You just don't know which because from the initial conditions, the physical process can lead to two (or more results), not just one.
This is my Indeterminism Interpretation of Quantum Theory. The system is either electron-up-and-positron-down or electron-down-and-positron-up. You just don't know which until you make an observation because the physical process of photon decay can lead to either consequence.
And a superposition of states describes our uncertainty in the outcome (again) because a physical process can lead to more than just one outcome. Such a view is completely contained in the Math of Quantum Theory. And most important, you do not lose the view that Reality is not created by observation nor consciousness. Sure, we disturb physical systems by an observation, but observation is also a physical process, which has to be described also by a Quantum Field Interaction process.
So the current interpretation is this:
The electron and the positron are (say) hundreds of light years apart, described by S (eq.1).
When you make a measurement, S changes (for example) to state A. That is, the physical system changes from being both A and B to just A.
That is, we perform a single experiment and see that the electron is spin up. Then, a hundred light years away, the positron instantaneously changes from being both up and down at the same time to being just spin down. Not only are both particles locked across hundreds of light years, but measuring one changes the state of the other right away, breaking the law of Local Causality. Wow.
But this is all wrong. When we see that the electron is spin up, we are just gathering one bit of data. We have to gather tons of data to verify or not the probability prediction from the object S. And of course, we know that the positron must then be spin down because of the conservation of angular momentum.
Before we observe a system that can be in more than one possible state, we describe it as in a superposition of states only because the mathematical modeling works, not because in reality, they are really in both states at once.
Before you open the box, the Schrodinger cat is either alive or it is dead, not both ... because it can be in either one, since nature does not evolve in time deterministically. It is described as as in a superposition, sure, but the plus term in equation 1 does not imply that Reality is fuzzy. It implies only that our knowledge is "fuzzy," because we don't know -- we can't know -- what is happening without observing it because one or more things could have happened.
A Short Story
Inspired by the song HOTEL CALIFORNIA
by the Eagles
The desert stretched endlessly before me, a blackened sea of sand under a moonless sky. My old pickup rattled along the desolate highway, the cool wind whipping through my hair, carrying a strange, sweet scent, like burning herbs, sharp and intoxicating.
Colitas, maybe, though I didn’t know the word then. It curled into my lungs, making my thoughts hazy. Up ahead, a faint light flickered, a beacon in the void. My eyelids drooped, my vision blurred, and the weight of exhaustion pressed me down. I had to stop. I didn’t have a choice.
The building materialized like a mirage, a sprawling, dilapidated structure, its neon sign buzzing faintly: Hotel. The light shimmered, unnatural, pulling me closer. I parked and stumbled out, my legs heavy as lead. At the doorway stood a woman, her silhouette framed by the dim glow of the entrance.
Her eyes glinted, sharp and unblinking, like a predator’s. A distant bell tolled, low and mournful, vibrating...
I appreciate your perspective and your emphasis on the metric tensor as the central factor in spacetime dilations, and I acknowledge your understanding of the distinction between kinematic and gravitational effects. Your interpretation that all space and time dilations are caused by the metric tensor is indeed consistent with the mathematics of General Relativity (GR), as the metric tensor ( g_{\mu\nu} ) fully describes the geometry of spacetime, which governs all relativistic effects, including time dilation. Let me align with your viewpoint, clarify the role of the metric tensor in the scenario, and address the time dilation between the two clocks at the same spatial location, ensuring we stay consistent with the mathematics.
Your Scenario and the Metric Tensor
You’ve specified two clocks at the same spatial location in a given coordinate system, with Clock 1 at rest and Clock 2 in motion relative to that system. The metric tensor ( g_{\mu\nu} ) defines the spacetime geometry at that point, and all time dilation effects are indeed encoded in ...
Oh, Peg, you’re standing there in the spotlight’s glare, aren’t you? The camera loves you, they say, and who am I to argue?
Your face, all sharp cheekbones and that practiced pout, is plastered across the call sheets, the casting director’s desk, the daydreams of every nobody who ever wanted to be a somebody.
You’ve got that role, Peg, the one you clawed your way through auditions for, the one you cried over in that dingy Hollywood motel when you thought the callback wasn’t coming.
It’s a big part, they tell you, big enough to make people whisper your name in line at Schwab’s, big enough to get you that photoshoot with Vanity Fair.
You’re on the cusp, Peg, teetering on that razor’s edge where dreams either bloom or bleed out. But you know how this town works, don’t you? You’ve seen the ghosts of starlets past, their faces fading from billboards, their names scratched off the marquee.
I see you now, Peg, in that rented gown, posing for the magazine spread. The photographer’s ...
