Does the superposition principle actually tell us about our inability to predict what happens during the course of the experiment? Does it tell that, since an experiment has multiple outcomes ( i.e , in the case of the double slit experiment , the electron can either pass through slit 1 or 2), all the outcomes have would an equal probability of manifesting (assuming that is true), but since we do not know which one would manifest, the object in question would be in a "superposition of all the outcomes", while in reality there is only actually one of the multiple outcomes is actually happening? Is it like throwing and catching a perfectly balanced dice in the air and while the dice is in the air, telling that the dice is in a "superposition of all nos 1-6" ?
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$\begingroup$ Good question albeit a bit verbose. Look forward to any answers. $\endgroup$– GertCommented Jun 17, 2020 at 5:30
2 Answers
Does the superposition principle actually tell us about our inability to predict what happens during the course of the experiment?
No, it tells us that what we can predict is the probability distribution of a large number of experiments with the same boundary conditions.
The single electron trajectory and footprint cannot be predicted , but the accumulated points are the probability of the experiment "electron of given energy scattering off double slits with given width and distance".
but since we do not know which one would manifest, the object in question would be in a "superposition of all the outcomes",
Do not confuse mathematics with reality. When you throw a ball at a basket your brain has made many probable calculations to order the impulse on your hand. Does it mean that the trajectory of the ball is made up by all those brain calculations?no, because the tiny changes in initial conditions boil down to one set of parameters controling the trajectory. The other possibilities are just mathematical representations. The same is true for the dice. The initial conditions classically point to exactly one solution, your ignorance is mathematical.
At the quantum level it is the probability distributions that are mathematially predictable,not individual events.
In quantum mechanics, the superposition principle tells us that quantum states can be added together and the result will be another valid quantum state. Conversely, every quantum state can be represented as a sum of two or more distinct quantum states.
Essentially the superposition principle says that if you have two quantum states $|\psi_1\rangle$ and $|\psi_2\rangle$, you are allowed to perform the following operation: $$|\psi_1\rangle +|\psi_2\rangle = |\psi_3\rangle,$$ where $|\psi_3\rangle$ is a valid quantum state. That is all the superposition principle says. It does not say anything about measurements, probabilities, experimental outcomes etc.
Does the superposition principle actually tell us about our inability to predict what happens during the course of the experiment?
No. In fact, we can predict what happens during the course of an experiment. Using the Schrodinger equation given by $$H|\psi(t)\rangle=i\hbar{\partial \over \partial t} |\psi(t)\rangle,$$ we can predict the time evolution of the quantum state $|\psi(t)\rangle$ which represents the state of the experiment.
Does it tell that, since an experiment has multiple outcomes... all the outcomes have would an equal probability of manifesting (assuming that is true), ... in reality there is only actually one of the multiple outcomes is actually happening?
No. The superposition principle only tells us that we can express a quantum state $|\psi\rangle$ as a sum of other quantum states $|\psi_i\rangle$, i.e.
$$|\psi\rangle=\sum_i\psi_i.$$ It is actually the postulates of quantum mechanics that tell us when we perform measurement on a quantum state $|\psi\rangle$, we will observe that the state is in one of the states $|\psi_i\rangle$ with a certain probability.
Is it like throwing and catching a perfectly balanced dice in the air and while the dice is in the air, telling that the dice is in a "superposition of all nos 1-6" ?
No. The superposition principle only allows the "superposition of all nos 1-6" to be physically possible. It does not tell the dice to do that. It is quantum mechanics that 'tells' the dice to do so.
As a side note this example on the dice is not an accurate analogy to quantum mechanics, but that is for another discussion.
