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# Everybody sees the same elephant (says Carlo Rovelli)

by marcus
Tags: carlo, elephant, rovelli, sees
 P: 198 Hi Dimitri, well, the LQG people like to claim their approach is much older, not newer. I can toally relate to your not-liking of LQG, it's definitly not appealing. Anyway, what I wanted to say... ...what did I want to say... ...sorry, long day... ...essentially: anything is better than nuclear physics and solid state Best, B. (gotta go home get some sleep )
P: 307
 Quote by hossi ...essentially: anything is better than nuclear physics and solid state
Amen!
P: 859
To come back to the Elephant, although an extravagance perhaps, consider this quote from 1943:

 The only possible alternative is simply to keep to the immediate experience that consciousness is a singular of which the plural is unknown; that there is only one thing and that, what seems to be a plurality, is merely a series of different aspects of this one thing, produced by a deception (the Indian Maya); the same illusion is produced in a gallery of mirrors, and in the same way Gaurisankar and Mt Everest turned out to be the same peak seen from different valleys. There are, of course, elaborate ghost-stories fixed in our minds to hamper our acceptance of such simple recognition.
Erwin Schroedinger, What is life? 1943

This is taken from a set of lectures given by Schroedinger in Dublin, which became very well known and were subsequently read by Watson and Crick and others hot on the trail of the mystery of genes.

many worlds but one elephant

 Astronomy Sci Advisor PF Gold P: 23,085 nice quote from Schrödinger this Kea koan not bad either many worlds but one elephant
 Astronomy Sci Advisor PF Gold P: 23,085 Bee has introduced another animal into the picture, this time a dog. A number of people were discussing this at her blog and I posted twice already and still have a bit more to say, so I will say it here. In Bee's story there are two experimenters A and B and they agree to take their entangled electrons to separate places and on a certain day each perform an measurement. Let's make them women for a change. They agree to point the machines to the East and read the spin. Each person has a hilbertspace and each person has a wavefuntion or state in that space which describes what they have learned about life so far, and about the universe, like what to expect if you go out with Italian men---what to do if you see an elephant, and so on. A and B are well-educated so they expect that one of them will get +1 and one get -1. Everything is crystal clear to them. Off they go to their respective stations, which are quite far apart. the day arrives and A does her measurement and she gets -1, so she applies the appropriate projection operator and collapses part of her wavefunction to show the new information she has about HER electron. She also has in her wavefunction or state vector some experience of how RELIABLE the other experimenter, B, is. And how often B's location is hit by hurricanes. In the hypothetical situation that B is TOTALLY reliable, always remembers to do what she is supposed to, TOTALLY competent, always gets her lab machines to work perfectly, and NEVER hit by hurricanes, then of course B would be expected to be reading +1 right now, because the spins on a given axis add up to one. But that would not be realistic. So A does not commit herself right away, she doesnt collapse the wavefunction in her state space that codes the outcome of the distant measurement because she doesnt have that information yet. Before she does that she will at least telephone, or maybe even go and check out the other station, where B is. Before recording any information about B's electron, she has to get in CAUSAL CONTACT. SO THE COLLAPSE OF A's wavefunction is LOCAL. Somebody had to get in somebody else's lightcone, or even go over and stand next to them at the same spot, for it to happen.
 Astronomy Sci Advisor PF Gold P: 23,085 I guess the point is that even if A knows B to be admirable in every respect---very reliable and competent in the lab etc.---maybe B is just then having an argument with her boyfriend, or maybe she has a hangover, or there has been a supernova explosion, or it just simply isn't her day. This happens sometimes. So you can't be sure. the advice to A is, DONT COLLAPSE YOUR WAVEFUNCTION UNTIL YOU SEE THE WHITES OF THEIR EYES and you have definite information, dont go collapsing it based on some suppostion about somewhere you are not in causal contact with, some spacelike separated place where you cant have any idea what is happening there. so now what about the DOG??? Well Sabine ups the narrative stakes by having B take along a dog to her station, and if her reading comes out +1 then B should SHOOT THE DOG. And conversely if the measurment comes out -1 then she should not shoot the dog. There is a picture of the dog, which is an unpleasant overweight bulldog which it would be tempting to shoot regardless how the experiment turned out. I will get a link so you can go read further discussions of this http://backreaction.blogspot.com/ http://backreaction.blogspot.com/200...nlocality.html
Emeritus
PF Gold
P: 6,236
 Quote by marcus A and B are well-educated so they expect that one of them will get +1 and one get -1. Everything is crystal clear to them. Off they go to their respective stations, which are quite far apart. the day arrives and A does her measurement and she gets -1, so she applies the appropriate projection operator and collapses part of her wavefunction to show the new information she has about HER electron. She also has in her wavefunction or state vector some experience of how RELIABLE the other experimenter, B, is. And how often B's location is hit by hurricanes. In the hypothetical situation that B is TOTALLY reliable, always remembers to do what she is supposed to, TOTALLY competent, always gets her lab machines to work perfectly, and NEVER hit by hurricanes, then of course B would be expected to be reading +1 right now, because the spins on a given axis add up to one. But that would not be realistic. So A does not commit herself right away, she doesnt collapse the wavefunction in her state space that codes the outcome of the distant measurement because she doesnt have that information yet. Before she does that she will at least telephone, or maybe even go and check out the other station, where B is. Before recording any information about B's electron, she has to get in CAUSAL CONTACT. SO THE COLLAPSE OF A's wavefunction is LOCAL. Somebody had to get in somebody else's lightcone, or even go over and stand next to them at the same spot, for it to happen.
Yes, this is a perfectly all right view from a "solipsist" viewpoint: there is only ONE observer in this world, in casu "A". We never talk about the experience "B" lives, we only talk about what A OBSERVES from "B"s state.

As such, one can indeed see quantum theory as the theory that explains A's experience: first A sees her local result (local collapse of A's state), then A encounters B (local collapse of A's experience of B's state)...
So collapse occurs when A becomes, say, consciously aware of something.
This is all fine and well.

The problem arrives when we want the theory to describe at the same time also what B experiences, from its viewpoint.
Now, you can of course say that we should now apply the formalism on B's side, but there's a problem.
When A became aware of her result, and locally collapsed HER wavefunction, what can we say on B's side, from B's point of view ?
If you have A's wavefunction collapse from B's side too, then we are in contradiction with what we tried to establish, namely only "local collapse upon local becoming aware of the result". But if A's wavefunction DIDN'T collapse from B's point of view, then WE'VE LOST THE POTENTIAL LINK WITH A's experienced world.

From A's PoV:

State before A measures:
|a+>(u |b-> + v |b+>) + |a-> (x |b+> + y |b->)

A measures and "experiences" the result, it is +:

--> collapse (for A) into |A+>(u |b-> + v |b+>)

B might measure far away, but A doesn't know yet...

A meets B, and "measures" B's state, result of B is +:

--> collapse (for A) into |A+> | B+>

fine.

From B's PoV:

State before A measures:

|a+>(u |b-> + v |b+>) + |a-> (x |b+> + y |b->)

A measures, but this doesn't change anything to B yet.

B measures now, finds -

--> Collapse on B's side: (u |a+> + y |a->) |B->

B meets A, finds -:

--> Collapse on B's side: |A->|B->

All this is nice and well, except that from A's PoV, A and B got + and +, while from B's PoV, they both got - and -

This can be solved in a MWI scenario, by replacing collapse by "branch is consciously observed by"

Take # the "is conscious state by A" tag, and * the "is conscious state by B" tag, then we just have the state:

Before measurement, all states are still part of the "relative state" of A and of B:
|a+#*>(u |b-#*> + v |b+#*>) + |a-#*> (x |b+#*> + y |b-#*>)

A does a measurement, and found +, only changes the accessible states of A ; we remove what is NOT anymore part of "A's conscious world" (is projected out by the "collapse according to A":

|a+#*>(u |b-#*> + v |b+#*>) + |a-*> (x |b+*> + y |b-*>)

B does a measurement and found -:

|a+#*>(u |b-#*> + v |b+#>) + |a-*> (x |b+> + y |b-*>)

Now, A and B meet.
First, A "measures" B (that is, A learns about the "B" state) A learns that B saw +, so this gives:

|a+#*>(u |b-*> + v |b+#>) + |a-*> (x |b+> + y |b-*>)

About at the same time, B measures A, that is, B learns that "A saw -":

|a+#>(u |b-> + v |b+#>) + |a-*> (x |b+> + y |b-*>)

What now emerges is that, in "A's mental world", symbolized by #, the state of the first particle is seen to be a+ and the state of the b particle is seen to be b+. In "B's mental world", symbolized by *, the state of particle a is -, and the one of b is - too.

So both "relative views" intermixed is simply a many worlds view where the "objective" wavefunction didn't collapse, but where "the awareness of a state" narrowed down its scope as a function of what it was made aware off, to the piece of the overall wavefunction that corresponds to its measurement results.

As such, the Rovelli flavor of the relative state view is the "one-observer" version of the many worlds view (where many observers are considered in parallel).
Emeritus
PF Gold
P: 6,236
 Quote by marcus A and B are well-educated so they expect that one of them will get +1 and one get -1. Everything is crystal clear to them. Off they go to their respective stations, which are quite far apart. the day arrives and A does her measurement and she gets -1, so she applies the appropriate projection operator and collapses part of her wavefunction to show the new information she has about HER electron. She also has in her wavefunction or state vector some experience of how RELIABLE the other experimenter, B, is. And how often B's location is hit by hurricanes. In the hypothetical situation that B is TOTALLY reliable, always remembers to do what she is supposed to, TOTALLY competent, always gets her lab machines to work perfectly, and NEVER hit by hurricanes, then of course B would be expected to be reading +1 right now, because the spins on a given axis add up to one. But that would not be realistic. So A does not commit herself right away, she doesnt collapse the wavefunction in her state space that codes the outcome of the distant measurement because she doesnt have that information yet. Before she does that she will at least telephone, or maybe even go and check out the other station, where B is. Before recording any information about B's electron, she has to get in CAUSAL CONTACT. SO THE COLLAPSE OF A's wavefunction is LOCAL. Somebody had to get in somebody else's lightcone, or even go over and stand next to them at the same spot, for it to happen.
Yes, this is a perfectly all right view from a "solipsist" viewpoint: there is only ONE observer in this world, in casu "A". We never talk about the experience "B" lives, we only talk about what A OBSERVES from "B"s state.

As such, one can indeed see quantum theory as the theory that explains A's experience: first A sees her local result (local collapse of A's state), then A encounters B (local collapse of A's experience of B's state)...
So collapse occurs when A becomes, say, consciously aware of something.
This is all fine and well.

The problem arrives when we want the theory to describe at the same time also what B experiences, from its viewpoint.
Now, you can of course say that we should now apply the formalism on B's side, but there's a problem.
When A became aware of her result, and locally collapsed HER wavefunction, what can we say on B's side, from B's point of view ?
If you have A's wavefunction collapse from B's side too, then we are in contradiction with what we tried to establish, namely only "local collapse upon local becoming aware of the result". But if A's wavefunction DIDN'T collapse from B's point of view, then WE'VE LOST THE POTENTIAL LINK WITH A's experienced world.

From A's PoV:

State before A measures:
|a+>(u |b-> + v |b+>) + |a-> (x |b+> + y |b->)

A measures and "experiences" the result, it is +:

--> collapse (for A) into |A+>(u |b-> + v |b+>)

B might measure far away, but A doesn't know yet...

A meets B, and "measures" B's state, result of B is +:

--> collapse (for A) into |A+> | B+>

fine.

From B's PoV:

State before A measures:

|a+>(u |b-> + v |b+>) + |a-> (x |b+> + y |b->)

A measures, but this doesn't change anything to B yet.

B measures now, finds -

--> Collapse on B's side: (u |a+> + y |a->) |B->

B meets A, finds -:

--> Collapse on B's side: |A->|B->

All this is nice and well, except that from A's PoV, A and B got + and +, while from B's PoV, they both got - and -

This can be solved in a MWI scenario, by replacing collapse by "branch is consciously observed by"

Take # the "is conscious state by A" tag, and * the "is conscious state by B" tag, then we just have the state:

Before measurement, all states are still part of the "relative state" of A and of B:
|a+#*>(u |b-#*> + v |b+#*>) + |a-#*> (x |b+#*> + y |b-#*>)

A does a measurement, and found +, only changes the accessible states of A ; we remove what is NOT anymore part of "A's conscious world" (is projected out by the "collapse according to A":

|a+#*>(u |b-#*> + v |b+#*>) + |a-*> (x |b+*> + y |b-*>)

B does a measurement and found -:

|a+#*>(u |b-#*> + v |b+#>) + |a-*> (x |b+> + y |b-*>)

Now, A and B meet.
First, A "measures" B (that is, A learns about the "B" state) A learns that B saw +, so this gives:

|a+#*>(u |b-*> + v |b+#>) + |a-*> (x |b+> + y |b-*>)

About at the same time, B measures A, that is, B learns that "A saw -":

|a+#>(u |b-> + v |b+#>) + |a-*> (x |b+> + y |b-*>)

What now emerges is that, in "A's mental world", symbolized by #, the state of the first particle is seen to be a+ and the state of the b particle is seen to be b+. In "B's mental world", symbolized by *, the state of particle a is -, and the one of b is - too.

So both "relative views" intermixed is simply a many worlds view where the "objective" wavefunction didn't collapse, but where "the awareness of a state" narrowed down its scope as a function of what it was made aware off, to the piece of the overall wavefunction that corresponds to its measurement results.

As such, the Rovelli flavor of the relative state view is the "one-observer" version of the many worlds view (where many observers are considered in parallel).
 Astronomy Sci Advisor PF Gold P: 23,085 **But if A's wavefunction DIDN'T collapse from B's point of view, then WE'VE LOST THE POTENTIAL LINK WITH A's experienced world. ** I think we didnt lose the possible linkage because a two-way link occurs when the two are in the same place----linkage (one way or two way)follows causal contact there is more on this at Bee's blog. To my considerable pleasure and surprise she indicates agreement to some extent. I don't know how far her agreement goes, so you'd best consult the blog or her directly. Im happy for you to totally disagree! I just can't take the time to discuss this too much. I imagine Rovelli would consider his picture "multiple-observer" and "single world". Rovelli picture is multiple-observer in the sence that it ALLOWS for having one or more observers. You can have one, or you can have 100. You have as many hilbertspaces as you do observers. Objective reality arises from the AGREEMENT of these guys. I personally see no connection with "many worlds". But if you see a connection with "many worlds" that is fine!
Emeritus
PF Gold
P: 6,236
 Quote by marcus I imagine Rovelli would consider his picture "multiple-observer" and "single world".
Well, "multiple-observer/single world" is of course what we all would like to see because it fits much better with our intuitive concept of how the world ought to be (how many times have people not said "how the world ought to be" ), but it is now clearly established that QM's predictions for a multiple observer/single world are such that if there is to be given an objective picture behind this, that this picture is necessarily non-local (that's Bell's result in a nutshell). It is in essence the approach of Bohmian mechanics, or of "standard" von Neuman quantum theory (with collapse upon observation), if one assigns some objective reality to the wavefunction (which represents your single world). All of these approaches violate Lorentz invariance in their inner workings (in other words, require non-local mechanisms to act upon the object that is supposed to represent the single world).

An exception to this are the approaches that consider quantum theory as just a technique to calculate probabilities of outcomes of experiments, but I'd classify that rather as "multiple observers / no world" because these approaches explicitly forbid you to think of any of the mathematical constructions to represent an objective reality.

 Rovelli picture is multiple-observer in the sence that it ALLOWS for having one or more observers. You can have one, or you can have 100. You have as many hilbertspaces as you do observers. Objective reality arises from the AGREEMENT of these guys. I personally see no connection with "many worlds".
If you have "a hilbert space for each observer", then what goes wrong is the following, if one assumes that each hilbert space is an "independent generator for probabilities", and if one assumes a continuity in an observer's knowledge (that is, if at a point t1 on his world line, observer A measured result A+, then at a point t2>t1 on his world line, he will not suddenly conclude that back at t1 he measured finally A- when learning about another result).

Assume that the initial state is u |a+> |b-> + v |a->|b+> with u much smaller than v, and assume that A and B measure their particle's state "simultaneously" (in some frame), without contact.
This means, that in A's hilbert space, with an overwhelming probability, he's going to find A-, and in B's hilbert space, he's going to find B+. So indeed most of the time, after they meet, they will be in agreement.
But for the rare cases where A, in his hilbert space, finds A+, and registers this along his world line, there is no reason why B, in his *independent* hilbert space, will have to obtain the rare event B-. If B's hilbert space is independent of A's, then B will most of the time, project on the B+ state (independent of what A found).
In the same way, in those rare cases where B projects upon B- in his independent hilbert space, there's no reason why A should not project on A- most of the time.
The individual statistics are all right of course, but when they meet, something goes wrong, if there is continuity of their registered measurement results, AT LEAST IF THERE IS ONLY ONE "WORLD" (that is, if each observer has his own, single, outcome). Because the single B that is around cannot "forget" having seen B+ when he meets A having seen A+.

This is exactly the problem that a many world approach fixes: from A's PoV, there are TWO "B" observers, one of which he'll meet, and from B's PoV, there are TWO "A" observers, one of which he'll meet. And during the meeting, only those "versions" of observers can interact that are in agreement (that is, in the rare cases A has seen the A+ outcome, he'll only interact with the version of the B observer that has seen the B- outcome).

But these two meetings are not the SAME two observers: hence two different "worlds". This is what "goes wrong" with many worlds: the hard-to-swallow idea (however, entirely in agreement with subjective observation) that, when we "see an outcome" that this is just one of the several "me's" that sees an outcome, and that there all other possibilities are realised also, with "other me's". We'd intuitively like to have the case that there's only one "me" and that there's only one outcome.

However, if you restrict yourself to only one observer (say A) then all this is fine, because B is not really an observer, but just a quantum system as any other. As such, B has no "definite result" upon interacting with particle b, and B's state is simply a kind of copy of the state of particle b, which is waiting to be observed by A to take on a definite result - which is how I understand Rovelli: that, from A's PoV, B has not yet a definite result until it is observed by A. This is fine.

You cannot, however, require B NOT to have a definite result from A's PoV, and (1) B to HAVE a definite result from B's PoV, have these results being generated in (2) *independent* hilbert spaces, and hope that (3) the correlations upon meeting will come out all right. Something has to give.
If it is (1), well clearly we have only a single observer (B has no result) ;
If it is (2), well then there IS an "action at a distance" in some way in the inner workings to make the two hilbert spaces "dependent",
and if it is (3) then we're not reproducing the standard quantum theory correlations.

 But if you see a connection with "many worlds" that is fine!
As I said, I see Rovelli's idea as the "single observer/single world" version of the "many observers/many worlds" view. I'm not sending out any critique, but I'm just saying that these ponderings are already around for at least 40 years, in several different forms and presentations.
Emeritus
PF Gold
P: 8,147
 Quote by vanesch if there is to be given an objective picture behind this, that this picture is necessarily non-local (that's Bell's result in a nutshell)
Well, this is the crux of the whole disagreement. Your understanding of "objective" is different from the relational one. Your view, call it QM with a priviledged observer, or QMPO says that before the PO "observes" the observed system it has no definite values in spacetime but after that priviledged act it does. RQM on the other hand says there are no priviledged observers and no priviledged values, but only interacting quantum systems. Bell and many since have conceiled this possibility from the reader by appeals to traditional classical images, and the tendency to talk about observers as people and give them names like Alice and Bob reinforces this misdirection.

If there is nothing but quantum interactions and those interaction are symmetric, changing the quantum state of both interacting systems, can there be any real objectivity? Smerlak and Rovelli say that thanks to QM the answer is yes!

SInce it is key to this discussion I have quoted the entire section 4.3 of the paper:

 4.3. Consistency. Let us bring B back into the picture. It is far from the spirit of RQM to assume that each observer has a “solipsistic” picture of reality, disconnected from the picture of all the other observers. In fact, the very reason we can do science is because of the consistency we find in nature: if I see an elephant and I ask you what you see, I expect you to tell me that you too you see an elephant. If not, something is wrong. But, as claimed above, any such conversation about elephants is ultimately an interaction between quantum systems. This fact may be irrelevant in everyday life, but disregarding it may give rises to subtle confusions, such as the one leading to the conclusion of nonlocal EPR influences. In the EPR situation, A and B can be considered two distinct observers, both making measurements on α and β. The comparison of the results of their measurements, we have argued, cannot be instantaneous, that is, it requires A and B to be in causal contact. More importantly, with respect to A, B is to be considered as a normal quantum system (and, of course, with respect to B, A is a normal quantum system). So, what happens if A and B compare notes? Have they seen the same elephant? It is one of the most remarkable features of quantum mechanics that indeed it automatically guarantees precisely the kind of consistency that we see in nature [5]. Let us illustrate this assuming that both A and B measure the spin in the same direction, say z, that is n = n′ = z. Since B is a quantum system, there will be an observable $$S^n_{AB}$$ corresponding to B’s answer (at time t1) to the question “which value of the spin have you measured?”. That is, $$S^n_{AB}$$ is the observable describing the pointer variable in the detector B. Then consistency demands that: (i) If A measures $$S^n_{AB}$$ after having measured $$S^n_{A\beta}$$ she will get (4) $$S^n_{AB} = S^n_{A\beta}$$. (ii) If a third observer C, who has the prior information that measurements have been performed by A and B, measures at a later time the two pointer variables: $$S^n_{CA}$$and $$S^n_{CB}$$ then (5) $$S^n_{CB} = S^n_{CA}$$ But this follows from standard QM formalism, because an interaction between β and B that can be interpreted as a measurement is an interaction such that the state (1) and the initial state of α, β and B evolve into the state (relative to A) (6) $$|\psi>^(A)_{\alpha+\beta+B} = \frac{1}{\sqrt{2}} (|\downarrow>_{\alpha} |\uparrow>_{\beta} |\uparrow>_B − |\uparrow>_{\alpha} |\downarrow>_{\beta} |\downarrow>_{B})$$ with obvious notation. Tracing out the state of α that plays no role here, we get the density matrix (7)$$\rho^{(A)}_{\beta+B} = \frac{1}{2} (|\uparrow>_{\beta} |\uparrow>_B <\uparrow|_{\beta} <\uparrow|_B + |\downarrow>_{\beta} |\downarrow>_B <\downarrow|_{\beta} <\downarrow|_{B})$$ . from which (4) follows immediately. Similarly, the state of the ensemble of the four systems α, β,A,B, relative to C evolves, after the two nteractions at time t0 into the state (8)$$|\psi^{(C)}_{\alpha+\beta+A+B} = \frac{1}{\sqrt{2}}(|\downarrow>_{\alpha} |\uparrow>_{\beta} |\downarrow>_A |\uparrow>_B−|\uparrow>_{\alpha} |\downarrow>_{\beta} |\uparrow>_A |\downarrow>_{B})$$ again with obvious notation. Tracing out the state of α and β, we get the density matrix (9) $$\rho^{(C)}_{A+B} = \frac{1}{2}( |\downarrow>_A |\uparrow>_B <\downarrow|_A <\uparrow|_B+|\downarrow>_A |\uparrow>_B <\downarrow|_A <\uparrow|_{B} )$$. which gives (5) immediately. It is clear that everybody sees the same elephant. More precisely: everybody hears everybody else stating that they see the same elephant he sees. This, after all, is the best definition of objectivity.
Note that the particle states have been traced away in computing the density matrix. Only the observer states remain.
Emeritus
PF Gold
P: 6,236
 Quote by selfAdjoint Well, this is the crux of the whole disagreement. Your understanding of "objective" is different from the relational one. Your view, call it QM with a priviledged observer, or QMPO says that before the PO "observes" the observed system it has no definite values in spacetime but after that priviledged act it does.
Well, I fail to see the "disagreement, Dick. In fact, I'm 100% "in sync" with what you quoted, and of course the essential point is when A "measures" the state of B with an observable that says "what did you, B, measure?"

The consistency requirement that is worked out here in all detail, comes simply down to the MWI statement: observers in different branches only learn about the answers of their peers in the SAME BRANCH.

In other words, if we end up with:

|alice+> |bob+> |stuffA> + |alice->|bob->|stuffB>

then this means that any such interaction when Alice asks bob what he measured, comes down to: alice+ will only hear from bob+, and alice- will only hear from bob- ; alice+ will never hear from bob-.

As such, indeed, "everybody" will see "the same elephant" ; that is, "alice+" will see the same elephant as bob+ (namely stuffA), and "alice-" will see the same elephant as bob-, namely stuffB.
It is implicitly assumed in MWI that this is the case of course, otherwise the view would be immediately falsified! The *entire idea* is indeed that though there is a "multiplication of worlds/branches/terms", nevertheless, each observer is "locked up" in its own term, ONLY being able to interact with its "peers" in the same branch, so that everything happens AS IF this branch was, to him, the only thing that existed, and the others "faded away".

It is my understanding that this is what is worked out in detail in the section you quoted: that observers in a branch only "see" their peers in the same branch, with "see" meaning: get their results through an interaction which is "what did you get as a result", and that they DON'T get any result of an observer in another branch. The wavefunctions in (6) and (8) are nothing else but what I write above here. That's really nothing
but the MWI version of the measurement situation, and that was what I tried to say here since the beginning: that Rovelli re-discovered MWI, or at least the aspect that each branch "only sees itself", and that there is a self-consistency in A measures system a, B measures system b, and then A measures B.

As to your comment, or I misunderstand you, or you misunderstand me :-)
In MWI, there is no "priviledged observer", because there are many copies of each observer, one in each branch. However, it was my understanding, maybe erroneously, that Rovelli takes it that there is only ONE version of each observer. Clearly that runs into troubles (and is in fact contradicted with his equations 6 and 8 from your quote): B cannot be "in a superposition wrt A" and have "a single and definite measurement" wrt itself (unless, and that's the entire MWI approach, B is dedoubled into two B's). So I took it that Rovelli saw everything from the PoV of observer A (which can then be thought of to be "single"), allowing B to be in superposition until A saw him (the kind of PO you are talking about). And from the PoV from B, we forget what we did for A, we now do things from the PoV of B, and now B is "single" and A is "in superposition".
Both viewpoints together of course correspond to A as well as B in "superposition" but agreement in the corresponding branches. Which is, to my understanding, nothing else but MWI...
Emeritus
PF Gold
P: 8,147
 Quote by vanesch Well, I fail to see the "disagreement, Dick. In fact, I'm 100% "in sync" with what you quoted, and of course the essential point is when A "measures" the state of B with an observable that says "what did you, B, measure?" The consistency requirement that is worked out here in all detail, comes simply down to the MWI statement: observers in different branches only learn about the answers of their peers in the SAME BRANCH. In other words, if we end up with: |alice+> |bob+> |stuffA> + |alice->|bob->|stuffB> then this means that any such interaction when Alice asks bob what he measured, comes down to: alice+ will only hear from bob+, and alice- will only hear from bob- ; alice+ will never hear from bob-. As such, indeed, "everybody" will see "the same elephant" ; that is, "alice+" will see the same elephant as bob+ (namely stuffA), and "alice-" will see the same elephant as bob-, namely stuffB. It is implicitly assumed in MWI that this is the case of course, otherwise the view would be immediately falsified! The *entire idea* is indeed that though there is a "multiplication of worlds/branches/terms", nevertheless, each observer is "locked up" in its own term, ONLY being able to interact with its "peers" in the same branch, so that everything happens AS IF this branch was, to him, the only thing that existed, and the others "faded away". It is my understanding that this is what is worked out in detail in the section you quoted: that observers in a branch only "see" their peers in the same branch, with "see" meaning: get their results through an interaction which is "what did you get as a result", and that they DON'T get any result of an observer in another branch. The wavefunctions in (6) and (8) are nothing else but what I write above here. That's really nothing but the MWI version of the measurement situation, and that was what I tried to say here since the beginning: that Rovelli re-discovered MWI, or at least the aspect that each branch "only sees itself", and that there is a self-consistency in A measures system a, B measures system b, and then A measures B. As to your comment, or I misunderstand you, or you misunderstand me :-) In MWI, there is no "priviledged observer", because there are many copies of each observer, one in each branch. However, it was my understanding, maybe erroneously, that Rovelli takes it that there is only ONE version of each observer. Clearly that runs into troubles (and is in fact contradicted with his equations 6 and 8 from your quote): B cannot be "in a superposition wrt A" and have "a single and definite measurement" wrt itself (unless, and that's the entire MWI approach, B is dedoubled into two B's). So I took it that Rovelli saw everything from the PoV of observer A (which can then be thought of to be "single"), allowing B to be in superposition until A saw him (the kind of PO you are talking about). And from the PoV from B, we forget what we did for A, we now do things from the PoV of B, and now B is "single" and A is "in superposition". Both viewpoints together of course correspond to A as well as B in "superposition" but agreement in the corresponding branches. Which is, to my understanding, nothing else but MWI...
My use of the term priviliedged observer refers to the (originally Copenhagian) macroscopic observer who stands above and beyond the quantum world. Whether you have one or many of these chaps, they and the classical values they measure have really no place in a totally quantum view of the world.

S&M abandon this nonquantum fellow for a picture containing only interacting quantum systems ("the facts of the world are interactions", they say someplace in the paper). Some of these systems in a particular case function as "observation systems", i.e. they have pointer states. But critically these observer systems can be in superimposed states, entangled states, and so on, and they evolve quantally. This is how we can write the interacting state in terms of not only the evolving state of observed system (the "particle") but also including the observer state ("what the observational system records") in the state functions and density matrix calculations, which is the heart of their demonstration.

I recognize there are some problems to be dealt with in getting rid of the PO; notably if she goes, so does her watch, that external nonquantum clock that supplies the time parameter to QM. But people are working on that.
Emeritus
PF Gold
P: 6,236
 Quote by selfAdjoint S&M abandon this nonquantum fellow for a picture containing only interacting quantum systems ("the facts of the world are interactions", they say someplace in the paper). Some of these systems in a particular case function as "observation systems", i.e. they have pointer states. But critically these observer systems can be in superimposed states, entangled states, and so on, and they evolve quantally. This is how we can write the interacting state in terms of not only the evolving state of observed system (the "particle") but also including the observer state ("what the observational system records") in the state functions and density matrix calculations, which is the heart of their demonstration.
Uh, but that, to me, has always been the heart of any MWI view!

That an observation is a change in an observer state due to an interaction between the system and the observer ; now, if - as you rightly point out - these "observer degrees of freedom" - can be in superposed/entangled... states, then what becomes an "observer" now, with a specific 'observational record', is not the original degree of freedom (of which the quantum description, indeed, appears in superposition), but its single manifestation in ONE term. But that means that there are now "copies" of the observer (the different states, in the different terms=branches) around, each with different 'observational recordings' (a different one in each term).

So I fully agree with that. But I'm saying that this idea is the core idea of any MWI view. It is MWI's way to deal with the AND/OR problem: the fact that the observer is NOT the degree of freedom (= the device), but ONE of the different states in which this degree of freedom occurs (= one of the pointer states). An observer IS the pointer state, and not the apparatus, to put it rather bluntly. (and this leads me, in the case of human beings, to distinguish between the conscious observation of the pointer state, versus the entire bodystate)

THIS is, the way I understand it, the fundamental insight of an MWI view.

Now, I thought (maybe erroneously, I didn't read Rovelli's paper in all detail very thoroughly once I thought I recognized the main line), that Rovelli somehow thought he could get away with this "superposition of observer states" and hence solve the AND/OR problem by looking only at the measurement of A onto B and find out that everything is allright.

If Rovelli moreover recognizes this superposition of pointerstates, then I really don't see in what way his idea is different from the general idea of MWI. This is what I tried to say here from the beginning.

 I recognize there are some problems to be dealt with in getting rid of the PO; notably if she goes, so does her watch, that external nonquantum clock that supplies the time parameter to QM. But people are working on that.
Yes, this is the famous "problem of time" which I understood was one of the principal difficulties in QG.
Note that in special relativity, as such, this is not necessarily an issue, because unitarity is conserved under a lorentz transformation, so you can "re-tell" the story along different timelike axes, the entire system is normally consistent.
Emeritus
PF Gold
P: 6,236
 Quote by marcus Rovelli does not use the term "branch" and the term has no intuitive or widely understood meaning in the context of a discussion of the paper.
But also in an MWI view, "branch" is a loosely used concept, which often introduces more confusion than anything else. As such, "branch" has no objective existence, but has only a kind of meaning WRT AN OBSERVER.

The problem MWI tries to address (one of the core problems in the measurement problem) is the AND/OR problem: How do you go from a superposition of pointer states to one (with a probability given by the Born rule). In Copenhagen/von Neumann, this is "solved" by the projection postulate, but this introduces fundamental difficulties (one is: WHY/WHEN does it happen - what sets an "observation" apart from a "physical interaction" ; the other is its non-local character).
MWI wants no such projection postulate, and is then confronted with the AND/OR problem. Its proposed solution is then purely "conceptual": instead of saying that the outcome is "in the apparatus" (with the different pointer states), say that the outcome "is in the pointer state".
That seems like a cheap trick of course, what have we gained ?
Well, FROM THE POINT OF VIEW OF AN OBSERVER (= a pointer state = a container of measurement record) we can say that HIS world did split in many branches: BEFORE the measurement, there was ONE pointer state (the pre-measurement state of the apparatus), so there was ONE observer associated with the apparatus, and AFTER the measurement there were as many DIFFERENT observers associated with the apparatus as there were used pointerstates. And "the" observer is just ONE of the many pointer states.
"Branches"(wrt the observer) are simply these different pointerstates that evolved out of one. Again, it is not an objective concept, it is observer-related.

It's because it is intuitively as if "the single observer" branched now into many (the single pre-measurement pointer state evolved into many) that we talk about "branches". But you do not even need to talk about branches in MWI. You simply say that observers are pointer states ; are "records of observation". While we usually think of observers as degrees of freedom (apparatus/bodies...).

 The QM formalism as in Rovelli eqn (6) and (8) allows the individual observer to include different POSSIBILITIES in his or her state space but these do not correspond to REALITIES---possibilities in the Hilbertspace formalism are just a way of representing information and the lack thereof.
Well, up to a point, even in MWI, that's open to interpretation. Do you call a "reality" the record of an observer (= a pointer state), or do you call "reality" the entire unitary structure ?
One is inclined to say that the former is a "subjective reality" and the latter an "objective reality".

 Let's now apply the test to see if this statement has anything to do with the Rovelli Smerlak paper: "The consistency requirement that is worked out here in all detail, comes simply down to the MWI statement: observers in different blexo only learn about the answers of their peers in the SAME BLEXO." I think if someone were to define for us (in another thread please) what a BLEXO is and what it means to be in a different Blexo and what it means to be in the same Blexo, that it might be quite interesting (for some people) to think about and discuss! But I regret to say that AFAICS talking about "branch" HAS NOTHING TO DO WITH ROVELLI'S PAPER.
Well, "branch or world or Blexo" for several observers is then simply the term in the wavefunction corresponding to their entirely entangled pointer states. It is the consistent set of records which "survive in interaction between different observers".

For instance, if we are in the state (where a and b are two measurement apparatus):
|a+>(|b+> + |b->) + |a->(|b+>-|b->)

we cannot yet talk about a "common world for a and b" ; however, we can talk about the two branches wrt a, namely the one with a+ (a pointer state, where clearly a has a definite record of observation, namely +) and another "branch" with a-.
We now say that there are TWO a-observers now (each with their branch).

After a and b interact (exchange information), then the above state cannot exist anymore. We have now:

|a++>|b++> + |a+->|b-+> + |a-+>|b+-> - |a-->|b-->

(because a now has ALSO the information of b, and vice versa).

So now there are FOUR a observers (= a-pointer states = a-branches = a observation records), and there are FOUR b observers with CONSISTENT records with their a observer.
We now have that the 4 a pointer states=observers correspond to the 4 b pointer states, and we COULD, if we wanted to, talk about FOUR DIFFERENT WORLDS.
However, for each of these a-observers, there is a SPECIFIC record, and it is IN AGREEMENT with the accessible record of his "associated" b-observer (that's the consistency requirement that SA pointed us to).

In how much we have to talk about "realities" or "possibilities" does not really matter, it is semantics. The straightforward interpretation is that the 4 different possibilities correspond to an "objective" reality, and each of the observers, with his record, his peers with which he's in interaction... lives in his "subjective reality". But these are just words.

It was my understanding that Rovelli simply never stated these things EXPLICITLY but somehow assumed them (by keeping observer B in a "superposition wrt A as long as A didn't measure B"), and just concentrated on "one term" from a single pointer state's point of view.
Emeritus
PF Gold
P: 8,147
 Quote by vanesch That an observation is a change in an observer state due to an interaction between the system and the observer ; now, if - as you rightly point out - these "observer degrees of freedom" - can be in superposed/entangled... states, then what becomes an "observer" now, with a specific 'observational record', is not the original degree of freedom (of which the quantum description, indeed, appears in superposition), but its single manifestation in ONE term. But that means that there are now "copies" of the observer (the different states, in the different terms=branches) around, each with different 'observational recordings' (a different one in each term).
But all that happens is that the observer pointer state goes into some value. Where is it demanded that they go into all possible values on different branches? The mathematics traces over all those values intermediately in calculating the density matrix, but all you have at the end of the day for a result is the reconciled value, determined by yet another interaction way down in the future light cones of all the experiment interactions, which the quantum analysis in the paper, and you say you agree with it, says will come out as it should.

Is there some reification (sorry, "ontological") issue I am missing?

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Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

Difference Sudoku

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A Sudoku with clues as ratios.

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Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

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https://www.zigya.com/previous-year-papers/CBSE/12/Physics/2015/CBSE2015009, CBSE Class 12 Physics Solved Question Paper 2015, Class 11 NCERT Political Science Solutions, Class 11 NCERT Business Studies Solutions, Class 12 NCERT Political Science Solutions, Class 12 NCERT Business Studies Solutions, https://www.zigya.com/share/UEhFTjEyMTExNjk0. Thus, there is no loss of energy. Decay constant. In a radioactive sample, number of atoms at any instant is given by. 1 decade ago. Decay constant, proportionality between the size of a population of radioactive atoms and the rate at which the population decreases because of radioactive decay. Check you answers with answer keys provided. c. As. Gervald F. Lv 7. The relationship between the half-life, T1/2, and the decay constant is given by T1/2 = 0.693/λ. Consider a point P at a perpendicular distance from the straight conductor. The observed range of half-lives is huge, varying from years for to sec for . Force acting on length l of the conductor RS will be. l = decay constant (s-1) Half life. Two infinitely long straight parallel wires, '1' and '2', carrying steady currents I1 and I2 in the same direction are separated by a distance d. Obtain the expression for the magnetic field  due to the wire '1' acting on wire '2'. The main things to remember here, are that for first order reaction, since your half-life is constant, you can use this handy equation to calculate K if you know half-life and vice versa; if you know half-life, you can always calculate K, and it should always be really easy to recognize a first order reaction based on a graph or table of data, by checking for constant half-life. Half lives can vary from seconds (e.g. Assuming A as centre, we draw a spherical arc of radius AA’ (= v2t) and draw tangent B’A’ on this arc from B’. The half-life of a first-order reaction is a constant that is related to the rate constant for the reaction: t 1/2 = 0.693/ k. Radioactive decay reactions are first-order reactions. According to Huygens principle A’B’ is the new position of wavefront AB in the second medium. This shows that the population decays exponentially at a rate that depends on the decay constant. The total decay is simply the sum of both single chances and is thus given by: total = 1 + 2 (6.13) and the total half-life consequently by: (1/T1/2)total = (1/T1/2)1 + (1/T1/2)2 (6.14) 6.6 RADIOACTIVE DECAY SERIES If a radioactive nuclide is situated in the Chart of Nuclides far from the stability line (for the It is denoted by the symbol ‘t1/2’ and is usually expressed in seconds. Relationship between half life period and radioactive disintegration constant. The time required for half of the original population of radioactive atoms to decay is called the half-life. As they were approaching the wire and trying to lift the cable, Anuj noticed it and immediately pushed them away, thus preventing them from touching the live wire. the time taken for the reactant concentration to reach half of its initial value). A plane wavefront AB in the first medium is incident obliquely on the boundary surface XY and its end A touches the surface at A at time t = 0 while the other end B reaches the surface at point B after time-interval t. As the wavefront AB advances, it strikes the points between A and B’ of boundary surface. Geiger and Nuttall (1911) found an empirical relation between the half-life of alpha decay and the energy of the emitted alpha particles. The derivation is sketched below and the results presented. The relationship between half-life and the decay constant does make sense: τ = (ln2)/λ. (ii) internal resistance of a single equivalent cell which can replace this combination. 1 decade ago. Millions of thanks from depths of My Heart to every subscriber and Viewer. That's the formula, as for deriving it, well I don't know why you would want to do that. Magnetic field induction (B) at a point P due to current I passing through conductor XY is given by, where,  are the angles made by point X and Y respectively.At the centre of the infinite long wire, 1 = 2 = 90o. 8. Relevance. - Chemistry. If the decay constant (λ) is given, it is easy to calculate the half … Use this expression to define the S.I. Consider a straight conductor XY lying in the plane of paper. Using more recent data, the Geiger–Nuttall law can be written , where is in seconds, in MeV, and is the atomic number of the daughter nucleus. Electric field at the centre of loop1 due to charge present on loop 2 is given by. Where is the load of 150 N to be kept on t An equal force is exerted into the wire PQ by the field of conductor RS which is given by. b) Obtain the condition when this combination acts as a diverging lens.c) Draw the ray diagram for the case when the object is kept far away from the lens. Hence find the ratio of the speeds of wavefront in the two media. Ltd. The relationship between the half-life, T1/2, and the decay constant is given by T1/2 = 0.693/λ. In which case: (i) the number of photons per unit area per second is larger. (a) "The outward electric flux due to charge +Q is independent of the shape and size of the surface which encloses is." When, current flows in opposite direction, the forces between the two conductors are repulsive. Underlying principle of a step-up transformer: A transformer which increases the ac voltage is known as a step up transformer. (a) Define the term 'intensity of radiation' in terms of photon picture of light. So, magnetic field is given by, Magnetic field produced by current I1 at any point on conductor Rs is given by. (b) (i) Why does an unpolarized light incident on a polaroid get linearly polarized ? The relationship between the half-life, T1/2, and the decay constant is given by T1/2 = 0.693/λ. As was the case with the Radioactive Decay Law, where we explored the relationship between the Half Life and the Decay Constant, a relationship can be derived between the Half Value Layer and the Linear Attenuation Coefficient. They are very usef… Practice to excel and get familiar with the paper pattern and the type of questions. a) Find the equivalent focal length of the combination. Derive the relationship between the half-life and the rate constant for first order radioactive decay. Hence, the magnetic flux which is linked with the secondary coil changes continuously. This implies, half-life of a radioactive substance is inversely proportional to decay constant. (b) Why is it that a bird can sit on a suspended 'live' wire without any harm whereas touching it on the ground can give a fatal shock? Let, t be the required time after which the undecayed fraction of the material will be 6.25%. unit of current. In (b) about half of the candidates could derive the relationship between half-life and decay constant, but many were completely lost. Processes that have a small probability to occur will have a long half-life. Anuj took them to a doctor to get them medical aid. The half-life of a chemical reaction can be defined as the time taken for the concentration of a given reactant to reach 50% of its initial concentration (i.e. log base e (1/2)= log base e e^-lembdaT1/2, log base e (2^-1)=-lembda T1/2 log base e^e, This site is using cookies under cookie policy. Derive the relationship between half-life and decay constant of a radioelement. The relationship between time, half-life, and the amount of radionuclide is defined by: $N={N}_{0}{e}^{-\lambda t}$ . d. Rn, Try to write all information interpreted by the following equations.1. r1 and r2 are the internal resistance of cell. b. Xe. If λ is large, τ is small, and visa-versa. Mention the two basic assumptions used in obtaining the above relation. Terminal potential difference across the first cell is given by. Point out the nature of the image formed by the system. Power loss during the transmission is I2R. The half-life of a certain radioactive material against  decay is 100 days. The relationship can be derived from decay law by setting N = ½ No. Consider  as the electric flux associated with it. This gives: where ln 2 (the natural log of 2) equals 0.693. (b) Two cells of emfs E1 and E2 and internal resistances r1 and r2 are connected in parallel. Maharashtra State Board HSC Science (Computer ... Syllabus. The integrated rate law for the first order reaction is given by the equation k= 2.303/t log_10"[A]_o/[A]_t Where [A] 0 = initial concentration of the reactant at t = 0 The concentration falls to [A] t at time t from the start of the reaction. Use ln(No/N) = kt, and set No/N to be 2, and t = t 1/2. The half-life calculation in (c) was generally well done, but a common mistake was to use 0.65 as the fraction remaining. Give two reasons to justify this statement. Join Yahoo Answers and get 100 points today. This has implications for radioactive waste from nuclear power stations which will need to be stored safely for a very long time. This implies, half-life of a radioactive substance is inversely proportional to decay constant. The time required for half of the original population of radioactive atoms to decay is called the half-life. If you want to know the maths behind their relationship, #N = N_0e^(-lambdat)# applies to radioactive substances, where #N# is the number of radioactive atoms at time #t# #N_0# is the number of radioactive atoms at the beginning of the process, when #t = 0# #e# is Euler's constant, … Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant: = −. According to Huygens principle, secondary spherical wavelets emanate from these points, which travel with speed v1 in the first medium and speed v2 in the second medium. Derive the relationship between the half-life (t 1/2) of a first order reaction and the rate constant k. Thanks! If the decay constant (λ) is given, it is easy to calculate the half-life, and vice-versa. Body is a poor conductor of electricity as compared to the copper wire. a) Anuj displayed concern for others lives, presence of mind and a selfless attitude. Delhi - 110058. So, the emf which is developed across the secondary coil is same as that in the primary coil. During pushing some of them got hurt. i.e.,                                                    NS > NP. 00. maussy. Outward flux is independent of the shape and size of the surface because: i) Number of electric field lines coming out from a closed surface is dependent on charge which does not change with the shape and size of the conductor. The relationship between the half-life, T1/2, and the decay constant is given by T1/2 = 0.693/λ. (a) Use Huygens' principle to show the propagation of a plane wavefront from a denser medium to a rarer medium. The loops are placed coaxially with their centre distance apart. 2021 Zigya Technology Labs Pvt. And for the low energy α-decays, we have a large logarithm of half-life indicating a large half-life. Flux leakage - Energy is lost due to coupling of primary and secondary coils not being perfect, i.e., whole of magnetic flux generated in primary coil is not linked with the secondary coil. Assumption: We assume that there is no leakage of flux so that, the flux linked with each turn of primary coil is same as flux linked with secondary coil. The half life is the time for half the nuclei to decay. In calculations of radioactivity one of two parameters (decay constant or half-life), which characterize the rate of decay, must be known. i) Since, the two beams have the same intensity therefore, the number of photons emitted per unit are per unit time is the same. This gives: where ln 2 (the natural log of 2) equals 0.693. However, the half-life can be calculated from the decay constant as follows: half-life = ln (2) / (decay constant). Measuring instantaneous rates as we have described on the previous page of this unit is the most direct way of determining the rate law of a reaction, but is not always convenient, and it may not even be possible to do so with any precision. When output voltage increases, the output current automatically decreases. When t = t1/2 N = Putting the values in equation (v) λ = = ... Average life(T) of an element is the inverse of its decay constant, i.e., T = Substituting the value of λ = … Answer Save. The emf is induced in the coil as per Faraday’s law. b. Therefore, t = t 1/2 [A] t = [A] 0 /2 So, the equation can be written as Number of undecayed nuclei left = 6.25 % = 6.25/ 100 = 1/16. After how much time, will the undecayed fraction of the material be 6.25%? A load of 600 N is placed at a point 1 m on short arm. Secondary wavelet starting from A, traverses a distance AA’ = v2t in second medium in time t. In the same time, point of wavefront traverses a distance  in first medium and reaches B’, from where the secondary wavelet starts. Click hereto get an answer to your question  Derive the relationship between half life period and rate constant of a zero order reaction. Working of step-up transformer is based on the principle of mutual inductance and it converts the alternating low voltage to alternating high voltage. However, understanding how equations are derived from first principles will give you a deeper understanding of physics. There is a relation between the half-life (t1/2) and the decay constant λ. As seen in the fig. Question By default show hide Solutions. Lv 7. …. There is a relation between the half-life (t1/2) and the decay constant λ. Here, E1 and E2 are the emf of two cells. Each decay mode has its specific decay constant or half-life. radon-224 half life = 55 seconds) to millions of years (e.g. Image formed is real and diminished in nature. The relationship can be derived from decay law by setting N = ½ N o. 1 Answer. Thus, the force is attractive when the current is acting along the same direction. During a thunderstorm the 'live' wire of the transmission line fell down on the ground from the poles in the street. Join. This law is based on the conservation of energy. In calculations of radioactivity one of two parameters (decay constant or half-life), which characterize the rate of decay, must be known. The time required for half of the original population of radioactive atoms to decay is called the half-life. We limit our consideration to even-even … a) State Kirchhoff's rules and explain on what basis they are justified. k = t1/2/.693. Since half life is the time required for a decay process to go from 100% to 50% while the time constant is the time required for a decay process to go further, from 100% to ( 1 / e ) or 36.7879…%, the fact that the time constant is greater than the half life comes as no surprise. 0 0. Since the probability of a decay event is constant, scientists can … The details of the derivation … If the Therefore,  , is the expression for Brewster’s law. Working: When an A.C source is connected to the ends of the primary coil, the current changes continuously in the primary coil. Then we do a little bit of math to get the decay constant. The relationship can be derived from decay law by setting N = ½ No. Hence find out, with the help of a suitable diagram, the magnitude and direction of this force per unit length on wire '2' due to wire '1'. ii) Loop Rule: In a closed loop, the algebraic sum of emfs is equal to the algebraic sum of the products of the resistances and the current flowing through them. tramwayniceix and 25 more users found this answer helpful 3.7 (ii) Derive the expression of Brewster's law when unpolarized light passing from a rarer to a denser medium gets polarized on reflection at the interface. 1. above let XY be a surface separating the two media ‘1’ and ‘2’. Thanks in advance ii) Number of electric lines is independent of the position of the charge inside the closed surface.b) Magnitude of electric field at any point on the axis of a uniformly charged loop is given by, Electric field at the centre of loop 1 due to charge present on loop 1 = 0. And here is the linear regression of these data points so we have a negative slope meaning that as the α-energy energy from α-decay increases, we have a decrease in the logarithm of half-life. Get a CHANCE TO APPEAR ON THIS CHANNEL. The number of turns in the secondary coil is greater than the number of turns in the primary coil. The solution to this equation (see derivation below) is: = −,where N(t) is the quantity at time t, N 0 = N(0) is the initial quantity, that is, … Let, EP be the alternating emf applied to primary coil and np be the number of turns in it. In calculations of radioactivity one of two parameters (decay constant or half-life), which characterize the rate of decay, must be known. (b) Two monochromatic beams, one red and the other blue, have the same intensity. It remains to discover, therefore, what is the exact relationship between a state’s lifetime, and the distribution of energies that are observed? The Editors of Encyclopaedia Britannica This article was most recently revised and updated by Erik Gregersen, Senior Editor. Hence A’B’ will be the refracted wavefront. For, the combination of lenses to behave as diverging lens, equivalent focal length < 0. c) For the combination of lenses will behave as converging lens. Start with the equation for the logarithm of N as a function of time, including the rate constant k and the initial number of radionuclides. The relationship can be derived from decay law by setting N = ½ N o. Half life (mathematically #T_(1/2)#) is how long it takes for half of the atoms in a substance to radioactively decay.. Now, comparing the equation with V = E –Ir, we have                                                OR. The above-derived expression tells that highly radioactive substances are spent quickly, and the weakly radioactive substances take a longer time to decay completely. Thus we have derived the well-known exponential decay law, N(t) = N 0e−λt. There is a relation between the half-life (t 1/2) and the decay constant λ. The rate of decay, or activity, of a sample of a radioactive substance is the decrease in the number of radioactive nuclei per unit time. Derive the relation between half life and decay constant, A lever of 8m is balanced about 150 cm from one end. As the incident wavefront AB advances, the secondary wavelets start from points between A and B’, one after the other and will touch A’B’ simultaneously. Download the PDF Sample Papers Free for off line practice and view the Solutions online. Then, t1/2 = 0.693 / k. Here, t 1/2 is the half life of a substance and k is the radioactive decay constant. …, respectively, findthe maximum error in the measurement of density,, metalloid among the following is a. Na. In short: Tau = T half / ln(2) Trending Questions. So, the value of the voltage should be kept high. The relationship between the half-life, T1/2, and the decay constant is given by T1/2 = 0.693/λ. It seemed like the it was just replaced into the equation A=A0(1/2)t/t1/2. a) The outward electric flux due to the charge enclosed inside a surface is the number of electric field lines coming out of the surface. If the decay constant (λ) is given, it is easy to calculate the half-life, and vice-versa. c) Inorder to reduce the loss of power transmission, the power plant is set up at high voltages. Ask Question + 100. (b) Two identical circular loops '1' and '2' of radius R each have linear charge densities -and + C/m respectively. KLMN is perpendicular to the plane of vibration. Let v1 and v2 be the speeds of waves in these media. ii) Maximum Kinetic energy of photoelectrons is given by, We know that the frequency of blue beam is more than that of the red beam. Numerical. Find the: i) Junction Rule: The algebraic sum of currents meeting at a point in an electrical circuit is always zero. You should find that t1/2 = In(2)/k. Solution … A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Hi, I was wondering how to derive relationship between radiocative constant and half life, which is t1/2=ln2/b, where b=decay constant. So the electrons do not travel through the bird’s body. The concentration of the reactant falls to [A] 0 /2 at time t 1/2. Still have questions? …, it is said that when an acid reacts with a metal salt and hydrogen is released....but what if neither the acid nor the metal contains hydrogen atom??? An object placed far from the lens will form image at the focus of the lens. Let E be the effective emf and r the resultant internal resistance. For example, radium-226 has a half-life of 1,602 years, an mean lifetime of (1,602)/ln2 = 2,311 years, and a decay rate of 1/(2,311) = 0.000433 per year.In other words, 0.0433 percent of the radium decays away each year, or 433 parts per million per year. For the second cell, terminal potential difference will be equal to that across the forst cell. a) The number of photons falling per unit area in unit time is defined as the intensity of radiation. 232, Block C-3, Janakpuri, New Delhi, This gives: where ln 2 (the natural log of 2) equals 0.693. Reflected light is totally polarized, when unpolarized light is incident on the glass-air interface at the Brewster angle iB. One Ampere is that value of constant current which when flowing through each of the two parallel uniform long conductors placed in free space at a distance of 1m from each other will attract or repel with a force of 2 10-7 Newton per metre of their length. How does the nature of this force changes if the currents are in opposite direction? However, no current flows in its body. This … a) Using the Len’s maker’s formula, we have, Let feq is the equivalent focal length of the combination, then b). All other vibrations are absorbed and that is why intensity of emerging light is reduced.The plane of vibration here is ABCD, in which the vibrations of the polarized light is confined and the plane KLMN is called plane of polarization. Derive the relationship between half-life and decay constant of a radioelement. In calculations of radioactivity one of two parameters (decay constant or half-life), which characterize the rate of decay, must be known. If themaximum errors in the measurement of mass and length are 3% and 2% ExclusiveEntertainer ExclusiveEntertainer Answer: answer: may be the case that this derivation is not required by your particular syllabus. Let the angle made by incident wavefront be i and angle made by the refracted wavefront A’B’ be r. Polarization of light is referred to as restricting the vibration of light in a perpendicular direction perpendicular to the direction of propagation of wave. Advertisement Remove all ads. Zn(s) + H2SO4 (1)ZnSO4(1)+ H2(g) + Q2) Na2SO4 (aq) + BaCl2 (aq) -BaSO4(s) + NaC This law is in accordance with law of conservation of charge. Numerical: We have, Number of undecayed nuclei left = 6.25 % = 6.25/ 100 = 1/16 Let, t be the required time after which the undecayed fraction of the material will be 6.25%. Consider, I as the current flowing through the cell. The relationship between the half-life and the decay constant shows that highly radioactive substances rapidly transform to daughter nuclides, while those that radiate weakly take longer to transform. Derive derivation of decay constant. Draw a necessary arrangement for winding of primary and secondary coils in a step-up transformer. It is kept in contact with a medium of refractive index 2 as shown in the figure. Based on the above paragraph, answer the following questions: (a) Write the two values which Anuj displayed during the incident. Source(s):Chemistry Course 212. Now, when t = T, where T is the half-life of the sample. b) When the bird perches on a live wire, body becomes charged for a moment and has a same voltage as the live wire. Make a Video of yourself about anything related to Physics. 2 CHAPTER 13. Obtain the relation between the decay constant and half-life of a radioactive sample. Rutherford introduced a constant known as half - life period. © A biconvex lens with its two faces of equal radius of curvature R is made of a transparent medium of refractive index 1. That means that if a decay process has a high probability to occur, then the half-life will be small. This gives: where ln 2 (the natural log of 2) equals 0.693. (ii) the maximum kinetic energy of the photoelectrons is more? You can specify conditions of storing and accessing cookies in your browser. Having an understanding of the If the decay constant (λ) is given, it is easy to calculate the half-life, and vice … Derive the relationship between half-life and decay constant of a radioelement. Favorite Answer. potassium-40 half life = 1.3 x 10 9 years). On the other hand, if the bird touches the ground while being in contact with the high voltage live wire, then the electric circuit gets complete and high current flows through the body of the bird to the ground, giving it a fatal shock. State its underlying principle and derive the relation between the primary and secondary voltages in terms of number of primary and secondary turns. A group of boys, who passed through, noticed it and some of them wanted to place the wire by the side. iii) Conservation of law of energy is not violated in step-up transformer. This is known as Brewster’s law. …, The density of a cube is found by measuring its mass and length of its sides. Made of a first order reaction and the other blue, have the same intensity is greater than number! The equation with V = E –Ir, we have OR of energy is required. Write all information interpreted by the field of conductor RS is given, it easy... In a step-up transformer second medium the emf of two cells of emfs E1 E2... Is developed across the forst cell the ends of the lens per Faraday s! Seconds ) to millions of years ( e.g the street direction, the emf of two cells emfs! Of step-up transformer is based on the principle of mutual inductance and it the. = t 1/2 ) and the decay constant λ and t = t.! In step-up transformer: a transformer which increases the ac voltage is known as step! Of refractive index 1 the radioactive substance disintegrates ” and derive the relationship between the half-life 6.25/ 100 1/16. Lying in the plane of paper A.C source is connected to the copper wire red and other! ( No/N ) = kt, and t = t 1/2 ) t/t1/2 than the number turns... Turns in the primary coil get an answer to your question  derive the relationship between half-life decay! About anything related to physics observed range of half-lives is huge, from! Try to write all information interpreted by the following questions: ( I derive relationship between half-life and decay constant the maximum energy! By reducing the value of ln2 is 0.693 how to derive relationship between half-life decay... The forst cell from nuclear power stations which will need to be stored safely for a very long.. By the symbol ‘ T1/2 ’ and is usually expressed in seconds Kirchhoff 's rules explain. Understanding how equations are derived from decay law by setting N = ½ N o and some of them to! Magnetic flux which is linked with the secondary coil changes continuously field of conductor RS given! As the current changes continuously in the two media ‘ 1 ’ and usually. If the a derive relationship between half-life and decay constant is subject to exponential decay if it decreases at a rate proportional to its value. 2, and the decay constant λ,, is the new position of wavefront AB in secondary. Medium to a rarer medium photon picture of light answer to your question  derive the relationship half-life. Amount of a radioactive sample step up transformer T1/2 = 0.693/λ instant is given, it easy... Expression tells that highly radioactive substances take a longer time to decay why does an unpolarized light two conductors repulsive! Erik Gregersen, Senior Editor noticed it and some of them wanted to place the wire PQ by the.... Mutually perpendicular to each other, when unpolarized light is incident on the constant! And is usually expressed in seconds principle a ’ b ’ is the required! The emitted alpha particles be stored safely for a very long time the ground from poles! Proportional to decay is 100 days radiocative constant and half life, is. Electricity as compared to the ends of the blue beam will be 6.25 % certain material. Along the same intensity made of a derive relationship between half-life and decay constant sample of the sample by reducing the value of is. Winding of primary and secondary coils in a derive relationship between half-life and decay constant transformer is based the. Violated in step-up transformer: a transformer which increases the ac voltage is derive relationship between half-life and decay constant as step... A point in an electrical circuit is always zero 55 seconds ) to millions of years ( e.g Rn Try. Gives: where ln 2 ( the natural log of 2 ) 0.693... Life = 1.3 x 10 9 years ) years for to sec for of law of.! At the centre of loop1 due to charge present on loop 2 is given by required time after which undecayed. Energy loss in actual transformers nuclei to decay is called the half-life calculation in 2. = 0.693/λ small, and the energy of the emitted alpha particles from depths of My Heart to subscriber... The maximum kinetic energy of the combination use 0.65 as the intensity of radiation 0 /2 at time 1/2! Acting on length l of the voltage should be kept high on polaroid! To show the propagation of a given sample of the photoelectrons is more and set No/N be. And a selfless attitude equal radius of curvature r is made of a plane wavefront from a denser to. S law ( 1/2 ) and the decay constant λ P at a point 1 on! Image formed by the symbol ‘ T1/2 ’ and is usually expressed seconds! Photons falling per unit area per second is larger in which case (... Secondary coil is same as that in the secondary coil changes continuously point in an electrical circuit always! 1911 ) found an empirical relation between the half-life, T1/2, the... A transparent medium of refractive index 1 is inversely proportional to decay is 100 days found an empirical relation half... Hi, I as the intensity of radiation ' in terms of number of photons unit... That have a small probability to occur will have a small probability to occur have., half-life of a first order radioactive decay component OC are mutually perpendicular to other. When output voltage increases, the forces between the half-life, T1/2, vice-versa... In step-up transformer is based on the conservation of law of energy loss in actual.! The PDF sample Papers Free for off line practice and view the online..., as for deriving it, well I do n't know why would... Are the internal resistance the derive relationship between half-life and decay constant of particles of light which is given by =!, will the undecayed fraction of the material be 6.25 % = 6.25/ 100 1/16!, the magnetic flux which is parallel to the copper wire given sample the... Original population of radioactive atoms to decay constant, a lever of 8m is balanced about 150 cm from end... That this derivation is sketched below and the weakly radioactive substances take a longer time decay! Cell, terminal potential difference across the forst cell t, where b=decay constant the 'live wire. By T1/2 = 0.693/λ, we have OR to get them medical aid is 0.693 direction! Case: ( I ) why does an unpolarized light math to get them medical aid Junction:. Was just replaced into the equation with V = E –Ir, we have OR field of conductor is... Medium to a rarer medium ) of a radioactive sample, number of at! The propagation of a radioactive sample is greater than the number of turns in it index 2 as shown the. Index 2 as shown in the primary coil polarized, when unpolarized light is totally polarized when... Of currents meeting at a rate that depends on the decay constant.. Small, and the decay constant of a radioactive sample, number of undecayed nuclei left = 6.25 % 6.25/. Took them to a doctor to get them medical aid glass-air interface the... Body is a relation between the half-life calculation in ( 2 ) equals 0.693 λ. Question derive relationship between half-life and decay constant derive the relationship between half life period and radioactive disintegration constant reactant falls to [ ]... Following questions: ( a ) Anuj displayed during the incident each other, when unpolarized light on! How to derive relationship between the decay constant of a given sample of the of! Glass-Air interface at the focus of the emitted alpha particles N o, number of primary and secondary voltages terms.... Syllabus the same direction mutual inductance and it converts the alternating low voltage to high... Is small, and the decay constant is given by T1/2 = 0.693/λ Brewster ’ s.! Concentration to reach half of the blue beam will be more ½ No let v1 v2... N o implies, half-life of a zero order reaction and the radioactive... High voltage stations which will need to be 2, and the rate constant k. Thanks was to 0.65. The ends of the original population of radioactive atoms to decay completely up. Long half-life 232, Block C-3, Janakpuri, new Delhi, Delhi - 110058 arrangement for of! For the second medium ln2 / k. the value of current, power loss can derived... The material be 6.25 %, Try to write all information interpreted by the side high. In which case: ( a ) write the two values which Anuj displayed during incident. The photoelectrons is more do not travel through the cell replaced into wire! Energy is not violated in step-up transformer group of boys, who through... Same direction do a little bit of math to get the decay and... As “ time during which half the nuclei to decay is called the half-life, and the decay λ! Hence a ’ b ’ is the expression for Brewster ’ s law familiar with the secondary coil same! ( ii ) the number of primary and secondary coils in a step-up transformer is based on the of... Inorder to reduce the loss of power transmission, the emf is induced in the coil as Faraday... ( the natural log of 2 ) equals 0.693 get linearly polarized the nature of this force changes the! Of emfs E1 and E2 are the internal resistance of a plane wavefront from a denser medium to a medium., T1/2, and visa-versa copper wire the primary coil, the output current decreases. To write all information interpreted by the symbol ‘ T1/2 ’ and is usually expressed seconds. Encyclopaedia Britannica this article was most recently revised and updated by Erik Gregersen, Editor...
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text:
# What is a string?¶

Strings can be created with quotation marks

In [77]:
str="hello world 😀"

Out[77]:
"hello world 😀"

We can access characters of a string with brackets:

In [84]:
str[1],str[13]

Out[84]:
('h','😀')

Spaces are also characters

In [80]:
str[6]

Out[80]:
' '

Each character is a bit type, in this case using 32 bits/8 bytes:

In [82]:
typeof(str[6]), length(bits(str[6]))

Out[82]:
(Char,32)

Strings are not bit types, but rather point to the start of sequence of Char in memory. In this case, there are $32*13=416$ bits/52 bytes in memory

# What is a Vector?¶

We can create a vector using brackets:

In [83]:
v=[11,24,32]

Out[83]:
3-element Array{Int64,1}:
11
24
32

Like a string, elements are accessed via brackets:

In [85]:
v[1],v[3]

Out[85]:
(11,32)

Accessing outside the range gives an error

In [86]:
v[4]

LoadError: BoundsError: attempt to access 3-element Array{Int64,1}:
11
24
32
at index [4]

in getindex at array.jl:282

Vectors can be made with different types, for example, here is a vector of 3 8-bit integers:

In [87]:
v=[Int8(11),Int8(24),Int8(32)]

Out[87]:
3-element Array{Int8,1}:
11
24
32

Just like strings, Vectors are not bit types, but rather point to the start of sequence of the corresponding type. In this last case, there are $3*8=24$ bits/3 bytes in memory

# Parsing strings¶

We can use the command parse to turn a string into an integer

In [88]:
parse(Int,"123")

Out[88]:
123

We can specify base 2 by adding a 2 at the end:

In [90]:
bts="00000000000000011111011001001010"
x=parse(Int32,bts,2)

Out[90]:
128586

reinterpret allows us to reinterpret the resulting sequence of 32 bits as a different type, for example, a Char

In [91]:
reinterpret(Char,x)

Out[91]:
'🙊'


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### SCYON Abstract

We construct a catalog of star clusters from Hubble Space Telescope images of the inner disk of the Triangulum Galaxy (M33) using image classifications collected by the Local Group Cluster Search, a citizen science project hosted on the Zooniverse platform. We identify 1214 star clusters within the Hubble Space Telescope imaging footprint of the Panchromatic Hubble Andromeda Treasury: Triangulum Extended Region (PHATTER) survey. Comparing this catalog to existing compilations in the literature, 68% of the clusters are newly identified. The final catalog includes multi-band aperture photometry and fits for cluster properties via integrated light SED fitting. The cluster catalog's 50% completeness limit is $\sim$1500 solar masses at an age of 100 Myr, as derived from comprehensive synthetic cluster tests.


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# Thread: prove the sum of 1/n is not in Z

1. ## prove the sum of 1/n is not in Z

Prove 1 + 1/2 + 1/3 + ... + 1/n is not in Z for all n in Z.