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By contrast the Many Worlds Theory only makes one assumption, Schrodinger's Equation means what it says. So Many Worlds wins.
It also makes the assumption that the eigenvalues of a measurement are realized probabilistically.
Brent
On 12/19/2021 5:25 AM, John Clark wrote:
By contrast the Many Worlds Theory only makes one assumption, Schrodinger's Equation means what it says. So Many Worlds wins.> It also makes the assumption that the eigenvalues of a measurement are realized probabilistically.
What is the eigenvalue of a temperature of 72°F? It doesn't have one. A measurement doesn't have an eigenvalue but a matrix does, such as the one that describes the Schrodinger Wave. And no quantum interpretation needs to assume there is a relationship between the square of the absolute value of that wave and probability because it is observed to be true.
> The Born Rule cannot be derived from the Schrodinger equation; it has to be added as a further independent assumption. So it is not true that Many Worlds makes only one assumption.
> The Born Rule cannot be derived from the Schrodinger equation; it has to be added as a further independent assumption. So it is not true that Many Worlds makes only one assumption.No quantum interpretation needs to derive the Schrodinger Equation nor does it need to be assumed because it can be experimentally verified to be true. And no quantum interpretation is inconsistent with observation, at least not so far.
On Sun, Dec 19, 2021 at 7:59 PM Brent Meeker <meeke...@gmail.com> wrote:
On 12/19/2021 5:25 AM, John Clark wrote:
By contrast the Many Worlds Theory only makes one assumption, Schrodinger's Equation means what it says. So Many Worlds wins.> It also makes the assumption that the eigenvalues of a measurement are realized probabilistically.
What is the eigenvalue of a temperature of 72°F? It doesn't have one. A measurement doesn't have an eigenvalue but a matrix does, such as the one that describes the Schrodinger Wave. And no quantum interpretation needs to assume there is a relationship between the square of the absolute value of that wave and probability because it is observed to be true.
A temperature operator, which would be matrix, might very well
return 72degF as the eigenvalue of a state eigenvector. It's
Hermitean operators that have eigenvalues and eigenvectors.
Decoherence theory shows that interactions with an environment
approximately diagonalize a density matrix, I don't think anyone
has shown how the Hamiltonian of the system+instrument+environment
does this; they just sort of assume that it does. Zeh has
proposed a Darwinian selection like effect but I don't see how
it's worked out as the level of the Schroedinger eqn.
Yes, it's empirically supported; So's the Schroedinger equation.
But it's part of the application of the Schroedinger equation.
It's not in the equation itself.
Brent
If it were not true Schrodinger's Wave would be completely useless and there would be no reason any physicist would bother to calculate it.
John K Clark See what's on my new list at Extropolis
eqa
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On Sun, Dec 19, 2021 at 9:05 PM Bruce Kellett <bhkel...@gmail.com> wrote:
> The Born Rule cannot be derived from the Schrodinger equation; it has to be added as a further independent assumption. So it is not true that Many Worlds makes only one assumption.
No quantum interpretation needs to derive the Schrodinger Equation nor does it need to be assumed because it can be experimentally verified to be true. And no quantum interpretation is inconsistent with observation, at least not so far.
It can't be experimentally verified that the other world branches exist and the Schrodinger equation cannot be verified except statistically by assuming the Born rule. Without the Born rule the Schroedinger equation just says that a lot of mutually contradictory possibilities have evolved in the state vector.
Brent
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On 20-12-2021 03:05, Bruce Kellett wrote:
> The Born Rule cannot be derived from the Schrodinger equation; it has
> to be added as a further independent assumption. So it is not true
> that Many Worlds makes only one assumption. It requires just as many
> assumptions as collapse theories.
>
> Bruce
Yes, but with those assumptions it yields an unambiguous framework for a
fundamental theory. In case of collapse theories, you're stuck with a
phenomenological theory that cannot be improved, because you are not
allowed to describe observers and observations within the collapse
frameworks.
Without invoking MWI which I adore, let us focus upon the less grandiose and ask can one entangle a tardigrade or can't one?
>>> The Born Rule cannot be derived from the Schrodinger equation; it has to be added as a further independent assumption. So it is not true that Many Worlds makes only one assumption.>> No quantum interpretation needs to derive the Schrodinger Equation nor does it need to be assumed because it can be experimentally verified to be true. And no quantum interpretation is inconsistent with observation, at least not so far.> Why do we need any theory at all then? We just have to observe the experimental results and they are true. Perhaps science is about understanding the experimental results, not just accepting them as the truth.
> >> It also makes the assumption that the eigenvalues of a measurement are realized probabilistically.
>> What is the eigenvalue of a temperature of 72°F? It doesn't have one. A measurement doesn't have an eigenvalue but a matrix does, such as the one that describes the Schrodinger Wave. And no quantum interpretation needs to assume there is a relationship between the square of the absolute value of that wave and probability because it is observed to be true.> A temperature operator, which would be matrix, might very well return 72degF as the eigenvalue of a state eigenvector.
> Yes, it's empirically supported; So's the Schroedinger equation. But it's part of the application of the Schroedinger equation. It's not in the equation itself.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/8cffa6afc016a115e5fa8bd104135059%40zonnet.nl.
The Born rule, understood as probabilities are predicted by state
vector amplitudes squared, is not a problem. Gleason's theorem
shows that this is the only mathematically consistent probability
measure on a Hilbert space. The other part of the Born rule, that
QM results are probabilistic and depend only on the state
vector, does not follow from Schroedinger's
equation, although they are natural and well tested hypotheses.
Where I have doubts about Everett and many-worlds is (1) the
many-worlds are NOT observable and have no empirical content and
(2) the diagonalization of the density matrix seems to beg the
question of how the Schroedinger equation defines a measurement
just as much as the projection postulate. Nobody writes down the
Hamiltonian of the instrument and the interaction explicitly and
applies the Schroedinger equation; they just assume the
Hamiltonian of the instrument and the interaction are such as to
act like a projection operator. Dieter Zeh has suggested that
there is a kind quantum Darwinism that produces this result, but
I've not seen an explicit calculation showing it.
Brent
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> >> It also makes the assumption that the eigenvalues of a measurement are realized probabilistically.
>> What is the eigenvalue of a temperature of 72°F? It doesn't have one. A measurement doesn't have an eigenvalue but a matrix does, such as the one that describes the Schrodinger Wave. And no quantum interpretation needs to assume there is a relationship between the square of the absolute value of that wave and probability because it is observed to be true.> A temperature operator, which would be matrix, might very well return 72degF as the eigenvalue of a state eigenvector.
A temperature measurement taken at a particular time and place is not a temperature operator, and a measurement is not a probability, although the square of the absolute value of a wave function might tell you the probability of you getting that temperature measurement at that time and place.
> Yes, it's empirically supported; So's the Schroedinger equation. But it's part of the application of the Schroedinger equation. It's not in the equation itself.
I don't know what you mean by that.
It's the projection postulate in the Copenhagen interpretation
that applies the Born rule. In MWI it's the Born rule plus some
kind of self-locating uncertainty to allow for the probabilistic
observations. So those are things not in the Schroedinger
equation.
No, you can't observe the Born rule to be true any
more (or less) than you can observe Schroedinger's equation to
be true. They are theories that predict a result in every time
and place, past and future. If they fail, even on a set of
measure zero, in this infinitude they are invalidated. Every
theory must go beyond what has been observed to be
useful...that's the whole point of having theories instead of
just catalogues of observations.
Brent
On 12/20/2021 7:17 AM, John Clark wrote:
> >> It also makes the assumption that the eigenvalues of a measurement are realized probabilistically.
>> What is the eigenvalue of a temperature of 72°F? It doesn't have one. A measurement doesn't have an eigenvalue but a matrix does, such as the one that describes the Schrodinger Wave. And no quantum interpretation needs to assume there is a relationship between the square of the absolute value of that wave and probability because it is observed to be true.> A temperature operator, which would be matrix, might very well return 72degF as the eigenvalue of a state eigenvector.
A temperature measurement taken at a particular time and place is not a temperature operator, and a measurement is not a probability, although the square of the absolute value of a wave function might tell you the probability of you getting that temperature measurement at that time and place.
> Yes, it's empirically supported; So's the Schroedinger equation. But it's part of the application of the Schroedinger equation. It's not in the equation itself.
I don't know what you mean by that.
It's the projection postulate in the Copenhagen interpretation that applies the Born rule. In MWI it's the Born rule plus some kind of self-locating uncertainty to allow for the probabilistic observations. So those are things not in the Schroedinger equation.
No, you can't observe the Born rule to be true any more (or less) than you can observe Schroedinger's equation to be true. They are theories that predict a result in every time and place, past and future. If they fail, even on a set of measure zero, in this infinitude they are invalidated. Every theory must go beyond what has been observed to be useful...that's the whole point of having theories instead of just catalogues of observations.
Brent
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On Tue, 21 Dec 2021 at 09:56, Brent Meeker <meeke...@gmail.com> wrote:
On 12/20/2021 7:17 AM, John Clark wrote:
> >> It also makes the assumption that the eigenvalues of a measurement are realized probabilistically.
>> What is the eigenvalue of a temperature of 72°F? It doesn't have one. A measurement doesn't have an eigenvalue but a matrix does, such as the one that describes the Schrodinger Wave. And no quantum interpretation needs to assume there is a relationship between the square of the absolute value of that wave and probability because it is observed to be true.> A temperature operator, which would be matrix, might very well return 72degF as the eigenvalue of a state eigenvector.
A temperature measurement taken at a particular time and place is not a temperature operator, and a measurement is not a probability, although the square of the absolute value of a wave function might tell you the probability of you getting that temperature measurement at that time and place.
> Yes, it's empirically supported; So's the Schroedinger equation. But it's part of the application of the Schroedinger equation. It's not in the equation itself.
I don't know what you mean by that.
It's the projection postulate in the Copenhagen interpretation that applies the Born rule. In MWI it's the Born rule plus some kind of self-locating uncertainty to allow for the probabilistic observations. So those are things not in the Schroedinger equation.
Self-locating uncertainty is not dependent on any particular theory. It’s the same whether it’s the Many Worlds, the Star Trek teleporter or God that does the duplicating.
Each copy does indeed feel as if they are the one true continuation of the original even though they know that they are not,
> You still need to introduce an independent notion of probability because each member must consider himself to be a random selection from the ensemble. The notion of a random selection cannot be defined without reference to some prior notion of probability.
> But can a macroscopic observer really be approximated by a simple algorithm?
On Tue, Dec 21, 2021 at 2:12 AM Bruce Kellett <bhkel...@gmail.com> wrote:
> You still need to introduce an independent notion of probability because each member must consider himself to be a random selection from the ensemble. The notion of a random selection cannot be defined without reference to some prior notion of probability.Even if there are an infinite, and not just an astronomically large, number of other worlds it would still not be difficult to introduce the idea of probability.
Each "you" in the Multiverse will live in a world that is different, and thus each "you" will be different, sometimes that difference will be very slight and sometimes it will be very large. The determination of how different "you" can be and still be considered "you" is arbitrary, but as long as consistency is maintained in your choice and the amount of difference allowed is greater than zero then there will always be more versions of "you" near the center of the Bell Curve than at the outer edges. So if I have a lottery ticket I can predict that tomorrow when the drawing is held I am far more likely to find myself in the losers center of the Bell Curve than at the millionaire trailing edge, although a small minority of "yous" will beat the odds and become rich
And I should add that if you demand perfection with zero slop then you'd have to conclude that you become a different person every time you take a sip of coffee, or even water.
>> Even if there are an infinite, and not just an astronomically large, number of other worlds it would still not be difficult to introduce the idea of probability.
> An actual countable infinity creates problems like Hilbert's Hotel.
>> Each "you" in the Multiverse will live in a world that is different, and thus each "you" will be different, sometimes that difference will be very slight and sometimes it will be very large. The determination of how different "you" can be and still be considered "you" is arbitrary, but as long as consistency is maintained in your choice and the amount of difference allowed is greater than zero then there will always be more versions of "you" near the center of the Bell Curve than at the outer edges. So if I have a lottery ticket I can predict that tomorrow when the drawing is held I am far more likely to find myself in the losers center of the Bell Curve than at the millionaire trailing edge, although a small minority of "yous" will beat the odds and become rich. And I should add that if you demand perfection with zero slop then you'd have to conclude that you become a different person every time you take a sip of coffee, or even water.
> Hmm. When I brought this up earlier you thought it was no problem that the same you would be living in innumerably many worlds simply because cosmic rays and radioactive decays were leaving macroscopic records that split the world. So innumerably many yous shouldn't be a problem either. But why not look at it the other way around and define "world" with some slop?