# On the definition of reallity by EPR

something is not quite clear to me, when going over the EPR paradox.
EPR said that both the measurement of the momenta and the measurement of the x-coordinate of the state are related to the same reallity? why is that true?
the way i see it, if you can't measure two physical quantities simultanously, they are not objects of the same reallity...

can someone clear this up for me?

Ron

NateTG
Homework Helper
You seem to be confused about some things.

The Heisenberg Uncertainty Principle (HUP) indicates that, (at a very high level of precision) it's impossible to measure both the accuracy, and the position of a particle. There are other non-communicative pairs of measurements, like the time of an energy change and the amount of an energy change, but position and momentum is the famous one.

Now, the EPR paradox takes advantage of the fact that Quantum mechanics respects notions of conservation similar to larger-scale mechanics, so, for example, (linear) momentum, and spin (an analogue of angular momentum) are conserved.

That means, for example, that if you have a situation with net zero spin, and particles with spin are created, the particles with spin must have net zero spin. Similarly, if you have an environment with net zero momentum, the net momentum of particles that are created must be zero.

So, if you have a pair of particles that are created you might be able to measure the position of one particle, and the momentum of the other, and, by conservation be able to determine both the position, and the momentum of both particles. This would violate the Heisenberg Uncertainty Principle - which is why it is called a paradox.

This was one of the arguments that Einstein (along with others) made against Quantum mechanics in the early part of the 20th century.

DrChinese
Gold Member
shomey said:
the way i see it, if you can't measure two physical quantities simultanously, they are not objects of the same reallity...

I think that would be a pretty good definition of the consistent histories approach.

At any rate, EPR postulated that if an observable could be predicted without disturbing the system, then it must correspond to an element of reality. If you have a entangled system of 2 spatially separated particles, then they reasoned that any 2 observables (elements of reality) could be looked at - even non-commuting ones. The problem with their reasoning is that entangled particles don't evolve independently, and the resulting measurements will show clear patterns of entanglement. The commuting operators will still respect the HUP, and non-commuting operators will have an undefined value for one. In other words, EPR had a good hypothesis but it simply turns out to be wrong when tested experimentally.

I wonder could that so called paradox NateTG is refering would disappear if the postulate of seperability of the complex hilbert space was dropped?

I think it would be interesting to present the logical line proposed by EPR:

Statements:

i. The standard formalism of quantum mechanics is not complete.
ii. Complementary variables [cannot] be both [simultaneously] real. [corrected!]

Now we have ~i. -> ~ii. [edited again to add: this seems to be so at least in the case of the Einstein Podolsky Rosen Bohm type of experiments, both ~i. and ~ii. being true] (~ means 'non', -> is logical implication; a theory is complete if to every existing element of reality there is a corresponding element in theory).

But the standard formalism of QM forbids that both ~i. and ~ii. are true in the same time (this would imply a contradiction inside QM): accepting together both the completitude of QM and the simultaneous reality of observables which correspond to noncommutative operators is a logical contradiction with QM's assumptions. So that, by the definition of implication, ~i. must be necessarily false, therefore i. is true. Hence it follows that quantum mechanics is not complete.

The hidden assumption in their logic (that ~i. -> ~ii. in the EPRB experiemnt) is that action at distance is not possible, that is when a measurement is made in a place this does not affect measurements made at enough far distance, a fact which make their argument unsound.

The interesting fact is that it is, still, perfectly possible that both i. and ~ii. are true in the same time, whilst classical locality is preserved in full. I do not think that we can reject the possibility of strong determinism at the ultimate level of reality, which preserves full locality, the results of Aspect's experiment being not at all surprising in such a case. Or that logic (modus tollens more exactly) cease to work at quantum level.

Another line of attack is that of 'nonclassical' connections (instead of talking of superluminal connections) by rejecting [to some extent] classical locality by assuming that spacetime is quantized, more 'portions' evolving separately in a full deterministic way; all that remain is to find an explanation of how do they 'fit' together to give the correlations observed in Aspect's experiment (this research program is 'in line' with loop quantum gravity).

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DrChinese
Gold Member
metacristi said:
But the standard formalism of QM forbids that both ~i. and ~ii. are true in the same time (this would imply a contradiction inside QM) so that, by the definition of implication, ~i. must be necessarily false, therefore i. is true. Hence it follows that quantum mechanics is not complete.

I am not sure where you get this from. QM does not assign simultaneous reality to non-commuting operators (such as spin components). Commuting operators (such as position & momentum) have limitations according to the HUP.

The EPR argument was that your ~i. and ii. cannot both be true. They assumed that ii was true, and therefore concluded that ~(~i.) was the case. I.e. i. was true.

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DrChinese said:
I am not sure where you get this from. QM does not assign simultaneous reality to non-commuting operators (such as spin components). Commuting operators (such as position & momentum) have limitations according to the HUP.

The EPR argument was that your ~i. and ii. cannot both be true. They assumed that ii was true, and therefore concluded that ~(~i.) was the case. I.e. i. was true.

This was a recollection from my readings in philosophy of science, written rather in a haste. Of course you're right I've corrected the original post.

shomey said:
something is not quite clear to me, when going over the EPR paradox.
EPR said that both the measurement of the momenta and the measurement of the x-coordinate of the state are related to the same reallity? why is that true?
the way i see it, if you can't measure two physical quantities simultanously, they are not objects of the same reallity...

can someone clear this up for me?

Ron

Suppose you have a source emitting paired particles, p1 and p2,
in opposite directions, that are entangled in position and
momentum. You've got detection screens placed equidistant
from the emitter, and experimentally you find that where
p1 registers on its screen corresponds to where p2 registers
on its screen.

Replace the screens with momentum measuring devices, and
experimentally you find that what you measure for p1 is
the same as what you measure for p2.

Replace the momentum measuring device at p1's end with
the screen so that you can do position measurements on
p1 and momentum measurements on p2. With this setup,
you can infer what the position of p2 from a measurement
on p1, and you can infer the momentum of p1 from a
measurement on p2.

The idea is that p1 and p2 are, in effect, the same
particle. If you know the position of one, then you know
the position of the other, and so for momentum.

Are the inferred values real?