Conservation of energy in Everett's MWI

[PeterDonis]

as you confirmed with the Copenhagen interpretation the coefficient is the probability of a certain outcome

Yes, in the Copenhagen interpretation. But not in the MWI.

With MWI all outcomes have a probability of 1 so how can the coefficient in the MWI have the same meaning as with the Copenhagen interpretation?

It doesn't. The coefficient's meaning in the MWI is different than its meaning in the Copenhagen interpretation.

I was assuming that the coefficients we are talking about in with the Copenhagen interpretation are the coefficients given by the Born Rule (the probability of the outcome). Have I misunderstood?

No. But you don't appear to grasp that that interpretation of the coefficients is specific to collapse interpretations, and does not apply to the MWI.

 

[name123]

No. But you don't appear to grasp that that interpretation of the coefficients is specific to collapse interpretations, and does not apply to the MWI.

So the coefficient is we are talking about is the coefficient given by the Born Rule. Which isn't as I understand it part of the waveform itself. But is used in the Copenhagen Interpretation to give the probability for a certain term being actualised at a given point in time based on the waveform. What I am not clear is what it represents in the MWI. You have stated "weight". But why would "weight" be applied to the waveform terms in MWI (other than an ad hoc fix) for both the probability of an outcome being observed in a branch (to explain the differences in observed probabilities) and as an adjustment to the energy the branch should be thought to contribute to the overall energy of the waveform (to allow the conservation of energy) ? What is "weight" thought to represent in the theory?

 

[PeterDonis]

So the coefficient is we are talking about is the coefficient given by the Born Rule. Which isn't as I understand it part of the waveform itself.

Strictly speaking, the probability given by the Born rule is the squared modulus of the coefficient that appears in front of the term in the wave function. That makes no difference to what I have been saying.

why would "weight" be applied to the waveform terms in MWI (other than an ad hoc fix)

I have already explained why, and why it is not an ad hoc fix. My explanation is going to remain the same no matter how many times you keep asking the question, so I don't see the point of repeating it.

What is "weight" thought to represent in the theory?

The MWI is not a theory, it is an interpretation of QM. In that interpretation, the "weight" of each branch is simply the weight used whenever you take a weighted average over all branches to obtain some value that is attributed to the total wave function of the universe, which, as I have already explained, is what you do in any case when you have a wave function with multiple terms. I don't know that there is any consensus among MWI proponents about what, if any, meaning it has beyond that.

 

[name123]

The MWI is not a theory, it is an interpretation of QM. In that interpretation, the "weight" of each branch is simply the weight used whenever you take a weighted average over all branches to obtain some value that is attributed to the total wave function of the universe, which, as I have already explained, is what you do in any case when you have a wave function with multiple terms. I don't know that there is any consensus among MWI proponents about what, if any, meaning it has beyond that.

Is there another wave function interpretation which suggests that for the energy of the wave function, for each term you should apply the Born Rule to that term to get a coefficient that should then be applied to the energy of that term in order to get the energy that term should be considered contributing towards the energy of the wave function?

Although you insist applying the Born Rule is not ad hoc, consider the following to perhaps see if you can understand why it seems that it is to me. Consider Theory A that suggests that prior to the measurement of a quantum event there are several possible outcomes, some more likely than others, but that only one will happen. Then consider Theory B which suggests that prior to the measurement there are the same potential outcomes, but the likelihood of each is 1. It would seem to suggest an experiment that could distinguish between them. Theory A would suggest a different likelihood of observing certain events to Theory B. Here both would be theories, and both theories would suggest different experimental outcomes, and one could be falsified. Supposing the experiment was done, and Theory B was falsified, but the Theory B proponents said, no wait a minute we're going to modify our theory and claim that what you should do is apply the Born Rule coefficients to the likelihood of observing the various terms. And when asked why, could offer no good reason for why you should given their theory, but it would prevent the results falsifying their theory. It could reasonably claimed that the weighting of the expected frequency of observation in Theory B was ad hoc. Do you agree?

If you do, then I am not clear why you think it would be ad hoc for the Theory B proponents but not for the MWI proponents. If you don't then perhaps we have a different understanding of the term ad hoc.

Likewise if the Theory B proponents had it pointed out to them that according to Theory A the energy of outcome p is $E$ and the energy of an alternative outcome q would also be $E$. And that experimentally with whatever outcome p or q the observed the energy was indeed measured to be $E$. But with Theory B both outcome p and outcome q would have occurred, and would have both been measured to have energy $E$. It could be suggested by proponents of Theory A that this would mean that Theory B would not conserve energy. As the energy of two separate systems would be their sum. And they p and q would be two separate systems as they would no longer interact. But the proponents of Theory B said, no, although the energy of p would be measured as $E$ and the energy of q would be measured as $E$ when considering the overall energy that it implies, these values shouldn't be summed but instead their values should be multiplied by the coefficients given by the Born Rule. You can presumably see why that might be seen by the proponents of Theory A as an ad hoc adjustment by the proponents of Theory B to avoid the suggestion that the theory implies the non-conservation of energy.

 

[PeterDonis]

Is there another wave function interpretation which suggests that for the energy of the wave function, for each term you should apply the Born Rule to that term to get a coefficient that should then be applied to the energy of that term in order to get the energy that term should be considered contributing towards the energy of the wave function?

This is not a matter of interpretation. It's a matter of the basic math of QM. When you have a wave function with multiple terms (more precisely, multiple terms with no interference, which is what you have when you have multiple branches after a measurement in the MWI), that's how you calculate the total anything of the wave function: a weighted average of that thing over the terms. As I've already pointed out, the same is true in Copenhagen--but in Copenhagen, after a measurement there is only one term, so there is no need to do any averaging.

Although you insist applying the Born Rule is not ad hoc, consider the following to perhaps see if you can understand why it seems that it is to me.

What I understand is that you have asked the same question multiple times and I have given the same answer multiple times. I don't see the point of continuing to go around in a circle.

Consider Theory A that suggests that prior to the measurement of a quantum event there are several possible outcomes, some more likely than others, but that only one will happen. Then consider Theory B which suggests that prior to the measurement there are the same potential outcomes, but the likelihood of each is 1.

What does "likelihood" mean? If it just means they all happen, then you are just comparing Copenhagen and MWI. So why don't you just say Copenhagen and MWI?

If it means something else, then it looks like your Theory B is something you made up. Personal theory and personal speculation are off limits here.

It would seem to suggest an experiment that could distinguish between them.

If you think there is a way to experimentally distinguish between different interpretations of QM, then you should write up a paper and submit it to a journal, since it would be a groundbreaking advance if true.

In the meantime, however, this, again, is personal speculation on your part.

Theory A would suggest a different likelihood of observing certain events to Theory B.

Not if Theory A is Copenhagen and Theory B is MWI. All interpretations of QM agree on all experimental predictions.

Please refrain from personal speculation, and please read my previous replies again, carefully. As I've said, I don't see the point of continuing to go around in a circle. It looks to me like your original question is answered.

 

[PeterDonis]

@name123 if your basic issue is that you don't think the MWI is true, many people would agree with you. But "it violates energy conservation" is not a good argument for such a position. You would be on much better ground in questioning, for example, why the Born Rule should work in the MWI, which has been a common criticism in the literature. I believe we have had a number of previous threads on that here.

 

[name123]

This is not a matter of interpretation. It's a matter of the basic math of QM. When you have a wave function with multiple terms (more precisely, multiple terms with no interference, which is what you have when you have multiple branches after a measurement in the MWI), that's how you calculate the total anything of the wave function: a weighted average of that thing over the terms. As I've already pointed out, the same is true in Copenhagen--but in Copenhagen, after a measurement there is only one term, so there is no need to do any averaging.

The Born Rule isn't a coefficient in the wave function though is it?

So why should the terms be multiplied by that coefficient as opposed to the "PeterDonisNumber"?

 

[PeterDonis]

The Born Rule isn't a coefficient in the wave function though is it?

It's the squared modulus of the coefficient in the wave function. I've already explained this.

why should the terms be multiplied by that coefficient

I've already explained this too. I'm not going to repeat myself.

It seems to me like you need to learn more about the basic math of QM. Look up "expectation value" for a start.

 

[PeterDonis]

@name123 I am closing this thread since your question has been answered and we are just going in circles at this point.