আমারই চেতনার রঙে পান্না হল সবুজ,
চুনি উঠল রাঙা হয়ে।
আমি চোখ মেললুম আকাশে,
জ্বলে উঠল আলো
পুবে পশ্চিমে।
গোলাপের দিকে চেয়ে বললুম “সুন্দর”,
সুন্দর হল সে।
—(আমি) Rabindranath Tagore
With my senses’ hues
Emerald as green I muse
And the Ruby as red
As my sight I spread
The sky is luminous’
East to West with light glorious;
To Rose I said, “Bonny is thee”
And so did she be.
[Translated by Rajat Dasgupta]
Many of us who grew up with an adequate exposure to Tagore, know this and the following lines by heart. Every time I read, heard or recited this poem, a strange sense of mysticism came over me. In those teen years, I had not reached a level of maturity, either emotional or intellectual, to comprehend its full significance. After I studied quantum mechanics, and started encountering it on a daily basis, the meaning slowly started dawning on me. But about three years ago, a research paper published in Nature Physics suddenly lifted the veil, and I could feel the meaning of it all. I not only saw these lines in a new light, I sensed my science in a new way. What I realized is that this counter-intuitive finding of science is validating what Tagore expressed in his poem nearly a century ago. This also reminded me of the famous dialogue between Tagore and Einstein when they met in Berlin in 1930. What was thought to be a spiritual-scientific binary may turn out to be a false one, and a wrong way of looking at their dialogue. I attempt to explain these ideas for readers who are not experts in physics in this post.
In Newtonian physics, each material particle comes with a certain mass, and has a definite position and a velocity. Product of mass and velocity is defined as momentum. Evolution of position and momentum of a particle with time depends on the forces acting on it. The particle accelerates in the direction in which the net force acts on it. For example, if I release a stone from a certain height it accelerates towards the earth because of the force of gravity. The crucial point for us here is that a material particle has precisely defined position and momentum at any instant of time, and we can know both of these with arbitrary accuracy (only constrained by how accurate measuring instruments we can devise). This is where the quantum world differs fundamentally. The uncertainty principle, proposed by Heisenberg, tells us that we cannot know (i.e., measure) both the position and momentum of a particle with arbitrary precision. Another way of putting it is that when we do a measurement to find the momentum of a quantum particle, the measurement process itself disturbs it to such an extent that information about its position is lost, and vice-versa. Mathematically one puts it in the following form
ΔxΔp ≥ h/2π, where h is the Plack’s constant, one of the fundamental constants of nature.
Here Δx and Δp are the uncertainties in our knowledge of the position and momentum respectively of the particle. If we precisely know one of these quantities, we know nothing about the other.
Yet another way of viewing this is that a particle is not just a particle, it can behave as a wave also. This is the so-called wave-particle duality. This is completely against our classical, everyday way of experiencing and understanding nature. If something is a particle, it always is a particle. For example, a ball, car, table and chair, though not single particles, are collection of particles, and they always behave as that. They have definite positions and momenta at any given instant of time. So do the heavenly bodies: the sun, the moon or the earth. In contrast, a wave does not have a precise location in space. If I throw a stone in a pool of water, ripples propagate. I cannot say where exactly the wave is. It is spread over a region of space, and it moves. That’s exactly how particles, the tiny, sub-atomic ones, behave. How do we know they behave that way? Well, that’s the only way, so far as we can tell today, we can explain the stability of the material world around us. In a classical world, atoms would not even be stable! Even if they formed, they would decay rather soon. There are more direct experiments to establish wave nature of particles, and one of these concerns us here.
A canonical experiment to test whether something behaves as a wave or a particle is the so-called double-slit experiment. The idea is best illustrated through a diagram (Figure 1). S is a source of plane waves which can be light, for example. A little to its right, down the path the waves propagate, there is an obstacle with two openings S1 and S2. placed symmetrically on two sides of S. On the extreme right is a screen on which can see images and make our observations as shown in the figure. If S is a light source, one gets alternate bright and dark patches on the screen. This pattern is called in interference pattern. Interference is a definite signature of wave nature of the propagating entity. Interference happens because waves can pass through both the slits S1 and S2 at the same time.
A canonical experiment to test whether something behaves as a wave or a particle is the so-called double-slit experiment. The idea is best illustrated through a diagram (Figure 1). S is a source of plane waves which can be light, for example. A little to its right, down the path the waves propagate, there is an obstacle with two openings S1 and S2. placed symmetrically on two sides of S. On the extreme right is a screen on which can see images and make our observations as shown in the figure. If S is a light source, one gets alternate bright and dark patches on the screen. This pattern is called in interference pattern. Interference is a definite signature of wave nature of the propagating entity. Interference happens because waves can pass through both the slits S1 and S2 at the same time.
[See this youtube video] If S was a source of classical particles of matter, each particle would pass through either S1 or S2 (or not at all). They would hit definite points on the screen, and we would have two spots corresponding to these.
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| Figure 1 [From: https://www.youtube.com/watch?v=MDX3qb_BMs4] |
If we close one of S1 and S2, then also the interference pattern vanishes because the waves now pass through one slit only. Interference pattern in a double-slit experiment with light has been observed umpteen number of times. This has become so commonplace that this is now a part of bachelor level physics experiments. But the interesting question is, what if we have an electron source or an atom source at S in stead of a light source? Would we still get interference patters? The answer is yes. The reason being the wave-particle duality. Electrons or atoms can behave as either particles or waves depending on how we chose to observe them, and this will be a major point of discussion in this article.
Now that we understand what a double-slit experiment is, and how to say whether the object we are studying behaves as wave or particle, we are ready to discuss what is called a delayed-choice experiment. This is a variant of the double-slit experiment. Wheeler first proposed this idea [1]. Let me explain this in some detail.
Suppose to start with both the slits S1 and S2 are open. Waves from the source S pass the region of S1 and S2. After that, and only after that, a decision is taken to close one of them with a probability 1/2. In plain language this would involve something like this. After the waves pass through S1 and S2, a coin is tossed. If the result is heads, one of the slits is closed, else both remain open. Wheeler called it the delayed-choice experiment. Also suppose that if the experiment is performed with atoms, one can make sure that at a time only one atom is released from S. It (or the wave associated with it) passes though S1-S2, and after that one of the slits is closed with probability 1/2. What do we expect to see? Will there be an interference when one of the slits is closed? After all, the atom passed through both slits, and only after that one of them was closed. Any event (closing of one slit) cannot, and should not affect past events (the behaviors of the atom when it passed through the slits S1 and S2), the sacred principle of causality. If the atom behaved as wave then, because both slits were open, it should remain a wave, and we should see its signature as interference patters.
And here comes the biggest surprise. If one of the slits is closed after the atom has passed through the slits S1 and S2, the interference pattern vanishes. That is, the atom, as if, passes through only one of the slits, and behaves as a particle. How can this be? This apparently violates causality: causes must precede effects. How do we explain this?
The problem arises if we insist that there is a reality irrespective of whether we choose to observe it or not. In this view, the atom exists (behaves) as waves when it passes through S1-S2 if both are open, independent of whether or how we observed it. This view clashes with causality because then one has to conclude that the future decision to close one of S1 and S2 changes the behavior of the atom in the past from wave-like to particle-like.
Suppose we take a completely different view of physical reality: that, in the context of this experiment, the atoms do not have either wave or particle nature till we decide to measure them, till we decide to observe them. In this view, nature of physical reality is essentially dependent on the way we view it, measure it, observe it. If we decide to observe the atom by keeping both slits open, we observe its wave character. If we decide to observe it by closing one of the slits, we find its particle character. Thus it does not make sense to ascribe either wave or particle nature to a particle before the measurement is done. In Wheeler’s words [1]:
... the past has no existence except as it is recorded in the present. ... The universe does not "exist, out there," independent of all acts of observation. Instead, it is in some strange sense a participatory universe.
But with this the whole Cartesian view of nature is thrown into a crisis. As we see, there is not sharp observer-observed separation. Together they make up physical reality; they form an integrated whole. There is no meaning to a natural reality independent of the observer.
This brings me to the dialogue between Einstein and Tagore that I mentioned earlier. Here are some excerpts from it.
…..
EINSTEIN: Even in our everyday life we feel compelled to ascribe a reality independent of man to the objects we use. We do this to connect the experience of our senses in a reasonable way. For instance, if nobody is in this house, yet that table remains where it is.
TAGORE: Yes, it remains outside the individual mind, but not the universal mind. The table which I perceive is perceptible by the same kind of consciousness which I possess.
EINSTEIN: If nobody would be in the house the table would exist all the same — but this is already illegitimate from our point of view — because we cannot explain what it means that the table is there, independent of us.
Our natural point of view in regard to the existence of truth apart from humanity cannot be explained or proved, but it is a belief which nobody can lack — no primitive being even. We attribute to Truth a super-human objectivity; it is indispensable for us, this reality which is independent of our existence and our experience and our mind — though we cannot say what it means.
TAGORE: Science has proven that the table as a solid object is an appearance and therefore that which the human mind perceives as a table would not exist if that mind were naught. …
It is not difficult to imagine a mind to which the sequence of things happen not in space but only in time like the sequence of notes in music. For such a mind such conception of reality is akin to the musical reality in which Pythagorean geometry can have no meaning. There is the reality of paper, infinitely different from the reality of literature. For the kind of mind possessed by the moth which eats that paper literature is absolutely non-existent, yet for Man’s mind literature has a greater value of Truth than the paper itself. In a similar manner if there be some Truth which has no sensuous or rational relation to the human mind, it will ever remain as nothing so long as we remain human beings.
EINSTEIN: the problem begins whether truth is independent of our consciousness.
TAGORE: What we call truth lies in the rational harmony between the subjective and objective aspects of reality, both of which belong to the super-personal man.
…..
EINSTEIN: Even in our everyday life we feel compelled to ascribe a reality independent of man to the objects we use. We do this to connect the experience of our senses in a reasonable way. For instance, if nobody is in this house, yet that table remains where it is.
TAGORE: Yes, it remains outside the individual mind, but not the universal mind. The table which I perceive is perceptible by the same kind of consciousness which I possess.
EINSTEIN: If nobody would be in the house the table would exist all the same — but this is already illegitimate from our point of view — because we cannot explain what it means that the table is there, independent of us.
Our natural point of view in regard to the existence of truth apart from humanity cannot be explained or proved, but it is a belief which nobody can lack — no primitive being even. We attribute to Truth a super-human objectivity; it is indispensable for us, this reality which is independent of our existence and our experience and our mind — though we cannot say what it means.
TAGORE: Science has proven that the table as a solid object is an appearance and therefore that which the human mind perceives as a table would not exist if that mind were naught. …
In any case, if there be any Truth absolutely unrelated to humanity then for us it is absolutely non-existing.
It is not difficult to imagine a mind to which the sequence of things happen not in space but only in time like the sequence of notes in music. For such a mind such conception of reality is akin to the musical reality in which Pythagorean geometry can have no meaning. There is the reality of paper, infinitely different from the reality of literature. For the kind of mind possessed by the moth which eats that paper literature is absolutely non-existent, yet for Man’s mind literature has a greater value of Truth than the paper itself. In a similar manner if there be some Truth which has no sensuous or rational relation to the human mind, it will ever remain as nothing so long as we remain human beings.
I leave it for the reader to draw connections between Tagore’s views in the poem I started with, in his dialogue with Einstein, and what the delayed-choice experiment teaches us.
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