Tipu

(Tipu, a 15 years old boy, walks home from school)

Tasnim: Tipu! Tipu! Wait...

Tipu (Turns back): Hey Tassy, whats up? :) Hi Brad. Whats up Jay?

(They continue walking)

Tasnim: Why did you do that today?

Tipu: Do what?

Jay: Mess with the teachers! It's not right.

Tipu: Oh! That history teacher? That fool does not understand me. Haha..

Tasnim: I know you are good in the natural sciences, no! Maybe the best of us, but that does not mean every other subject is nonsense. How can you call him a fool? Look at yourself. He's got a PhD. And you? How dare you compare? (Looks away, angry.)

Tipu (Laughs mockingly): Oh why, dint you see how he lost his nerves and started yelling at me when I was only trying to put some sense into him. Is that how a sane man behaves? He says legends of kings and stories of wars and the exact dates and all those stuffs of the past are necessary to understand the present. I remarked, let the dead past bury its dead, while... (interrupted)

Brad: I know sweetheart. You dont have to lecture again. I was there.

Tasnim: Why Tipu, at least study for exams' sake. You will fail if you stick to this attitude. Teachers are important.

Tipu (Smiles): Knowledge is.

Brad: No, wisdom is more important. That comes with experience. We are only children. Why dont you understand this? We are ignorant of many complex realities of life. Teachers are not to be ignored. They have the experience of life.

Tipu: That's a belief fed to us by these elderly blockheads. They have grown old. And that which you call experience is rust that has made them so resistant to new ideas and new attitudes. That way progress cannot come. Progress is a change – a goodly change. That comes with innovation and creative thinking. Tell me what's the point in remembering by heart the dates of history? You can always look them up in the internet.

Jay: O I second you Mr. Einstein, so exactly how are you going to bring the change? Proving E equals m c squared wrong? (Giggles)

Tasnim: You get passed with excellent marks if you have a good memory. Simple as that! :)

Brad: However there are clear reasons why we must respect our teachers, why we must try to learn from them as much as we can. At this age, we cannot do anything on our own. I think on some issues we are trying to be oversmart.

(Tipu stops walking. Looks into Brad's eyes.)

Tipu (unhappy): Show me ample reasons if you think we are being oversmart. Let me also see if we are indeed. We dont have to worry though. Truth always stands clear from error. We only need to have a clear unbiased unprejudiced scientific mind.

Tasnim (pulling on Tipu's hands): Oh common Tipu!

Tipu: I am sorry.

(Tipu resumes walking)

Tipu: I do not say I am always right. To err is human. But what I say is, this applies to them as well. They are not some kind of gods from heaven.

Brad: Yeah. But we are arrogant in our understanding and interpretation. Sort of disrespecting the intellect of the greybeards. I dont like that.

Tipu (smiles): “Blind respect for authority is the worst enemy of truth.” Einstein.

Jay: Dont you respect Einstein, even though his theory is flawed at some point? Does not imply that he is a complete old fool.

Brad: Yeah!

Tipu: I dont care about Einstein. What matters me is his ideas. I judge his works, not his person. Not blind respect, but recognition for what is worthy in him. Same applies to everybody else.

Though his theories have no flaws to correct you. ;)

Brad: Yeah. So for one flaw, will you disregard all of his claims and theories? No. You are obtuse and you dont wish to learn and disregard things which does not suit you.

Tasnim (chuckles): Right.

Jay: Point! :D

Tipu (embarrassed): If his claims and theories are not related to this flaw or are not derived from the flaw, they are a separate world, and I have no reasons to reject them adamantly. Anyway, the greybeards with their heavy heads are not smart enough to be human. PS If they have something good in them, they get their due respect.

Brad: You have ingrained hatred for authority and greybeards which has nothing to do with their credibility. You are inclined towards rebellion. At times, unnecessary! Disregarding someone unfit to be humans is a contempt which I feel displays vanity. Brother, do respect them. Because you have a clear perspective on things, it's your responsibility to spread it, not picking up fights with greybeards just 'cause they cant dye their beard black, and understand the different perspective you so ardently follow.

Tipu: I hate no man. But I cannot stand... (interrupted)

Tasnim (with gravity): Enough is enough! Here Tipu, you have reached home. Go get some sleep. For God's sake do the homeworks today. Bye. See you tomorrow.

(Tipu enters gate. Friends leave. End of scene.)

A Child's Approach to the Quantisation of Space

We will not define space (or the more fundamental concept of position) here, but rather will try to discuss on the issue of whether there are any elements of space that could be eliminated. We know that space is the set of all possible positions of any physical system, and it exists because of the way systems exhibit changes in position as an inherent property or in response to physical forces. Space does exist, because of perceived changes in position. Therefore, we may take a probe-system and see what the possible changes in position are during its motion and thus define space operationally. If, however, we discover some regions of the predicted space that show unobservable changes in position, we may render that as a thing to be eliminated from the theory. Space does not exist, because of unperceived changes in position. Now, the perception of position is made possible by radiation; most commonly, it is the visible range of the electromagnetic spectrum – “light” (a magnificent element of the universe, as fundamental as space and time). However, any radiation such as gravitational waves could be used to measure positions (in common words, just by ‘feeling’ the gravity we could tell that there was something over there). So we see that the existence of space is fundamentally determined by the perception of radiation. Space does exist, because of perceived radiation.

But, according to Plank’s quantum theory, all radiation must be discontinuous consisting of distinguishable individual tiny packets of the radiation, the energy of each packet varying linearly as the frequency of the radiation. This little fact adds a new turn here. The quantization of radiation is perceived, if and only if the time lag between every two consecutive packets of the radiation is perceived to be a non-zero quantity. The time lag being zero implies the radiation being continuous. So the corollary is: this time lag without which radiation is continuous, between two successive quanta of radiation eliminates the space of observation in between. This, it seems, breaks the continuity of space. The space vs. time plot of our probe-system moving across space would exhibit periodic dark splashes in time when the radiations breaks because of quantization and so does our perception of space which is due to radiation. For all practical purposes, this breakdown of the continuum of space would be in so negligibly small scales that we would not notice it in our daily life. It must be noted here that the information of the positions of our probe-system during the said time lags would be completely lost. One of my colleagues argued that radiation is not the only means of conveying the information of positions of objects in motion: we could for instance, measure the entropy change of the universe during these time lags and thus retrieve the information of where the object has been during that time. But the problem here is that even entropy changes are due to energy transactions which are fundamentally quantized. Therefore it is apparent that whatever means is taken to measure changes in position, the dark splashes in time are an intrinsic part of a complete description of motion. Space is kind of quantized in time.

            Here is a rough sketch of what the space vs. time plot of a uniformly moving object would look like at extremely tiny scales.

             Note in the figure that the dark splashes are periodic in nature. And we lose information of the graph in those splashes. It is to be remembered that the dark splashes are the collapse of perception in times when there is no radiation due to quantization.

            Let us now make a quantitative evaluation of some specific case regarding this issue. We have talked on length about time lag between successive quanta of radiation. Let us now determine experimentally a very rough estimate of the time lag between two successive photons of known frequency ‘f’. We take a certain amount of a gas, say ‘N’ molecules of it, which has reasonably ideal behavior and put it in a container that maintains isochoric conditions at all times. We assume that the degrees of freedom of the gas molecules are ‘σ’ and the Newton’s cooling constant associated with it is ‘K’. Now we expose the gas to an environment that has a temperature equal to ‘T_a’, and shine monochromatic light of frequency ‘f’ on it as the only external source of heat transfer to the gas. At some point of time we measure the temperature of the gas to be equal to ‘T₀’, and exactly after a time interval ‘t’ we again measure the temperature of the gas and find it to be equal to ‘T’. These data that we have collected can predict the time lag ‘τ’ between two successive photons according to the following equation.
$$ \tau \approx - \frac{2hf}{\sigma N K k \Delta T} \log \Big( \frac{T - T_a}{T_0 - T_a} \Big) $$

where,              $h$ = Plank’s constant,     $k$ = Boltzmann constant,     $\Delta T = T - T_0$.

If we conduct the experiment in empty space, the equation would reduce to the following.
$$ \tau \approx - \frac{2hf}{\sigma N K k \Delta T} \log \Big( \frac{T }{T_0} \Big)$$

According to Newton’s law of cooling,
$$ T(t) = T_a + (T_0 - T_a) e^{-Kt} \\ i.e. \quad t = -\frac1K \log  \Big( \frac{T - T_a}{T_0 - T_a} \Big) $$

We know from the laws of thermodynamics that during an isochoric change in temperature, the corresponding change in total internal energy of the gas is governed by the following equation.
$$ \Delta E = \frac12 \sigma Nk\Delta T $$

This change in energy is due to the energy delivered by the incoming photons. If ‘n’ photons were required to produce the above energy, then by Plank’s equation we have the following.
$$ \Delta E = nhf $$

Equating the two, we can solve for ‘n’.
$$ \frac12 \sigma Nk\Delta T = nhf \\ i.e. \quad n = \frac12 \frac{\sigma Nk\Delta T}{hf} $$

Now we know how many photons arrived in how much time. Therefore if we distribute the photons evenly over the time interval, we can measure the spacing in time between two successive photons. So we have the following.
$$ \tau = \frac{t}{n} \\ i.e. \quad \tau = \frac{-\frac1K \log  \Big( \frac{T - T_a}{T_0 - T_a} \Big)}{\frac12 \frac{\sigma Nk\Delta T}{hf}} \\ i.e. \quad \tau = - \frac{2hf}{\sigma N K k \Delta T} \log \Big( \frac{T - T_a}{T_0 - T_a} \Big) $$

This is how we arrived at the equation. Please note here that we have derived the above relation based on Newton’s law of cooling which is only an approximate description of the phenomenon and is at most times inaccurate and a merely a very rough estimate. Hence the truest thing to write would be the following. $$ \tau \approx - \frac{2hf}{\sigma N K k \Delta T} \log \Big( \frac{T - T_a}{T_0 - T_a} \Big) $$

Note here that the negative sign has here popped in because we have implemented Newton's law of "cooling" on a "heating" effect. Therefore the negative sign can be ignored and dropped without any logical blunder. That gives the magnitude of the required time. Obviously, negative time has no meaning at all.

I do not have the apparatus or any means to conduct the experiment. Therefore I go no further. In thought experiments, we have seen that it is possible to estimate, although very roughly the time lag that exists between two successive photons and determines the breakdown of the continuity of space.

[This text is an excerpt from a project I completed last year, March 14, 2011]

An Introductory Text on Physical Existence

          “An entity is said to exist if it is communicates with other existing entities.” Let it be explained. To be is to be perceived. Existence is actually a relative property of physical entities determined by the interactions of the entity with other standard entities relative to which it is measured, standard in the sense that it is the measuring frame of reference. Therefore it is meaningless to speak of entities possessing absolute existence by their own. An entity exists relative to another entity if and only if the former communicates with the latter. For example, let us consider two universes A and B, one being our own universe, the universe we live in, and the other, say, an alien universe of the megaverse. If there are no interactions between A and B, then the existence of B can be ignored by A and vice versa, because of the reason that in the explanation of any single phenomenon of one universe the theories require no use of the elements of the other for if it requires a use it would imply that a interaction did take place. Moreover the physical world does not characterize underlying realities beyond observation. Practically speaking, a neutrino would not have existed had it not made itself felt through the weak interactions it does. So basically interactions take place and this makes possible for entities to exist to entities that they interact with. This is what constitutes the physical reality of all the entities of the universe. Therefore we can define existence in the following words:

            “That which exists, can be perceived.”

            It is to be noted that existence is a physical quality, and I am not quite sure whether it is also a physical quantity that can be measured and mathematically analyzed. I leave this task to others to find the best mathematical expressions for this quantity, if possible, which is here qualitatively defined. I will be using this concept in further treatments to other quantities such as space and time.

Before proceeding ahead, I would like to discuss some important things the knowledge of which would be required as a prerequisite. In this paper, terms such as communication, interaction and observation are used synonymously. These terms represent the same thing – the defining aspect of existence. Interactions, however, take place in space and time (or spacetime) which literally means that if an object interacts with another in even a single point in space and at just one instant of time, then that would be enough to make the object to exist relative to the other. The concepts of space and time are very fundamental to Physics, which will be defined later in this paper. Following the lead of Albert Einstein, it is thought that space and time do not exist independently of each other, but are rather mingled into a single quantity called spacetime. Physics primarily consists of two concepts, the ‘object’ defined as the set of aspects of a physical system (a localized entity of investigation) that remains invariant during motion (the change of state of an object), and the ‘state’ of the object defined as the set of all the variable aspects of a system. Physics is thus defined as the study of motion. Therefore, spacetime is but one of the many aspects of the state of a system. So far the existence of physical entities has been discussed: what about the existence of the states of a system! The definition of existence is applicable to states as well. Clearly no such state can ‘exist’ of a system which cannot be perceived (or interacted with) by the system itself which is the observer, or an external observer who observes the system (as the law of conservation of information allows the external observer to access the information of the interaction that took place between the state and the system, thus making it possible, in a chain process, for the state to exist relative to the external observer). If such a state is hypothesized that cannot be observed, it would be more than clear a logical blunder. In the above sense, even states (such as spacetime) interact with an object as do other objects in the rest of the universe i.e. the surrounding, so that they might exist.

            Another important implication of this definition of existence is this: that which exists can be perceived, hence that which cannot be perceived, does not exist. It is an important conclusion of the definition, because it eliminates from a theory all the proposed attributes of a system that cannot be observed. For example, let us assume that a theory predicts the following sequence of changing states of a system: {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o} where a, b, c … represent the states which change in the given sequence, and a and o represent the initial and final states of the system respectively. But when the system is allowed to ‘move’, the changing states are precisely observed as thus: {a, b, c, d, e, g, i, k, m, n, o}. Now it cannot be reasoned that the states f, h, j, and l does exist but they did not come into observation. If these states are unobservables after all, then they do not exist at all, for all that exists is observable. Hence we reduce the theory to predict the sequence of changing states to be {a, b, c, d, e, g, i, k, m, n, o} eliminating the unobserved. (This is exactly what has happened when the Quantum revolution came into the history of Physics).

 

 

 

[This text is an excerpt from a project I completed last year, March 14 , 2011]

THE EINSTEIN CONSPIRACY

Once upon a time (?), there lived two legendary friends in Mars, called Bob and Jack. Bob was born in poverty, while Jack in aristocracy. This is their story of birth and death, and the tale of how Nature played them false. I will tell you all for their angels reported me thus.

Mars is a different planet in a different universe. The numbers that Nature plays with are a bit different there. However, Nature is as cunning there as she is here. But since the numbers are not the same, it happens to be that the Martians are well aware of Nature’s deceitful nature. For instance, the speed of light – the universal constant of Nature – is approximately 11.547 ms^-1.  As perhaps can be sensed from what has been just said, Bob and Jack by mere chance happen to use units from the metric system. But that is not the point. The point is, Bob and Jack happen to see with their bare eyes the conspiracy that builds up from there.

The Martians live a long perspicuous life of exactly a period of five seconds. That’s the way things are in Mars. Wait! The statement is not complete yet. They live for five seconds if they do not move, but stay at rest for their entire lifetime. Why is that? Because motion increases their lifetime by several factors. And that is because the decree of Nature is, “Thy shalt find moving clocks run slow.” Now Nature does not care about the engineering abilities of the Martians, or what dials and gears and wheels, in what order and arrangement, they use to construct their clocks. What she knows is ‘time’ that they intend to measure using devices they call clocks. Therefore, the decree is that time must run slow in the first place. The Martians could use a bucket full of water (or whatever liquid they drink) with a tiny pore in it that lets drops of water fall periodically, as a way to measure time, as a clock. Or, they could use their own pulses in their wrists. Or, perhaps atomic clocks. But the thing is, whatever they look at as a clock, must run slow. Therefore, even biologically, their metabolism slows down, they grow slowly, they talk slowly, and everything is slow: even if a cup drops from their hands, it comes to the ground and breaks and pieces fly apart, it is as if in a slow motion movie. But there is a hitch, what does it mean to say that something slows down? Of course, the person that is slow finds everything running at normal pace because his world slows with him. Words like big, small, fast or slow have no meaning in the absolute sense, they are used in comparison of two things. To say that moving clocks run slow is to say that they run slow when compared with the clocks at rest. Therefore, moving aliens live longer (although they themselves perceive it not) according to those that remain motionless in the ground.

Having said that, there comes this BIG question that why Nature must lay forward such a decree. The answer lies in one of the cute natures of Nature that she is a cosmopolitan socialist. To Nature, all are equal, all people, microbes, even dust or the different ways they behave – equal as the tooth of a comb, irrespective of whether they are at rest, or moving uniformly with some speed in some direction. No one is preferred by Nature, in the sense that whether they are at rest, or moving uniformly with respect to someone else. Now there is this another aspect of Nature called electricity and magnetism that is a bit nasty. By the very nature of the laws of electricity and magnetism, there comes into being a phenomenon called light that travels at a certain tremendous amount of speed determined exclusively by the product of two fundamental constants – one from electricity, and the other from magnetism. Because Nature is one and the same for all (that move with respect to one another), one must not be able to differentiate between moving systems by an excuse in the name of the electric and magnetic phenomena observed in them. And therefore, electromagnetic constants ought to be constant. Therefore, the speed of light ought to be a natural constant irrespective of one’s state of motion. And lo! It is.

So in some sense, Nature is now squeezed a bit by the very things her own hands have put forth. So, she plays around with a few numbers to make both ends meet and keep the speed of light a constant, that is to say, make the person at rest and the one in relative motion measure the same speed of light. The first of her strategy is slowing down of time in the moving system with respect to the one who considers himself at rest. What is so clever in that? Nature knows that she need not worry about the thing called light, but about the speed of light that they measure. It does not matter who or what has this speed called the speed of light, but if she can arrange that everyone else (whether at rest or relatively moving) agree upon this that his speed is always the same independent of who measures it, her job is done. Take for instance, a bullet shot inside a ship, and the bullet travels with the speed of light as seen from the ship. Now as seen from the ground, if the ship catches a speed equal to the speed of light, time must appear to freeze inside the ship, for only when it is so, the ground observer claims that the bullet being frozen in air inside the ship, it travels with the same speed as the ship, the speed of light. So you get the rough idea of what really happens – time slows with motion, and at the extreme, freezes with the highest possible motion, the speed of light – all to keep Nature cosmopolitan. That’s not so hard to understand. The main fact is that moving aliens live longer.

Coming back to Bob and Jack, it is worth mentioning that Bob’s parents were so stricken by poverty that they decided they could not afford to have another child, so before he was even born, his parents planned to murder him. These idiots become Wordsworth in spring, and turn into Devil by winter. So they gave him birth in a railway track. You perhaps got their intention. And with time, the train arrived. The train came running with a crazy speed of almost the speed of light. Such technology they had. The train had a speed of 10 ms^-1. Crushed by such a train, there is no chance of survival. The train rushed towards Bob. Death awaited him as he was bound to the ground with indestructible chains.

But destiny was clever. When Bob was born, the train was very far away, 50 meters from him. Coincidentally, Jack the lucky rich was also born exactly the same time that Bob was born, but inside the train. Since the train moved with a tremendous speed as seen from the ground, time slowed inside the train, and Jack’s lifetime got doubled as compared to Bob’s. Take my word for it, the mathematics of Nature’s conspiracy resulted in this factor of 2. The train with the speed it had, took 5 seconds to cover the 50 meters and finally come to Bob. And by that time, Bob had already lived his full lifetime and died of old age. So the train only crushed Bob’s dead, and he was spared from the tragedy.

By the time that Bob’s body was crushed, Jack had lived only half his life, and there were 5 more seconds for him to live. This is the description of all that happened as seen by an angel standing on the ground.

But explanations are quite different as given by an angel who saw the same thing from the train. From the train, everything kept zooming past the ‘train at rest’ – the trees, the buildings, the ground, the railway track, with this ominous speed of 10 ms^-1. It is true that Jack had lived only half his life when Bob came running under the wheels of the train the time when he had just completed his natural lifespan and died of ripeness. This is Nature being same to all. What Nature really changed in this perspective are only a few numbers used to come to this conclusion. The main thing is, since Jack was at rest according to this angel, his lifetime was only 5 seconds now. However, since the planet moved past the train with a speed of 10 ms^-1, time slowed everywhere outside the train because moving clocks run slow, and therefore Bob’s lifetime doubled to 10 seconds.

So how did Nature direct numbers to change in the train for everything to make sense? First of all, simultaneity broke down. Bob and Jack were not born at the same time. Bob was elder than Jack by 7.5 seconds precisely (which was technically 0 seconds to those who found Bob at rest). Nature exclaims, “This, because ye art born at places that are not the same.” Secondly, the length scales changed. Looking back into the past, 7.5 seconds before the birth of Jack, as Bob came into being, he was 100 meters away from the train. So as the ground rolled below the train, it dragged Bob with it and brought him to the wheels at a rate of 10 ms^-1 which took exactly 10 seconds to cover the distance. This was the lifetime of Bob. And only his corpse got crushed. It made sense.

But the strange thing was, as seen from the train, out of these 100 meters of distance, Bob had traveled 75 meters without Jack. Only 2.5 seconds before the death of Bob, Jack was born. So for the common time that they spent their life together, Jack found Bob travel only 25 meters of the total journey. But recall, this common distance of 25 meters was 5o meters to Bob as he saw it from the ground. Therefore, the angels noticed that 50 meters of the stationary railway track had shrunk to just 25 meters when the perspective was changed where it was no longer stationary but moved with a speed of 10 ms^-1. They conclude, in harmony with Nature’s commandment, “Moving rods, ye shall contract.”

Now the happy ending! Jack could not live more than 5 seconds. He had lived 2.5 seconds when Bob died. Therefore he had yet to live half of his life. So everything’s perfect for this one moment.

Thus did the angels tell me, simultaneity breaks, lengths contract and time dilates to make things sensible. These are no fantasy but reality that has been observed in this world experimentally. Any question that can be raised experimentally has a physical reality behind it that cannot be denied as an answer. Nature wins this time and every time, for she is cunning but not malicious. If you do not believe in the numbers that I gave you, ask the angels – they are the Lorentz Transformations.