Vilas Tamhane

Your anger and arrogance are not substitutes for reason. On the contrary they are signs of defeat. However you forget that we are not contesting; we are debating and learning. But we are not schoolchildren to say yes to everything you say. In case you find us unworthy, decency demands that you ignore us rather than be intemperate. It is amply proven and stated even by an illustrious persons like Bertrand Russell and Richard Feynman that mathematics is just a tool for calculations. It cannot replace concepts. I request you not to get offended by our expressions. Because opinions of expert like you are valuable to us, but if you wish to gag us then I think that would be unreasonable. So far as ability of mathematics to explain everything, I would request you to explain me what meaning Maxwell’s wave equations convey in absence of ether.

Right from Aristotle to the days before SR, physicists always sought reality. World of hallucinations lie only in religious scriptures. I cannot understand how you can object to ‘Model of Reality’. In fact all experiments, without exception, try to establish reality. Reciprocal results of relativity cannot be tested directly in the lab. Because they are apparent and apparent results can never be tested. Your example of spherical earth suggests that, we should not reject counter intuitive theory. At the same time if you take a look at such theories, you will find that all such theories were rational and possible. Earth spins which accounts for day and night. Earth attracts as apple always falls on earth. Earth is spherical as its shadow on moon is always circular. In SR, predicted reciprocal results of length contraction and time dilation are not only counter intuitive but they are irrational and impossible.

I don’t have any alternate model in my mind. It is simply that I find myself unable to agree with the present model. So far as insights are concerned, unfortunately there are very few who are interested in these. You must have noticed that even my legitimate enquiry is treated disdainfully. I can’t help it. The way you are trying for the interaction, I am trying to find out if I make a mistake when I make contradictory statement. Correct, but enquiry should not be and cannot be stopped.

Mathematics is a tool and to describe in the words of Feynman, to count. You can never describe physics in the language of mathematics. When it is done, it is for the convenience in absence of correct concepts. Physics is how nature works. It is about concepts. Mathematics makes it useful, precise and predictable. Take the example of Maxwell’s wave equations. Maxwell used vector analysis to describe EM fields. When you apply curl operation on a vector field, mathematics cannot convey you nature of that field. Field is assumed. Mathematics cannot decide if it is a field of water velocity or vector field of electric field. Nor can it decide if the application is wrong. Maxwell believed in ether and thought of electromagnetic fields as stresses and strains in ether. Gradient, divergence and curl operations were successfully applied in hydrodynamics. Maxwell visualized that situation is similar and so decided to use this tool in the case of EM fields. He was not only successful but predicted EM waves. But ether is discarded. Now what? Theory of EM waves becomes invalid. But not the equations. If I wish to find out depth of penetration of alternating magnetic field in the steel plate, I use Maxwell’s equations. I am able to make calculations without bothering about the correctness of concepts. I am not ready to abandon Maxwell’s equations even if they are unsustainable with respect to concepts. But physicist is not an engineer. He loves concepts more. Concepts are the heart of any physics theory. At the same time we have to admit that nature is not too liberal in revealing itself. We had to wait for 2000 years before a comparatively simple concept of gravitation became known. Therefore there is no reason for anybody to get disturbed if we do not know many things about nature. Your description of what mathematics is is excellent. I would like to add how Bertrand Russell described it. “Pure mathematics consists entirely of assertions to the effect that if such and such a proposition is true of ‘anything’, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. Both these points would belong to applied mathematics. We start in pure mathematics, from certain rules of inference, by which we can infer that if one proposition is true, then so is some other proposition. These rules of inference constitute the major part of the principles of formal logic. We then take any hypothesis that seems amusing, and deduce its consequences. If our hypothesis is about ‘anything’, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, not whether what we are saying is true.”

We would have been riding horses in absence of math. No technology can be developed without it. Humans would have still progressed but slowly and insufficiently. I do not agree that one cannot understand physics without math. If this is the case then it is a sure sign of deficiency in conceptual theory. Though I agree that to understand physics in its full grandeur, knowledge of math is necessary. Rather than math, I think we should not hold any theory sacrosanct.

Some great scientists have said that truth lies in simplicity. Physics without mathematics is not physics, it is philosophy. I am told that in some universities subject of relativity has been made optional. What does it indicate? QM too is based on hazy concepts and so, on this count, there might be need for advanced mathematics. Once we come to know correct concepts governing a particle in motion, then everything, including mathematics, will become simple. UK example might be an exception. It is important to find out what they did. I am told that in some universities, subject of relativity is optional. What does it indicate? Another reason for the repulsion might be autocratic, arrogant and religious nature of authorities. Everybody likes freedom. Isn’t it astonishing that a journal, ‘American journal of physics’ openly states that they don’t accept papers that go against established theories? This is religion and not science. Institution becomes religion when it has to protect vested interests. These interests are based on race, cast, religion or nationality. It is then ‘what is said’ becomes subordinate to ‘who said it’. Basic principle in special relativity is completely irrational. It says that time dilation is reciprocal (and so meaningless). To sustain a meaningless theory, meaning was forced into it. If you look at a space-time diagram then you will find that when the twin turns around to return, time on earth suddenly jumps, and so after returning travelling twin will find earthling to have aged more. Even if you don’t like space-time diagram, you can easily calculate time dilation using Lorentz’s equation for time coordinate. At turn around, distance dependent term (vx/c^2) for clock reading of the earthling, suddenly changes sign and by this amount, time on earth ‘jumps’ ahead. But this is all mathematical manipulation. Do you think your watch will suddenly jump when somebody turns around to return? If you don’t wish to question theory, then the answer is that, travelling twin will return younger, not because he was travelling but because, he turned around. If the travel doesn’t involve turnaround, then too, one clock will dilate and not the other depending on the preferred frame. This cannot be explained properly by equations. You will have to tag a frame. If you are comparing time with earth’s frame, then in the space-time diagram, coordinates of this frame will be orthogonal. You can now use invariant quantity, involving space and time, and see that accelerated clock will always run slow.

Surely and steadily, mathematicians are dragging physics to gallows. In India students are rapidly loosing interest in physics. According to reports, situation is similar in developed countries. This is how great civilizations die. Sanskrit is a highly accomplished language (just like Latin). It is now dead.

Between the three frames of the trains and myself on the platform, I know that my frame is a preferred one. This is because I know that the trains accelerated, not me. I cannot accelerate away from the train. This is not only a physical impossibility but I cannot accelerate differently for three different trains. This is also a fact because I never accelerated w.r.t. the trains in the first place. Reality is that, in my frame, there are innumerable objects that are moving with different velocities. Though velocity is relative, we can tag accelerated frames and that is what we do when we shift from theory to experiments. On the reality of the actual contraction, your reply is not satisfactory. You said, “It cannot mean precisely what we mean in our daily usage as the mechanism is different from that of any type of everyday usage.” There cannot be two definitions and two mechanisms for length contraction. Length contraction in SR is just a mathematical derivation and it never takes place because it cannot take place.

I haven’t understood how length can contract. It is not the question of measurements alone. Problem is not mathematical. I find it impossible that a physical rod can contract. Imagine three trains running, with different speeds, between stations A and B. I am perplexed because you tell me that the stations come closer by an amount different for three different trains. But standing on the platform I can see that there is no contraction and so I conclude that the measurements of the train drivers are apparent.

If you wish to worship theories, nobody can force you not to. I expect the same liberty in our free world. Obedience you expect from laymen is wrong. Consider them as students and counter their criticism with your expertise. I am also amazed at the anger we generate when we put up our critical viewpoint. Anger is a sign of intolerance that is most common among the faithful. In fact you should encourage criticism. That is the only way, we the heathens can learn.

In the first three examples, you are talking about components of a vector. Only one component cannot represent reality of a vector. Vector is real and components are not. These are human constructs. If one dimensional creature says that x-component is the only reality, then his perception is wrong. In the fourth example, length cannot have component in time. When we talk about length alone, time doesn’t come into picture. Please come out of the world of mathematics and explain the question of length contraction. Explain how a rod can contract if I run along it. What makes it contract? Considering this real world situation, please tell me how can rod contract for me? In real world we don’t have any projections to depend on. Mathematics is for calculations and not for description.

I am assuming that photon emission is not affected by time dilation. Because this will give rise to another paradox as follows, A collimated beam of light falls on a sufficiently large photo detector in the rest frame (so that length contraction does not play any part). Current that is produced is passed through the resistor. Its temperature has to be same for both the frames. According to you, there will be frequency shift on account of the velocity between source and the moving frame. However this takes place in the rest frame only if there is relative motion between the source and the detector. Photons are not received by the moving frame. Even otherwise, direction of the moving frame can be made such that velocity of the moving frame is from detector to source, so that effect of increased intensity is enhanced. So far as thickness of the cell material is concerned, it can be selected sufficiently large so that no photons are missed.

Unlike your last post, this reply is not helpful. Time doesn’t play any part in this thought experiment. I am also unable to see how energy of photons can change and in what way activation process can change for a moving frame. Was a similar thought experiment posted to which DrRocket replied? If so will you please let me know how to locate it?

It is true. Criticality increases with density, but it is not impossible to think of a length contraction paradox. Consider following set up. In the rest frame, source of light is so arranged that it sends photons in a spreading beam in the x-direction. On the opposite side, at a distance d, there is a photo detector connected in the electric circuit C1. It receives light from the source, intensity of which will increase with reducing distance d. Proportional to light intensity, current I1 is circulated in C1 which can be further amplified. In the circuit C1, magnetic switch sw is connected. Normally off terminals of sw are in another circuit C2, connected to a separate voltage source. A bulb B is connected in the circuit C2. Current I1 is not enough to activate the switch sw and so the circuit C2 remains open. The bulb B therefore remains off. For the observer moving in the direction x, distance d between light source and the detector is reduced. Photo detector will now receive more light and current in the circuit C1 will increase. This current is sufficient to activate the switch sw and so current in the circuit C2 will switch on the bulb B. Hence the paradox. In the rest frame B is off but in the moving frame it is on.

When the sphere of U235 has critical size, number of neutrons produced in the space of this material is more than those which escape the area enclosing the sphere. This way chain reaction can be sustained. For chain reaction to take place, only the number of atoms and area of the sphere enclosing this material are important. So I don’t know in what way density plays a part in the reaction.