Do weak measurement prove randomness is not inherent?

In summary: Question: When we try to get which-way info (we cause de-coherence, we create phase difference), do we increase or decrease randomness or does it remain the same?In summary, when we try to get which-way info (we cause de-coherence, we create phase difference), we decrease randomness.
  • #1
San K
911
1
Weak measurement show that you can get "partial/probabilistic" which-way info and get a "partial" interference pattern.

Deduction 1:

Does this mean that weak measurements prove that we can control the degree of randomness?

(either of individual photons or average of a thousands of photons)

Deduction 2:

If we can control the degree of randomness, does it mean that randomness is not inherent BUTRandomness is simply a way to describe forces/phenomena/dimension that we are unaware of and thus describe/model it stochastically (for example how we do with Brownian movement)

Deduction 1 in my opinion requires a lesser "leap of faith" as its follows out fairly logical.
 
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  • #2
No. The "randomness" you are referring to is a fundamental limit imposed by the HUP. That is why the quality of the interference pattern degrades as the "strength" of the weak measurement is increased.
 
  • #3
I doubt randomness actually exists in nature.
It's more of a side product of the HUP, it's not ACTUAL randomness, although some crazy people do believe true randomness exists, actually quite a lot of otherwise smart people do so.
 
  • #4
Fyzix said:
I doubt randomness actually exists in nature.
It's more of a side product of the HUP, it's not ACTUAL randomness, although some crazy people do believe true randomness exists, actually quite a lot of otherwise smart people do so.

I don't understand what you mean ... what is "ACTUAL randomness"? Are you saying you agree with the Bohmian hypothesis that everything is deterministic, but that we can never know the initial conditions precisely enough to make predictions? I think that is the Bohmian view on the HUP ... i.e. that it restricts how well we can know the initial conditions for any quantum system, so the results of experiments appear probabilistic.
 
  • #5
SpectraCat said:
No. The "randomness" you are referring to is a fundamental limit imposed by the HUP. That is why the quality of the interference pattern degrades as the "strength" of the weak measurement is increased.

i see your point.

Question: when we try to get which-way info (we cause de-coherence, we create phase difference), do we increase or decrease randomness or does it remain the same?
 
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  • #6
SpectraCat said:
I don't understand what you mean ... what is "ACTUAL randomness"? Are you saying you agree with the Bohmian hypothesis that everything is deterministic, but that we can never know the initial conditions precisely enough to make predictions? I think that is the Bohmian view on the HUP ... i.e. that it restricts how well we can know the initial conditions for any quantum system, so the results of experiments appear probabilistic.

Yes, I am as certain as a human can be that the universe is 100% deterministic, from big bang to now.
Every single particle is deterministic.
I just don't see how reality could be any other way.
If randomness were truly part of quantum theory, I doubt we could even get probabilistics out of it.

Think about it, if something was RANDOM, how could we ever predict ANYTHING, even somethings probability?

I'm not sure whether Bohm is correct, or some other hidden variable interpretation (gerard 't hooft is working on this) or perhaps some brand new physics will be discovered that will shed light on the issue, but what I am sure of is that realism and determinism/causality is going to be a part of whatever the truth is.
 
  • #7
Fyzix said:
Yes, I am as certain as a human can be that the universe is 100% deterministic, from big bang to now.
Every single particle is deterministic.
I just don't see how reality could be any other way...

Nice that you are so certain when there is no evidence to support your view whatsoever. And I do mean none.

Going back to Hume's work on causality, folks have continually assumed that which they are trying to prove. He did that explicitly. And you too, for example:

I wonder: was the Beatles' work inevitable? Because I can't imagine a world without their music. QED! :smile:
 
  • #8
DrChinese said:
Going back to Hume's work on causality, folks have continually assumed that which they are trying to prove. He did that explicitly.
Are you talking about David Hume? If you do, then let me quote his famous words very applicable here:
"If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning, concerning matter of fact and existence? No. Commit it then to flames: for it can contain nothing but sophistry and illusion."
 
  • #9
Demystifier said:
Are you talking about David Hume? If you do, then let me quote his famous words very applicable here:
"If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning, concerning matter of fact and existence? No. Commit it then to flames: for it can contain nothing but sophistry and illusion."

"THOUGH there be no such thing as Chance in the world; our ignorance of the real cause of any event has the same influence on the understanding, and begets a like species of belief or opinion."

-Hume
 
  • #10
Fyzix said:
Yes, I am as certain as a human can be that the universe is 100% deterministic, from big bang to now.
Every single particle is deterministic.
I just don't see how reality could be any other way.

I often wonder why people believe the universe is deterministic. Not only, as DrChinese says, is there no evidence for this, but our everyday experience doesn't support this view. It certainly feels like I have free will - I can choose whether to type an A or a B as the next character - here goes - B. Do you really believe that my decision to type a B was pre-ordained at the moment of the Big Bang? If there were objective evidence that the universe were deterministic, then I could understand believing this in spite of the evidence of my senses, but with the evidence of my senses telling me that the universe is not pre-determined, why would I choose to believe that it is?
 
  • #11
What's more, I would add that both "random" and "deterministic" are always attributes of a theory or model. Science has no way to even discuss whether or not these are attributes of the real world, and I would add that a seasoned view of what science actually does warns us against extrapolating the nature of theories to the nature of reality. If the history of science has taught us nothing else, let it teach us that.
 
  • #12
DrChinese said:
"THOUGH there be no such thing as Chance in the world; our ignorance of the real cause of any event has the same influence on the understanding, and begets a like species of belief or opinion."

-Hume
Though IIRC, he wasn't out to prove determinism there (the futility of such an attempt, I imagine, would be something Hume of all people would have been most acutely aware of), he merely assumed it, the alternative making no sense to him. And it is a difficult thing to wrap one's head around, to the point of appearing almost self-contradictory.

One might, for instance, quite reasonably assume that everything that happens has a way by which it does so, some mechanism through which it occurs -- but if that's the case, then randomness seems nonsense: for any indeterminate choice between alternatives A and B, either some mechanism chooses A over B (say) -- but then, obviously, that mechanism provides for determinism; or, neither A nor B gets chosen -- but then, neither happens. So (if indeterminism is real) one must renounce the assumption that everything that happens has a mechanism through which it happens, so that without a choice being made, A (or B) is chosen.

Smarter people than me have asserted that such a thing is perfectly possible, that things can 'just happen', without sufficient cause, but to me, that's kinda like an underdetermined system of equations having an unique, and right, solution -- the information just isn't there --, and furthermore, if things just happen, then why bother with this whole physics stuff at all? If ultimately everything turns out to be the way it is because that's how it happens to be, then it seems we should cut to the chase and throw in the towel.

But luckily, quantum mechanics is perfectly compatible with determinism -- so one might argue that parsimony tilts the scales heavily in favour of such an interpretation (since there is otherwise no indication that indeterminism is possible at all).

And, so as not to be completely off-topic, there is of course no experiment that can decide between different interpretations of QM -- otherwise, they wouldn't be different interpretations, but rather, different theories.
 
  • #13
phyzguy said:
I often wonder why people believe the universe is deterministic. Not only, as DrChinese says, is there no evidence for this, but our everyday experience doesn't support this view. It certainly feels like I have free will - I can choose whether to type an A or a B as the next character - here goes - B. Do you really believe that my decision to type a B was pre-ordained at the moment of the Big Bang? If there were objective evidence that the universe were deterministic, then I could understand believing this in spite of the evidence of my senses, but with the evidence of my senses telling me that the universe is not pre-determined, why would I choose to believe that it is?
The argument for (human) free will does not require inherent/quantum randomness.

Thought I believe in both: human free will and inherent/quantum-level randomness. But neither is a precondition for supporting other.
 
  • #14
Lately I've been enjoying the deterministic perspective (probably, it seems more 'relaxing' ;) ) but I think the concept of 'true randomness' sits just fine with many people. You could claim that the universe is a balance between a Pattern that is ordered/understandable/predictable and an element of Chaos that is fundamentally 'irrational'/unpredictable/arbitrary. After all, that whole concept is embedded in various mythologies which is a sign it holds some deep intuitive appeal.

And regarding 'throwing in the towel': well, science is never going to answer the question 'why does anything whatsoever exist at all' (i.e. why do 'laws of physics' exist, why is there a 'reality' at all). So we are always going to be stuck with an element of 'arbitrariness' in the ultimate axioms of our TOE, "things just happen to be this way".
 
  • #15
Well weak measurement plays an important conceptual role in Aharnov's time-symmetric interpretation of quantum mechanics which is an interpretation which does away with the probabilistic nature of quantum mechanics.
 
  • #16
I love how people say "determinism doesn't fit our everyday life", YES IT DOES.
More than anything.
EVERYTHING in the classical realm has been shown to be 100% deterministic, in other words, ANYTHING you ever experience was 100% detemined.

Now DrChinese I know you got some weird views on QM so I won't even bother.

I never said I could prove it, because it can't be proven.
Neither can randomness.

However, everything we ever assumed was random, turned out to be deterministic, most likely this is so at the quantum scale too.
Just because we, humans, can't access it doesn't mean anything.
 
  • #17
phyzguy said:
I often wonder why people believe the universe is deterministic. Not only, as DrChinese says, is there no evidence for this, but our everyday experience doesn't support this view. It certainly feels like I have free will - I can choose whether to type an A or a B as the next character - here goes - B. Do you really believe that my decision to type a B was pre-ordained at the moment of the Big Bang? If there were objective evidence that the universe were deterministic, then I could understand believing this in spite of the evidence of my senses, but with the evidence of my senses telling me that the universe is not pre-determined, why would I choose to believe that it is?

Ofcourse you don't got free will, what the hell, do science minded people still believe in this illusion in 2011?!
That's beyond belief...

It also feels like colors are objective.
If you cut someones arm off, they can often experience "phantom sensations", experiencing that they have a hand that isn't there.
Just because you FEEL that you make the choice free willingly doens't prove anything.
Actually I'm pretty sure they have already proven that you have no choice through measuring brain activity.
 
  • #18
Fyzix said:
Now DrChinese I know you got some weird views on QM so I won't even bother.

Weird views, sure: I believe it.

(By the way, that would be like the pot calling the kettle...)

:smile:
 
  • #19
Fyzix said:
Just because you FEEL that you make the choice free willingly doens't prove anything.
Actually I'm pretty sure they have already proven that you have no choice through measuring brain activity.
No, they haven't proven any such thing. What has been shown and seems pretty reliable is that part of your brain is modeling itself, so when you make a mental decision, part of your brain has the job of "telling the story" of how you made that choice. This storytelling comes after the decision, which can easily be mistaken for evidence there wasn't a decision, but the truth is we still have no real idea of how to test for the difference between a "true free choice" and a "predetermined choice", and many people think those two things are apples and oranges that can easily coexist. But that gets into neuroscience and philosophy, not really relevant to "weak measurement" so we should probably just nip off the whole "free will" detour.
 
  • #20
Fyzix said:
EVERYTHING in the classical realm has been shown to be 100% deterministic, in other words, ANYTHING you ever experience was 100% detemined.

Really?

If I watch single photons hitting a detector, or listen to a Geiger counter clicking, has it been shown that I'm experiencing something 100% determined?

What about random mutations in DNA, or even weather patterns do to chaos principles?

I would have thought those examples come back to the unresolved debate between different QM interpretations.
 
  • #21
rgmcc said:
Really?

If I watch single photons hitting a detector
Classical?

Geiger counter clicking, has it been shown that I'm experiencing something 100% determined?
Radioactive decay is classical?

What about random mutations in DNA, or even weather patterns do to chaos principles?

mutations in DNA, I'm pretty sure this is outside of the quantum realm and thus classical yea, so yea.
I would have thought those examples come back to the unresolved debate between different QM interpretations.

Yupp, just like my argument says...
At the end of the day, the quantum raelm is at the bottom.

However throughout history we always thought things were random, then we investigate, find it's not random, then there is a new level we think is random, then it isn't etc etc etc etc etc.
Then we hit quantum mechanics and people somehow believe this is different...
 
  • #22
Actually, here is a different way to present your exact same argument. Throughout history, whenever we thought something was deterministic, we found a deeper level that was random. Did you really just argue that this means the people who think there will always be inherent randomness are ignoring the lessons of history?
 
  • #23
Fyzix said:
EVERYTHING in the classical realm has been shown to be 100% deterministic, in other words, ANYTHING you ever experience was 100% detemined.

My point was:

Clicks of Geiger counter are considered 'quantum random'. Clicks of a Geiger counter have not been _shown_ to be 100% deterministic (it is a matter of unresolved competing QM interpretations). Also, clicks of a Geiger counter are something I can experience.

Therefore it is not true that 'anything I can experience was 100% determined'.

Is there a flaw in what I'm saying?
 
  • #24
Do you consider thermal statistics determinate? in brownian motion, all particles take deterministic path but they are seen to be random. Was this why Einstein proposed his statistical interpretation and was it about determinism? About clicks in geiger counter being random. If one plots the distribution in time. It is no longer random. So maybe by linking it with spaceTIME. Determinism is the ultimate result as the probability distribution is only arranged in time from past present and future. Is this possible?

Bottomline is. By taking time as illusion, determinism is retained?
 
  • #25
Varon said:
Do you consider thermal statistics determinate? in brownian motion, all particles take deterministic path but they are seen to be random.
Have you heard about chaos theory? Determinism is a mathematical concept that applies to mathematical models. Real systems show similar behavior to chaotic deterministic mathematical systems, but that does not mean the real systems are deterministic, again because the way they are deterministic in the mathematical models simply does not apply to real world systems. In experimental physics, unlike mathematics, determinism can only be equated with "predictable", because experimental physics has no capability to define any other concept of determinism. And what we know is, in experimental physics, Brownian motion is not predictable, so cannot be called deterministic. Mathematical models of Brownian motion can be called deterministic, but their deterministic character, because of chaos, is part of what we can never match to observations. Hence in regard to determinism, we can never know if the mathematical models correctly reflect the true nature of the reality, or not. Indeed, if we hold to the deterministic belief, we end up with the rather absurd conclusion that butterflies can cause tornadoes, even though a flapped wing never changes the statistical tendencies of any weather patterns.

About clicks in geiger counter being random. If one plots the distribution in time. It is no longer random.
I'm not sure where you got that idea, but it's going to come as a pretty big surprise to a lot of experimental physicists who routinely model their data using Poisson (random) statistics.
 
  • #26
Ken G said:
Have you heard about chaos theory? Determinism is a mathematical concept that applies to mathematical models. Real systems show similar behavior to chaotic deterministic mathematical systems, but that does not mean the real systems are deterministic, again because the way they are deterministic in the mathematical models simply does not apply to real world systems. In experimental physics, unlike mathematics, determinism can only be equated with "predictable", because experimental physics has no capability to define any other concept of determinism. And what we know is, in experimental physics, Brownian motion is not predictable, so cannot be called deterministic. Mathematical models of Brownian motion can be called deterministic, but their deterministic character, because of chaos, is part of what we can never match to observations. Hence in regard to determinism, we can never know if the mathematical models correctly reflect the true nature of the reality, or not. Indeed, if we hold to the deterministic belief, we end up with the rather absurd conclusion that butterflies can cause tornadoes, even though a flapped wing never changes the statistical tendencies of any weather patterns.

I'm not sure where you got that idea, but it's going to come as a pretty big surprise to a lot of experimental physicists who routinely model their data using Poisson (random) statistics.

Supposed there was no true quantum randomness. Can it be already predicted 13.75 billion ago at the time of the Big Bang that a certain hurricane would occur in Katrina 13.75 billion years later in a certain part of a globe called Earth in a certain part of a galaxy in a certain part of the universe. Is this determinism possible at all if there is no true quantum randomness.. or can classical world produce true randomness such that the future is not written in stone? If so, what is this theorem called?
 
  • #27
Classical chaos would have made that prediction impossible with any reasonable uncertainty in a measured initial condition. But here we come to the crux of the problem-- is physics inherently a prescription for our intelligence to link initial measurements to final ones, which means it is a theory with uncertainties built into it, and "deterministic" means "predictable", or is it some deeper truth that the universe itself follows, such that we can imagine "perfect accuracy" in the initial conditions, a kind of "Platonic ideal" that measurements are trying to access to closer and closer precision? This is the key question, what we think physics actually is. This is also where the quantum interpretations differ, not just on what the wave function is, but what physics is.
 
  • #28
Weak measurements don't necessarily prove or disprove that randomness is inherent because:

Weak measurements are not effecting randomness.

Weak measurements change the coherence "partially" (or increase de-coherence partially) and hence result in "partial" interference pattern.

Even when we have "complete" which-way information (or complete eraser for that matter) the randomness persists and does not increase or decrease. however the state changes (i.e. degree of coherence increases/decreases)

does the above sound correct?
 
  • #29
Ken G said:
Actually, here is a different way to present your exact same argument. Throughout history, whenever we thought something was deterministic, we found a deeper level that was random. Did you really just argue that this means the people who think there will always be inherent randomness are ignoring the lessons of history?

That argument works both ways. You can only find a new descriptive level to reintroduce randomness when a deterministic model is found for what came before. In fact classical thermodynamics was thought to be fundamental and random till the equivalence of statistical mechanics was demonstrated, and even demonstrated superior with Brownian motion.

@Fyzix
I have debated DrChinese and his views are NOT weird. What is weird is to proclaim that which the preponderance of evidence is against is somehow intellectually superior, and this is coming from a person who disagrees with DrChinese. Having an opinion and proclaiming that opinion is superior in absentia of evidence is two different things, and DrChinese is ahead on the evidence count. Not by enough to fully convince me but the truth is the truth. Learn to live with it or live without science.
 
  • #30
my_wan said:
That argument works both ways. You can only find a new descriptive level to reintroduce randomness when a deterministic model is found for what came before. In fact classical thermodynamics was thought to be fundamental and random till the equivalence of statistical mechanics was demonstrated, and even demonstrated superior with Brownian motion.
I'm not entirely clear what you are saying here, because I would have said that classical thermodynamics is the deterministic theory, and statistical mechanics is the random one. For example, thermodynamics uses variables like temperature that are supposed to mean something specific, whereas statistical mechanics uses ensemble averages that are really just mean values. So I would interpret the discovery that statistical mechanics can derive the theorems of thermodynamics to be a classic example of how randomness is continually found to underpin theories that we initially thought were deterministic. Quantum mechanical trajectories would be another prime example, as would chaos theory in weather.
 
  • #31
I want to put forth a challenge to the crazy people who actually manage to believe in randomness:

Define randomness?

Causation is easily defined.

So what does "random" REALLY mean?
When we use "random" in everyday speech, we are only talking about things we personally couldn't predict.

Like throwing a dice, if we knew all the variables we would know exactly what it would turn out as...

So please WHAT is randomness? how could it even exist?
I don't think that its' even possible to define randomness, things would just "randomly" happen without ANY cause what so ever, never been observed, never will be observed, because it doesn't and couldn't exist.
 
  • #32
Fyzix said:
Define randomness?

“If the state y of a system at time t is uniquely defined by its state x at an arbitrary moment t0 through a unique function f such that y=f(x, t0, t), situations of this general type is called schemes of a well-determined process. On the contrary, if the state x at time t0 only determines a probability distribution for the possible future state y, these are called schemes of a stochastically definite process”, taken from von Plato, J. (1994). Creating Modern Probability: Its Mathematics, Physics, and Philosophy in Historical Perspective, Cambridge University Press.

These stochastically definite processes are basically Kolmogorov's definition of randomness.


Fyzix said:
So what does "random" REALLY mean?
When we use "random" in everyday speech, we are only talking about things we personally couldn't predict.

Like throwing a dice, if we knew all the variables we would know exactly what it would turn out as...

This is not randomness. This is unpredictability.

Fyzix said:
So please WHAT is randomness? how could it even exist?
I don't think that its' even possible to define randomness, things would just "randomly" happen without ANY cause what so ever, never been observed, never will be observed, because it doesn't and couldn't exist.

Things happening without cause are arbitrary, not random. In randomness the link between cause and effect(s) is not unambiguous.
 
  • #33
Fyzix said:
I want to put forth a challenge to the crazy people who actually manage to believe in randomness:

Define randomness?

Causation is easily defined.

So what does "random" REALLY mean?
When we use "random" in everyday speech, we are only talking about things we personally couldn't predict.

Like throwing a dice, if we knew all the variables we would know exactly what it would turn out as...

So please WHAT is randomness? how could it even exist?
I don't think that its' even possible to define randomness, things would just "randomly" happen without ANY cause what so ever, never been observed, never will be observed, because it doesn't and couldn't exist.

I would define true randomness as something that could not be predicted be anyone or anything.

A simple example would be pair production from vacuum. We know that it can happen, but no one can predict when it will happen. It can happen at one particular time, and this exact time is completely without cause. There is no reason why it would happen at one particular time compared to some time later. Similar things, like spontaneous decay, has been observed many times in the lab...

Just because you don't like the notion of randomness doesn't mean it isn't there. Of course, there may still be a deterministic explanation for all this, but so far this has not been found/proven and you simply cannot claim that without proof. So far, experiments are entirely consistent with the possibility of a random world.
 
  • #34
To the nice points already made about randomness, I would add one more. I believe Fyzix's main issue with the concept of randomness is not the mathematical entity, but rather its application to the real world. He/she does not see how the real world can "really be random". There is good company for that unease, Einstein famously shared it.

But to help relieve that unease, I would point out that "randomness" is never an attribute of the real world, it is always an attribute of a mathematical model of the real world. This fact points the philosopher in two very different possible directions-- one can believe that underneath all randomness is some deterministic process that is unknown to us (obviously Fyzik's favored course, as well as deBroglie-Bohm for example), or alternatively one can embrace the randomness as fundamental in the reality as much as it is fundamental in the mathematical model of reality.

But I would suggest a third course. Simply take no stance at all on the issue-- we need no such stance, because all we ever get is our models, and physics is demonstrably not a study of the real world by using models, it is a study of models of the real world by testing to what extent they serve our purposes. In that light, neither the concept "random", nor the concept "deterministic", can ever be applied unambiguously to the actual workings of the real world.
 
  • #35
Fyzix said:
I don't think that its' even possible to define randomness, things would just "randomly" happen without ANY cause what so ever, never been observed, never will be observed, because it doesn't and couldn't exist.

Fyzik - How can you make this statement?? When a uranium nucleus, which has been happily sitting there for 4 billion years, suddenly decays, why couldn't this be something that 'just happened'? It MAY be that there is some underlying mechanism that caused it to decay, but there is no evidence for this, and no successful model has been proposed to explain this as the result of some underlying deterministic model. So how can you say that something that 'just happens' has never been observed? How can you be so certain that there is not randomness inherent in the operation of the universe, when the evidence suggests very strongly that there is?
 
<h2>1. What is a weak measurement?</h2><p>A weak measurement is a type of quantum measurement that involves making a small disturbance to a quantum system, allowing for the measurement of properties that are typically difficult to observe in traditional measurements.</p><h2>2. How do weak measurements relate to randomness?</h2><p>Weak measurements can provide insight into the inherent randomness of quantum systems by allowing for the observation of subtle fluctuations and uncertainties in the system.</p><h2>3. Can weak measurements prove that randomness is not inherent?</h2><p>No, weak measurements cannot definitively prove that randomness is not inherent in quantum systems. While they can provide evidence against the existence of inherent randomness, it is ultimately a philosophical and theoretical question that cannot be definitively answered.</p><h2>4. What are some limitations of weak measurements?</h2><p>Weak measurements are subject to various limitations, such as the potential for measurement errors and the fact that they can only provide statistical information about a system rather than precise measurements of individual particles.</p><h2>5. How are weak measurements used in scientific research?</h2><p>Weak measurements have been used in various scientific studies, particularly in the field of quantum mechanics, to gain a better understanding of the behavior and properties of quantum systems. They have also been used in practical applications, such as in quantum computing and cryptography.</p>

1. What is a weak measurement?

A weak measurement is a type of quantum measurement that involves making a small disturbance to a quantum system, allowing for the measurement of properties that are typically difficult to observe in traditional measurements.

2. How do weak measurements relate to randomness?

Weak measurements can provide insight into the inherent randomness of quantum systems by allowing for the observation of subtle fluctuations and uncertainties in the system.

3. Can weak measurements prove that randomness is not inherent?

No, weak measurements cannot definitively prove that randomness is not inherent in quantum systems. While they can provide evidence against the existence of inherent randomness, it is ultimately a philosophical and theoretical question that cannot be definitively answered.

4. What are some limitations of weak measurements?

Weak measurements are subject to various limitations, such as the potential for measurement errors and the fact that they can only provide statistical information about a system rather than precise measurements of individual particles.

5. How are weak measurements used in scientific research?

Weak measurements have been used in various scientific studies, particularly in the field of quantum mechanics, to gain a better understanding of the behavior and properties of quantum systems. They have also been used in practical applications, such as in quantum computing and cryptography.

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