About relativity

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nishat purbasha
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About relativity

Unread post by nishat purbasha » Sat Oct 05, 2013 11:49 am

আমি গতকালকে অ্যাস্ট্রোনমি কুইজ-এ অংশগ্রহণ করেছিলাম। সেখানে একটি প্রশ্ন ছিল ,"তুমি একটি রকেটে করে আলোর বেগে যাচ্ছ। তোমার বিপরীত দিক থেকে আরেকটি রকেট আলোর বেগে আসছে। এখন আপেক্ষিকভাবে তোমার কাছে রকেটটির গতি কিরকম মনে হবে?" কেউকি বলবেন উত্তরটা কি হবে?

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Fatin Farhan
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Re: About relativity

Unread post by Fatin Farhan » Mon Oct 14, 2013 12:44 pm

রকেটের বেগ আলোর বেগের সমানই মনে হবে। কোন পরিবর্তন হবে না। :roll: :roll: :roll:
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SMMamun
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Re: About relativity

Unread post by SMMamun » Mon Oct 14, 2013 8:12 pm

If the question is exactly as you wrote, then it is ill-defined. Because when speaking about a speed, we must first specify the reference object with which the speed has been considered. Therefore, “তুমি একটি রকেটে করে আলোর বেগে যাচ্ছ” is not a clear statement as there is no mention of the reference object here. Since you are traveling with the rocket, you certainly cannot move at the speed of light with respect to yourself or the rocket! :)

Similarly, “তোমার বিপরীত দিক থেকে আরেকটি রকেট আলোর বেগে আসছে” is also ill-defined. If the speed of the second rocket is with respect to you, then you already know the answer: its speed will appear to you as the speed of light. Obvious answer, and not an intelligent question at all!

In brief, the question is confusing. It will appear more confusing when discussed in light of the special theory of relativity. But it seems that the quiz organizers had something else interesting in their minds about relativity. So, I guess they meant that the speeds of the rockets were $c$ with respect to a third observer, say someone on the earth. Let’s analyze this situation.

Now, a person on the earth sees that you (and your rocket) pass her at the speed $c$ (i.e. light speed).
She also sees that another rocket passes her at the speed $c$ behind you.

According to the classical relativity, you would see the second rocket coming at $(c-c)$ or 0 speed. It will thus appear stationary to you. Conversely, the other rocket will also see you stationary.

According to the special relativity, you would see the rocket coming at $\frac{c-c}{1- \frac{c.c}{c^2}}$ or 0/0 speed. In other words, it is meaningless in special relativity to talk about the relative velocity of two objects that are traveling at the speed of $c$ in the same direction with respect to a third object. Well, this is one of the many confusing points and paradoxes of special relativity. But that can be another discussion. :)

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Fatin Farhan
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Re: About relativity

Unread post by Fatin Farhan » Tue Oct 15, 2013 5:09 pm

ভরসম্পন্ন কোন বস্তুই আলো বা এর বেশি বেগে চলতে পারে না, বস্তুতে যত বল প্রয়োগই করা হোক না কেন। :idea: :| :|
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nishat protyasha
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Re: About relativity

Unread post by nishat protyasha » Wed Oct 16, 2013 5:55 pm

আসলে পূর্বাশা প্রশ্নে একটা ভুল করেছে । প্রশ্নের একেবারে প্রথমে "মনেকর" হবে।

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Fatin Farhan
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Re: About relativity

Unread post by Fatin Farhan » Sun Oct 20, 2013 7:33 pm

শূণ্যস্থানে c সর্বদা ধ্রুব থাকে। এ মান দর্শকের স্থিতি বা গতিশীলতার উপর নির্ভর করে না।
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SMMamun
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Re: About relativity

Unread post by SMMamun » Mon Oct 21, 2013 8:19 pm

Fatin Farhan wrote:শূণ্যস্থানে c সর্বদা ধ্রুব থাকে। এ মান দর্শকের স্থিতি বা গতিশীলতার উপর নির্ভর করে না।
Yes, according to the prevailing view in physics, the speed of light in vacuum relative to any observer is always $c$ (i.e. 299,792,458 m/s), regardless of the motion of the observer. But it is important to remember that this constancy of $c$, which is the basis of Special Relativity, is an assumption or a postulate, not an experimentally verifiable fact. It is simply not possible in Special Relativity to design an experiment that will prove that the speed of light in vacuum from one point to another point is really constant. :)

ADIL ISHWARGONJ
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Re: About relativity

Unread post by ADIL ISHWARGONJ » Mon Dec 02, 2013 12:12 pm

Why EINSTIEN took the speed of light for relativity? why c is constant in vacuum? Is it theoretically proved? If not, is it possible to prove?

SMMamun
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Re: About relativity

Unread post by SMMamun » Sun Dec 08, 2013 7:34 am

Dear Adil,

Your questions, although sounding simple, are thought-provoking and require a critical analysis of the historical development of relativity theory for comprehension. However, I am providing a brief summary:

1. Why Einstein took the speed of light for relativity?
It was a common belief in the ancient times that the earth did not move because, if it moved, we would observe many noticeable effects. For example, a stone thrown above would land behind its original point of launch, a perpetual wind would blow all the year round, and apparent positions of stars as viewed from the earth would change in different seasons.

Galileo, influenced by his predecessors' works, argued that the earth could still move through space without our feeling of it. For example, if you are inside the locked cabin of a ship that uniformly moves on a calm ocean, you will not be able to tell whether the ship is really moving or not. If you have some birds and butterflies inside the cabin with you, they will still fly naturally and not bump onto cabin’s walls. No mechanical experiments performed inside a system can determine whether the system moves or not. All motions are relative.

Newton soon published his highly successful laws of motion. He also did important works on light. Newton thought that light was composed of tiny particles (corpuscles), and he could easily explain some properties of those corpuscles with his laws of motion. He had however uneasiness with the properties that he could not explain. On the other hand, Huygens believed that light was a wave, and he could also successfully explain some properties of light. On the nature of light, scientific community was therefore divided. So far, speed of light was not a problematic issue.

When Young decisively demonstrated that light was a wave, Newton's corpuscular theory was gradually relegated in importance. Light is a wave which propagates through a medium called aether was the predominant view for the next one hundred years.

Meanwhile Maxwell systematized the previous works of Coulomb, Orsted, Gauss, Ampere, Biot, Savart, Faraday, and others on electricity and magnetism through a number of equations. Using his equations and data of Weber and Kohlrausch, Maxwell was able to theoretically calculate the speed of the electromagnetic wave with respect to its assumed medium, aether. He was surprised to find that this theoretical speed of electromagnetic wave was remarkably close to the speed of light calculated experimentally by Fizeau and Foucault. Thus he concluded that light is also an electromagnetic wave.

Now the history becomes more interesting. If the speed of light, c, is with respect to aether, then where is the aether? Maxwell’s equations, coupled with Lorentz force law, also hint that an electromagnetic experiment conducted inside a system can distinguish whether the system is moving. For example, if you send a pulse of light first from a railway platform and then from a uniformly moving railcar, you should expect different speeds of light with respect to you in the two cases, because c is with respect to aether, and platform and railcar (must) have different speeds with respect to aether.

The big challenge for experiment is however the enormous speed of light. After many attempts, Michelson and Morley devised an ingenious experiment to detect the motion of earth through aether. They split light from a single source into two parts, sent them into two perpendicular directions of equal lengths, got them reflected back, and collect on the same spot in a detector. Now if the earth moves in aether, then the time taken by light along the two arms of their device will vary, just as a swimmer has different resultant speed and therefore takes different times to cross equal distance when he swims along the direction of the river current and when he swims perpendicular to the current. But Michelson and Morley could not detect any fringe shift between the two portions of light, beyond the limit of experimental error. Either the earth is stationary in aether or the experiment is a failure.

But the earth moves! Considering the experiment not a failure, several scientists jumped into hypotheses for possible explanations. For example, Fitzgerald and Lorentz said that the arm which was along the motion of the earth has been contracted compared to the other arm, by such an amount that despite different relative speeds of light in two paths, the travel time was exactly the same. Lorentz and others developed the equations to transform parameters, such as time, length, etc., from one state of uniform motion to another state of uniform motion.

There were many other similar experiments to detect the motion of the earth with respect to aether. Most failed to detect. Based on these majority experiments, Poincare extended the relativity principle of Galileo in 1904 by saying that no physical experiment, including electromagnetic, can distinguish between a state of uniform motion and a state of rest. He corrected and systemized the transformation equations and called them Lorentz Transformation, which is now the heart of the Special Theory of Relativity.

Einstein, influenced mainly by Lorentz and Poincare's works and Michelson-Morley experiment, derived the transformation equations in 1905, considering speed of light constant. This paper contains a number of errors, so he subsequently revised his works several times. Much of the controversy and many of the paradoxes of relativity however still remains today.

Therefore the brief answer is Einstein was not the first person to take the speed of light in relativity. It is light and electromagnetism that prompted the modern theory of relativity. The detailed history is more complex though.

2. why c is constant in vacuum?
I am not aware if c has been calculated in absolute vacuum. However, that the speed of a thing is constant is not so puzzling. It can be a law of nature. The puzzle is that speed of light is always constant in vacuum with respect to all observers. It means that even if we run toward or against light, we will still measure light speed as c, regardless of our state of motion.

Why is that? After many years of history, we know the trick. You first define speed of light as constant for all observers, abandon Newton's notion of absolute time and space, and then say that observers moving at different speeds will have different time dilations for the same event (or length contractions for the same space), thus c=d/t will remain constant. But in Galilean relativity, you do not have dilation or contraction, so you do not need the same speed of light for all. You also do not need light speed to be constant for all observers in Lorentz Ether Theory. So, it’s a matter of definition or point of view about speed of light. And it is okay as long as the trick works fine to describe the physical reality.

We also know why the trick resulted/was needed: (1) because we believe that Maxwell’s equations and Lorentz force law are correct, (2) because we believe that light is a wave but does not need any medium, (3) because we believe that uniform motion cannot be detected by any experiment.

3. Is it theoretically proved? If not, is it possible to prove?
Since it is a matter of definition, you cannot prove it theoretically or directly through experiment. Because to measure the speed of light between place A and place B, you need two clocks at A and B and need to synchronize them at the beginning of the experiment. But special relativity says that you must synchronize clocks by sending light signal from A to B and B to A assuming that light takes the same time from A to B and B to A. Thus, it will be a circular reasoning to say that light speed constancy can be verified in this way.

What is the indirect way then? See whether the predictions of the theory are verified. Suppose, we know that if x=a, then y happens. Now if we see that y always happens in our experiment, we may say that x=a, although from pure logic, it is not 100% true. Anyway, there are differences between mathematical theory and physical theory.

There are two other main problems with the indirect proof. First, Lorentz Ether Theory also predicts the same phenomena of time dilation and length contraction. Second, the alleged experimental verifications, such as the Hafele-Keating experiment and muon experiment, are controversial.

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