Momentum doesn't exist prior to measurement?

  • #1
Suppose there are two scientists in a laboratory containing measuring apparatus, and there is a particle whose momentum is unknown to those scientists.
(1) Does the particle have momentum before it is measured?

Suppose one scientist measures the momentum of the particle, and subsequently the second scientist also measures it.
(2) Does the particle have momentum before the second scientist measures it?

What if a third scientist, unbeknown to the other two, has measured the momentum of the particle before the first scientist measured it?
 

Answers and Replies

  • #2
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1) Does the particle have momentum before it is measured?
That depends on the definition of a particle "having a momentum" and your favorite interpretation of quantum mechanics.
(2) Does the particle have momentum before the second scientist measures it?
Again depends on the interpretation, but it is reasonable to say "it has the momentum the first scientist measured" as the second one will measure the same value, assuming nothing relevant happens in between.
 
  • #3
That depends on the definition of a particle "having a momentum" and your favorite interpretation of quantum mechanics.
Again depends on the interpretation, but it is reasonable to say "it has the momentum the first scientist measured" as the second one will measure the same value, assuming nothing relevant happens in between.
So the second scientist will think, "This particle now has this momentum, but before I measured it, it did not have momentum." And he will be mistaken.

This sort of thing is found only for certain "non-commuting pairs" of quantities, is that correct? What I mean is, we can always say that every electron has a Rest Mass, and we know that quantity and it is the same for all electrons, is that right? Even for those electrons we have not yet measured. Therefore many many quantities of a particle are definite (even if the values are unknown) even before, or in the absence of, any measurement of that particle.
 
  • #4
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So the second scientist will think, "This particle now has this momentum, but before I measured it, it did not have momentum." And he will be mistaken.
Depends on the interpretation, and it is completely irrelevant for physics.
This sort of thing is found only for certain "non-commuting pairs" of quantities, is that correct?
It is found for everything that does not have to have a fixed value. Note that we talked about momentum, but did not discuss position here.
What I mean is, we can always say that every electron has a Rest Mass, and we know that quantity and it is the same for all electrons, is that right?
Yes, but that is a direct consequence of the definition of "electron". Particles with a different mass would be called differently.
 
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  • #5
... that is a direct consequence of the definition of "electron". Particles with a different mass would be called differently.
And is a specific Rest Mass part of the definition of a Type 1 Neutrino? Is a definite rest mass part of the definition of composite particles such as the Iron nucleus and the Proton, or are those things that do not have to have a fixed value?
 
  • #6
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And is a specific Rest Mass part of the definition of a Type 1 Neutrino?
Yes, there are three different neutrino types with different masses, and they are called "1", "2" and "3".
Is a definite rest mass part of the definition of composite particles such as the Iron nucleus and the Proton, or are those things that do not have to have a fixed value?
They have a fixed value because they are all the same things made out of the same particles.
 
  • #7
Depends on the interpretation, and it is completely irrelevant for physics.
It is found for everything that does not have to have a fixed value.
So a statement such as, "If you look at the measurements and make the additional assumption that a property has a definite value even when it's not measured, then yes, you could draw that conclusion. But without that additional assumption, no, you cannot" would be nugatory.
 
  • #8
DrChinese
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So the second scientist will think, "This particle now has this momentum, but before I measured it, it did not have momentum." And he will be mistaken.

This sort of thing is found only for certain "non-commuting pairs" of quantities, is that correct? What I mean is, we can always say that every electron has a Rest Mass, and we know that quantity and it is the same for all electrons, is that right? Even for those electrons we have not yet measured. Therefore many many quantities of a particle are definite (even if the values are unknown) even before, or in the absence of, any measurement of that particle.
A measurement of a particle property makes the value of a non-commuting property completely indeterminate (and independent of any prior value it had). All of the situations you are asking about can be answered using that rule. If you consider spin or polarization rather than momentum, you can construct a series of examples for yourself. That is because you can measure the spin over and over on the same basis and expect the same answer each time.

There are some properties (such as charge) that won't have a non-commuting partner.
 
  • #9
A measurement of a particle property makes the value of a non-commuting property completely indeterminate (and independent of any prior value it had). All of the situations you are asking about can be answered using that rule.
I was not asking about a canonical conjugate property. I was focusing only on the previously measured property, and on whether or not one might say that the particle does have that property and that is its value even before it is measured the second time. The answer seems now to be, sure it has that value prior to the second measurement but that is only an interpretation, and which interpretation you prefer has no bearing on physics; therefore it is incorrect to say that "you can draw one conclusion from the assumption that the property has a certain value before measurement, and you cannot draw that conclusion if you do not make that assumption." That assumption has no physical significance whether you assume it or do not assume it.
 
  • #10
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So a statement such as, "If you look at the measurements and make the additional assumption that a property has a definite value even when it's not measured, then yes, you could draw that conclusion. But without that additional assumption, no, you cannot" would be nugatory.
This is becoming a discussion of semantics and definitions, and I will certainly not participate in that because I never see useful results from those discussions.
 
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  • #11
This is becoming a discussion of semantics and definitions, and I will certainly not participate in that because I never see useful results from those discussions.
I agree. But there are some who do make statements such as, "If you look at the measurements and make the additional assumption that a property has a definite value even when it's not measured, then yes, you could draw that conclusion. But without that additional assumption, no, you cannot."
 

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