Make that tree posts.
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ME: but how does it follow that the wavefunction can be split up from this experiment, while retaining connection to the mass?
The key to resolving this is shifting your perspective away from thinking of the wavefunction as a âthing traveling through 3D spaceâ and recognizing that the entire concept of mass is an artifact of the wavefunctionâs structure.
The connection between the wavefunction and mass is never broken because mass does not exist independently of the wavefunctionâs mathematics. [1]
Here is exactly how the split occurs while retaining a perfect connection to the mass:
1. The Splitting Happens in Hilbert Space, Not Physical Space [ 1]
- No Scissors in 3D Space: When a wavefunction âsplits,â it is not like a piece of bread being torn in half across left and right directions in a room.
- The Configuration Dimension: The splitting happens in a mathematical arena called Hilbert space. The wavefunction branches into two completely independent mathematical states (or phases).
- Two Sets of Answers: Instead of splitting the âstuffâ of the particle, the wavefunction splits into a superposition of two different âhistories.â Each history contains the full mathematical command for an electron. [1, 2, 3, 4]
2. Mass is the âFrequencyâ of the Wavefunction [ 1]
In quantum mechanics, mass is not an internal heavy core. According to the de Broglie relations and Einsteinâs E=mc^2, mass is directly proportional to the frequency of the waveâs oscillation:
f=\frac{mc^{2}}{h}
- Splitting the Wave vs. Splitting the Frequency: Imagine a sound wave splitting as it travels down two separate hallways in a house. The volume (amplitude) of the sound decreases in each hallway, but the pitch (frequency) remains exactly the same.
- Mass Is Preserved Like Pitch: In the Quantum Cheshire Cat experiment or a Many-Worlds split, the amplitude decreases (thinning), but the internal frequency of the wave packet in each branch is totally unchanged. Because the frequency does not change, the mass measured in that branch is mathematically guaranteed to remain exactly 9.11 \times 10^{-31}\text{ kg}. [1, 2]
3. How the âCheshire Catâ Keeps the Mass Tied
In the neutron version of the Cheshire Cat experiment (where the particle has a real rest mass): [1, 2]
- The mass/energy properties are tied to the neutronâs spatial path (where the wave packetâs center of mass is moving).
- The spin/polarization properties are tied to the neutronâs internal phase data traveling down the other path.
- The connection isnât broken because the master wavefunction still spans both paths simultaneously. The mass hasnât decoupled from the quantum state; it has just decoupled from the specific spin property. The branch with the mass still has its exact mass because its internal frequency is perfectly preserved. [1, 2, 3, 4, 5]
4. The MWI Conclusion
In the Many-Worlds Interpretation, there is only one single universe that contains a highly complex, multi-branched wavefunction. [1, 2]
- There are not multiple physical electrons being duplicated.
- There is only one electron field, behaving in a superposed way.
- When you look at the branch you are in, you are interacting with a slice of that field that is vibrating at the exact frequency of an electron. Thus, you perceive 100% of its mass.
but the experiment just showed that the mass could exist separately of the wavefunction.
That conclusion is a common misconception, but it is actually the exact opposite of what the physics proves. The mass never exists separately from the wavefunction.
In quantum mechanics, if you remove the wavefunction, the mass completely vanishes. The Quantum Cheshire Cat experiment demonstrates that mass can exist separately from another property (like magnetic spin or polarization), but both of those separated components are still entirely composed of the wavefunction. [1, 2, 3]
Here is how the experiment proves that mass remains deeply anchored to the wavefunction:
1. What Actually Travels Down the Two Paths?
The experiment uses a beam splitter to divide a particle (like a neutron, which has rest mass) into two separate paths. [1, 2]
- Path A (The âBodyâ): Contains a piece of the wavefunction that carries the mass, energy, and momentum operators.
- Path B (The âGrinâ): Contains a piece of the wavefunction that carries the magnetic spin operator. [1, 3]
The mass is not traveling down Path A as a naked, classical little ball without a wave. If you were to block Path A with a wall, the mass would hit it, because that path contains the spatial components of the wavefunction. The mass exists on Path A because a piece of the wavefunction is there to define it. [, 2]
2. Mass is a Numerical Property, the Wavefunction is the Substance [ 1]
You cannot have âmassâ floating through a lab without a wavefunction, any more than you can have the number â5â floating through a room without five physical objects.
- The Wavefunction is the Fabric: The wavefunction is the actual quantum field or physical substance.
- The Mass is a Measurement: Mass is just a value you get when you look at how that substance interacts with gravity or accelerates.
When the experiment splits the particle, it splits the wavefunctionâs data. It sends the âwhere the mass interactsâ data down Path A, and the âhow the magnet spinsâ data down Path B. [1, 2]
3. The Proof: Interfacing with the Mass Destroyed the Wavefunction [ 1, 2]
If mass could exist completely independently of the wavefunction, you could touch, block, or weigh the mass in Path A without affecting the quantum wave.
However, when physicists put a physical absorber (a filter) in Path A to prove the mass was there, it immediately altered the final interference pattern of the experiment. This proves that the mass in Path A was intimately, mathematically bound to a live, active piece of the wavefunction. [1]
Why This Matters for Many-Worlds
This experiment reinforces the Many-Worlds Interpretation rather than breaking it. It shows that the wavefunction is a highly complex package of different data types (mass, charge, spin). [1, 2]
When a universe splits, the wavefunction doesnât lose its connection to mass; it simply creates two branches where the mass data and the spin data can be manipulated independently, but always remaining fully enclosed inside the mathematics of the quantum state. [1, 2]
ME: but you earlier said this: âIn the standard mathematical framework of quantum mechanics (Dirac notation), a system is described by two completely different things:The State Vector (\vert{}\Psi\rangle): This is the wavefunction. It contains the probability amplitudes (the âweightsâ). This is what splits and thins out.The Operator (\^{M}): This is the mathematical matrix representing a physical property, like mass. It is a universal constant of nature that never changes, never splits, and never thins out.â
You caught a profound and very subtle distinction in the physics. It looks like a contradiction, but it reveals the exact line between pure mathematics and physical reality.
When we say the operator is completely separate from the state vector, we are talking about the abstract math tool. When we say mass cannot exist without the wavefunction, we are talking about the physical measurement.
Here is how those two statements fit together perfectly without contradicting each other:
1. The Operator is a Question, the Wavefunction is the Substance
Think of the operator (\^{M}) as a question written on a piece of paper, and the state vector (\vert\Psi\rangle) as the physical object you are studying.
- The Operator (\^{M}): The question is: âWhat is the mass of an electron?â This question is a universal mathematical constant. It never changes, it never splits, and it exists independently of whether there is an electron in the room or not.
- The Wavefunction (\vert\Psi\rangle): This is the actual physical electron field existing in the lab.
To get a physical reality (an answer), you must apply the question to the object: \hat{M}\vert\Psi\rangle.
- If you have a wavefunction, the math gives you an answer: 9.11 \times 10^{-31}\text{ kg}.
- If you remove the wavefunction entirely, you are left with an empty question (\^{M}) but zero physical mass in the room. The operator exists as a concept, but no physical object possesses that mass.
2. What Happened in the Cheshire Cat Experiment?
In the Cheshire Cat experiment, the wavefunction (\vert\Psi\rangle) was split into two spatial paths:
|\Psi \rangle =|\text{Path\ A}\rangle +|\text{Path\ B}\rangle
The universal operators for Mass (\^{M}) and Spin (\^{S}) did not change or split. They are just the eternal rules of physics. However, when we apply those unchanging rules to the split wavefunction, the math dictates:
- Applying the Mass operator to Path A gives a real number: \hat{M}\vert\text{Path A}\rangle = \text{Mass}.
- Applying the Mass operator to Path B gives zero: \hat{M}\vert\text{Path B}\rangle = 0.
The mass only manifested in Path A because the piece of the wavefunction in Path A was configured to answer âyesâ to the mass question. The mass did not escape the wavefunction; it was realized by the specific configuration of the wavefunction in that specific path.
3. The Resolution
The mathematical tool (the operator) is disconnected from the probability states. But the physical property (the actual mass you can touch or block) requires both parts to exist.
You cannot have a physical mass without a wavefunction, because the mass is the numerical answer you get when the universal, unchanging operator interacts with a living, breathing quantum state.
This distinction is the gateway to understanding how the universe can branch. If you want to keep pushing this boundary, let me know if we should explore:
- How the Schrödinger Equation forces the wavefunction to change over time while keeping the operators completely frozen (The Schrödinger Picture).
- The opposite view, where the wavefunction stays frozen and the operators change (The Heisenberg Picture).
ME: âThe mathematical tool (the operator) is disconnected from the probability states. But the physical property (the actual mass you can touch or block) requires both parts to exist.â so - in mathematics they can be treated as separately, but in experiment they must come together eventually?
Exactly. You have perfectly captured the bridge between the mathematical theory of quantum mechanics and what actually happens in a real-world laboratory.
In pure mathematics, they are treated as separate entities. But in a physical experiment, they must come together to produce a real, measurable result.
Here is how this relationship works between the blackboard and the laboratory:
1. In Mathematics: The âActionâ Separates Them
On paper, the operator and the state vector are completely different mathematical species.
- The State Vector (\vert\Psi\rangle): This is a column vector (a list of numbers) that holds the probabilities. It evolves, changes shape, splits, and thins out over time.
- The Operator (\^{M}): This is a square matrix (a grid of unchanging numbers). It acts like a mathematical machine.
- The Separation: You can write down the matrix for mass (\^{M}) on a blackboard without ever defining what the state vector looks like. They are separate concepts.
2. In Experiment: The âMeasurementâ Unites Them
In a lab, you can never look at a state vector directly, and you can never touch an operator directly. You can only observe what happens when they interact.
- The Physical Act: When a physicist turns on a detector to measure mass, the physical apparatus forces the unchanging âruleâ (the operator) to physically interact with the quantum system (the state vector).
- The Output: This interaction forces the system to yield a real, physical number (the mass) that you can record.
- The Requirement: To get a real measurement, you need both. If you have the operator but no wavefunction, your detector reads zero (empty space). If you have a wavefunction but no operator, no measurement is happening, and the particle remains a silent cloud of possibilities.
3. How This Finalizes the Many-Worlds Picture
This is exactly why the Many-Worlds Interpretation is mathematically consistent:
- The Splitting: The mathematics allows the state vector to split into thinned-out branches.
- The Measurement: When you, the observer, exist inside one of those thinned-out branches, your body and your lab equipment are part of that same thinned-out state vector.
- The Result: When you perform an experiment, the unchanging universal mass operator acts on your specific branch. Because the math of the operator is a constant, it multiplies your thinned-out reality by 100% of the electronâs mass.
To you, the mass feels solid and fully intact because the mathematical tool and the probability state have come together inside your branch to create your specific reality.
ME: So then, whereas in mathematics you can split up the probability distribution in its mathematical âstateâ where it is separate from the mass, but in experiment - how would a waveform split up in many realities, reconnect to the mass?
The short answer is: the thinned-out waveform does not need to âreconnectâ to the mass, because it never lost it.
The confusion comes from thinking that a split wavefunction becomes an âempty ghostâ that needs to find a chunk of physical mass to become real again. In quantum mechanics, it works the exact opposite way: the mass is embedded inside every single branch from the moment the split happens.
Here is the exact mechanism of how this works in an experiment and across many realities:
1. Mass is Already Inside Every Branch
When a wavefunction splits into multiple realities, it does not split the mass like a piece of cake. Instead, it replicates the mathematical configuration that defines mass. [1]
- The Math: If a universe splits into Branch A and Branch B, the total state is:
|\Psi \rangle =\alpha |\text{Reality\ A}\rangle +\beta |\text{Reality\ B}\rangle
- The Physical Reality: The mass operator (\^{M}) is a universal law of nature. It simultaneously blankets the entire multiverse. Therefore, the moment the split occurs, the operator is already interacting with both branches at the same time:
\^{M}|\text{Reality\ A}\rangle =\text{Full\ Mass}
\^{M}|\text{Reality\ B}\rangle =\text{Full\ Mass}
- There is no âreconnectionâ phase. The property of mass is instantly and fully realized in both realities the exact millisecond they diverge. [1]
2. How the Experiment Forces the Meet-Up
In a real laboratory experiment (like the Quantum Cheshire Cat or a particle detector split), the âreconnectionâ you perceive is actually just the process of quantum measurement (or decoherence).
- Step 1 (The Split): A particle hits a beam splitter. The wavefunction divides into two paths. At this exact moment, the universe has already branched. In Reality A, the particle went left. In Reality B, the particle went right.
- Step 2 (The Entanglement): You, the scientist, are standing in the lab. When the particle hits a detector on the left path, your physical body, your eyes, and your computer become entangled with that path.
- Step 3 (The Multi-Realities): You instantly split along with the wavefunction.
- In Reality A: You see a flash on the left detector. You apply your local measuring tools, the mass operator interacts with your branch, and you register 100% of the mass.
- In Reality B: You see a flash on the right detector (or no flash at all). You measure 100% of the mass over there. [1, 2, 3, 4, 5]
3. The âVolumeâ Analogy
Think of the universal wavefunction as a massive digital audio file, and âmassâ as the pitch of a musical note (e.g., 440 Hz).
- If you copy that audio file into two different folders on your computer, you have split the file into two ârealities.â
- If you turn the volume down to 1% on one of the files, you have âthinned it outâ (reduced its probability amplitude).
- When you finally double-click and play that thinned-out file, the pitch is still exactly 440 Hz. The file didnât need to âreconnectâ to the pitch; the pitch was a fundamental characteristic of the data structure itself.
In Many-Worlds, your branch might have a very small global âvolumeâ (probability weight), but because your brain, your hands, and the particle are all turned down to the exact same volume, the mass sounds perfectly loud, solid, and intact to you.
ME: so how do you define the part that thins out?
In the mathematics of quantum mechanics, the part that thins out is called the probability amplitude, which is represented by the coefficients (numbers) attached to each branch in the state vector.
To define exactly what this âthinning partâ is and how it behaves, physicists break it down into three specific properties:
1. The Mathematical Definition: The Coefficient
When a quantum state splits, it is written as a combination of branches, each multiplied by a complex number (usually written as \alpha , \beta , or c_{n}):
|\Psi \rangle =\alpha |\text{Universe\ A}\rangle +\beta |\text{Universe\ B}\rangle
- The Component: The âpart that thins outâ is \alpha and \beta .
- The Squaring Rule: According to the Born Rule, if you square the absolute value of this number (\vert{}\alpha\vert{}^2), you get the exact probability of an observer finding themselves in that specific branch.
- The Thinning Process: Before a split, a single branch has a weight of 1 (100\% reality). After a series of constant quantum splits, that number might drop to 0.00001. That numerical drop is the âthinning.â
2. The Physical Definition: âMeasure of Existenceâ
Because the Many-Worlds Interpretation treats the wavefunction as an objectively real, physical thing, physicists like David Deutsch and Sean Carroll define this thinning part as the measure or âthickness of realityâ of a branch.
- Not Physical Density: It does not mean atoms become less dense, farther apart, or translucent.
- A Slice of the Multiverse: It defines how much âroomâ or âvolumeâ that specific history occupies within the entire, global multiverse.
- Relative Thickness: It is a measure of the branchâs capacity to influence other quantum states before decoherence completely isolates it.
3. The Conceptual Analogy: The âShareâ of the Pie
The absolute easiest way to define the part that thins out without using complex matrices is to think of it as a corporate share or a fraction of a pie.
- The Whole Pie: The universal wavefunction is a single pie. Its total size is always exactly 1 (100\%).
- The Splitting: When a quantum event occurs, the pie is sliced. One slice goes to Universe A, and one slice goes to Universe B.
- The Share: The part that âthinned outâ is simply the size of your slice relative to the whole pie.
- The Inhabitantâs View: If you are a microscopic observer living inside one of the crumbs on Slice A, you cannot see the other slices. You look around your crumb, and to you, it feels like a complete, solid, 100\% physical world. You have no direct way of knowing that your entire slice only represents 1\% of the total original pie.
In summary, the part that thins out is strictly the probabilistic weight (amplitude) of the branch. It governs the global probability of the universeâs configuration, while leaving the internal, local physical properties (like mass) completely untouched.
ME: so is this probability amplitude the wavefunction?
Yes, but with one crucial distinction: The probability amplitude is the numerical value of the wavefunction at a specific point or for a specific branch.
To use a precise analogy: if the wavefunction is a physical wave in the ocean, the probability amplitude is the exact height of the wave at a single, specific location.
Here is the exact mathematical and physical breakdown of how they connect:
1. The Mathematical Relationship
In quantum mechanics, the wavefunction (usually written as the Greek letter \Psi ) is a mathematical function.
- The Wavefunction (\Psi ): This is the entire object. It describes the whole cloud of possibilities across space and time. It is a map of numbers.
- The Probability Amplitude: This is the specific value you extract from that map for a particular state.
For example, if you look at a wavefunction for a single particle, the wavefunction tells you the amplitude for every possible position. If you pick one exact spot, the number at that spot is the probability amplitude.
2. How It Defines âThinningâ in Many-Worlds
When we talk about the Many-Worlds Interpretation and branches âthinning out,â we are tracking how this amplitude shifts:
- The Full Wave: The total universal wavefunction (\Psi _{total}) never shrinks, never loses energy, and never thins out. Its total value across the multiverse is always perfectly conserved.
- The Shifting Amplitudes: When a quantum event causes a split, the wavefunction redistributes its values. The amplitude of the specific branch you live in becomes a smaller fraction of the whole.
3. The Core Concept: Amplitude vs. Probability
It is vital to remember that the amplitude itself is a complex number (it involves the imaginary number i, the square root of -1). Because of this, an amplitude cannot be a direct probability, because probabilities must be real percentages between 0% and 100%.
- The Amplitude (The Wavefunctionâs Value): Can be a negative or imaginary number (e.g., i/2).
- The Probability (The Reality): To get the actual probability of a branch, you must square the absolute value of the amplitude (\vert{}i/2\vert{}^2 = 1/4, or 25%). This is the Born Rule.
So, when a world splits, the wavefunction changes its shape, causing the probability amplitude of your specific branch to drop. That drop in amplitude is exactly what constitutes the âthinning outâ of a reality.
