Introduction
Before we move on, let us make this quantum concept clearer. The wave function is a true representation of the way we all exist, although it is difficult to imagine. It is really a mathematical way of representing the waviness of matter or a particle. The wave function of an electron or a car may be spread all over the universe but each of them has a very high probability of being found in a particular place and lesser probability of being found in other places. An electron, for example, may be found on your left, but it is also present on your right as well. Thus, the probability of finding an electron on your left side is much higher than on finding it on your right side. But Quantum Mechanics says that an electron exists on both the left and right sides at the same time! It's only when you decide to find its true position that it collapses on your left because this is where the higher probability of finding it exists.
How Can A Particle Be At Two Different Places At The Same Time?
When you are not looking at an electron moving from A to B, it is actually moving through all the possible paths be on A and B at the same time. It may, for example, be goin from A to B in a straight line, or it may be going first to t then to Jupiter and then to point B. But the moment yo to track its path, it actually moves from A to B in a pa straight line), which has a higher probability than through other paths. In the classical world where we all live, a billiard ball moves along a well defined path or trajectory with precise position and speed at all times. But in the small world of electrons and protons, these particles don't follow the simple laws of motion discovered by Newton. Instead, their motion is governed by quantum laws. When an electron travels from point A to point B in the absence of any external force, it does not follow a straight path between A and B. Quantum Mechanics says that this electron travels from A to B through all possible paths simultaneously. It is like a bus in our classical world, moving from stop A to stop B through all possible streets of the town simultaneously. Although an electron moves in all the infinite number of paths between A and B simultaneously, there is a very high probability of it moving on only one path between A and B. The probabilities of an electron moving through other paths are minimal. This may sound strange but it is true. This behaviour of the quantum world was formulated mathematically by one of the great minds of the 20th century, Nobel Laureate Richard Feynman. We will keep visiting this concept many times over in different contexts. There is a simple word in physics called Superposition, to illustrate the above concept. That is, an electron or any other particle exists in many superposed states at the same time. So, in quantum parlance, you are everywhere but with a higher probability of being found at only one place. Let's look at a story that will more or less demonstrate the weirdness associated with the quantum world.
The Experiment Of John, Dave And Bob.
John, Dave and Bob are great friends and find excuses to meet often. John likes magic and decides to play a few tricks on his friends one day. John invites his friends Dave and Bob to lunch. After lunch, John who is ever keen to play a magic trick, sets up a table with two empty wooden boxes and two marbles - one black and one white, required for the trick.
John first asks his friend Dave to wear a black cotton hood over his head so that he cannot cheat. Assured that everything is in place, John is now ready for the trick and completes his preparations for the experiment. John nominates Bob, who is unaware of John's magic tricks, to help him during the experiment.
In the first round of the experiment, John asks Dave to remove his hood and pose a question to determine which box has the marbles in it and which one is empty. Although he is not amused by this simple challenge, Dave agrees to ask the question, "Which box has marbles and which one is empty?" John, enjoying his moment, asks Bob to open one of the boxes and show the results to Dave.
Bob opens the first box to show the two marbles in it. He then opens the other box and confirms that there are no marbles in the second box. Dave obviously does not find it funny at all and he secretly doubts his friend John's ability to do serious tricks. Unaware of Dave's impression, John however continues saying, "Very well, you got the right answer to your question!" Let's repeat this experiment a few times."
John keeps repeating the experiment several times, each time asking Dave to pose the same question and asking Bob to open the box to show the results. Obviously Dave is frustrated, so he advises his friend, "John, I am not sure what you are driving at with this silly trick, but let's call it a day as I am getting late for an important appointment".
John pleads with his friends to stay for a few more minutes as the trick is not yet done. Seeing the resentment on his friend's face, John makes an unexpected statement, saying, "Dave, quite clearly, your asking the question about the whereabouts of the marbles caused the two marbles to end up together in one box leaving the other empty!" Dave tries to control his anger. He retorts, "Nonsense! What has my asking the question about the whereabouts of the marbles to do with the way you placed the marbles in the boxes? I am really a bit upset about your whole trick and your silly joke!"
John, knowing his friend's temper, convinces him to stay for the second round of the trick. Dave and Bob reluctantly agree.
In the second round of his trick, John asks Dave to wear his hood once again. This time he asks Dave to pose a different question to
determine which box has the white marble and which one has the black marble in it.
Dave, as bored as ever, asks, "Which box has a black marble and which one has a white marble?" As soon as Dave finishes his question, Bob opens both boxes simultaneously to reveal a black marble in one and a white marble in the other box.
Not waiting for Dave to react, John continues, "Look again!
Dave almost screams, "John! What are you trying to prove? | don't see any magic in your tricks, please let me go!"
John finally gives in, but not before making his angry friend Dave agree to a final and crucial round of the trick. Dave dons his hood one last time. John now requests his friend to pose the question, Not knowing which question to ask, Dave asks for a hint. John says, "You already know the two questions to ask, so you can ask any of the two!"
Taken aback, Dave decides to ask the question, "Which box has a black marble and which one has a white marble?" John quickly removes Dave's hood and asks Bob to open both boxes at the same time, as before, to show the white marble in one and the black marble in the other box.
Slightly amused for the first time, Dave asks for a repeat of this experiment. So, once again he is hooded and ready for the question. This time he asks "Which box has the marbles and which one is empty?" He then waits curiously for his friend Bob to show the results.
Bob opens the first box to show nothing in it and then opens the second box to reveal two marbles in it. Dave is clearly jolted. He does not believe this and asks for one more round.
After several rounds of the experiment, it is clear to Dave that it is as though the result depends on the question he chooses to ask. If he chooses to ask, "Which box has both marbles in it?" the result shows one of the boxes with both the marbles in it and the other box empty. On the other hand, if Dave chooses to ask the question "Which box has the white marble and which one has black marble?", the result shows one box with the white and the other with the black marble in it.
It was as if the results really depended on the way you asked the question. Dave is now desperate for an explanation. He is completely psyched. He asks, "John, how did you know which question I would ask before you put the marbles in the box?" John replies, "Dave, I didn't know! The marbles arranged themselves to be either in 'one box together' or in 'both boxes separately, depending on the question you asked! It was as if the marbles were listening and waiting for your question, so they could distribute themselves in the boxes accordingly! Before you asked the first question, 'In which box are both the marbles? both the marbles were in both the boxes! The moment you asked the question, the marbles decided to move into one box and vanish from the otherl Likewise, before you asked the question, 'Which box has the white marble and which one has the black marble, both marbles were in both boxes. The moment you asked the question, the marbles decided to separate one per box!"
Dave was lost in deep thought. John's explanation had hit him so hard that he decided to leave with his friend Bob.
The above story is obviously not true. But if science says this is what happens in the quantum world all the time, would you believe it? In many lab-based QM experiments, the marbles from our story are replaced with atoms, electrons, photons (light particles) or other sub-atomic particles. Instead of two marbles as in the previous fictitious story, if you have just one marble and two boxes and if Dave enquires which box contains the marble, he will always find the marble in one of the boxes. QM says that before Dave asked his question, the marble was present in both boxes at the same time. It is only after he asked the question to find out which box the marble was present in, that the marble 'decided to stay put in one box leaving the other empty. QM is such a strange concept that it is left to the best minds to figure this out, leaving laymen perplexed.
Conclusion
As we saw in the magic trick example, the marbles seemed to exist in both boxes at the same time till Dave asked the question about their whereabouts. The moment Dave inquired into the waviness state of the marbles, they collapsed into their physical state. The existence of an object in more than one place simultaneously is referred to as superposition, as stated earlier. So, the marbles were in a superposition state without physically belonging to any box until the question was posed. Later, when we deal with a thought experiment called Schrodinger's Cat, we will learn more about this innate feature.
To reiterate the point, in John's magic trick, the marbles were in a superposition state and their wave functions were spread across both boxes. The moment we asked the question (or consciously made an attempt to inquire), the marbles collapsed into one of the two boxes. Whether to remain together in the same box or separate into two boxes, was purely based on the probability of their ending up in that box.
It may be a bit hard to appreciate the concept of a wave function and it may give us the impression that it is equally hard to prove its presence. But, in fact, there are actual experiments that are carried out all the time in the physic lab to demonstrate the strange nature of the quantum phenomenon. The QM weirdness has been proved beyond doubt through scientific experiments but what is lacking is a scientifically acceptable explanation or an interpretation, that can bring down the curtains on the vague nature exhibited b the microscopic world. There is one simple experiment that a easy to understand and appeals to laymen that we will take up next. Again, we don't need any background of physics to appreciate the results of this experiment.
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