I have been reading Albert Einstein's book titled "Relativity: The Special And The General Theory". I am still reading the Special Theory part and have not yet reached the General Theory part.

It is made clear that older theory of relativity and constancy of speed of light are not compatible with each other. So he makes an effort to examine the concepts of time and space so that there is no contradiction between this newer theory of relativity and constancy of speed of light.

Motivation behind focussing on light, other than to explain the constancy of speed of light, seems to be that we can only "sense" changes through light. That's it. There is no other way. And we have known that light takes finite time to travel.

To me, the above observation might have been motivated from Heisenberg's uncertainty principle, which assumes the exact same thing. By the time we observe something (technically, by the time light reaches us after having gotten reflected from the object), the state of the body would have changed. So there is no way we can know for certain the state of any matter. Light itself, causes the change in the position of the matter so we just can never know its exact position by the time light would have reached us.

Going back to Relativity and Einstein's book, the real deal for me starts from Chapter 10 where he talks about the Lorentz transformation. The only thing I have against this theory is that it assumes that the speed of one reference frame K' relative to the so called original reference frame K to be a "known" value. Please note that this whole theory rests on the fact that speed of light is finite and constant irrespective of frame of reference.

Now, how on earth is one to know the relative velocity of K' with respect to K? Should't that have to be taken into account as well? Speed of light should have mattered when determining the speed of K' with respect to K. In fact, that is true for any object. If we need to know its speed with respect to reference frame K, then we need to account for the finite speed of light and this will also have to include the speed of the reference K'.

Also, based on Heisenberg's uncertainty principle, there is no way to know the exact state of any matter as light is the medium through which we can know and by the time light reaches us, the state has already changed. This raises another question for me.

How can you ever assume any velocity for any body when its position is known to be uncertain?

In summary, I have two questions.

  1. Relative velocity of K' with respect to K (in the Special Theory of Relativity) is assumed to be known and does not take the finite speed of light in determining it.

  2. The position of any matter is assumed to be "knowable" where as it makes sense, according to Heisenberg's uncertainty principle, that it is not "knowable". How come Einstein did not bother to take care of this fact?

Somewhere, there seems to be a circular logic involved in Einstein's theory. Please clarify.

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    $\begingroup$ Please try to find the answer yourself before posting it here. For your second question, a quick google search will tell you that Uncertainty Principle was formulated in 1927 whereas Special Relativity was proposed by Einstein in 1905. Also Special Relativity is a Classical Theory with nothing to do with quantum mechanics. Incorporating the effects of special relativity in quantum domain led to the formation of Quantum Field Theory $\endgroup$ – ravjotsk Jul 15 '18 at 21:55
  • $\begingroup$ So basically relativity is "strictly" speaking, not accurate. Wonder how "Quantum Field Theory" solves it :). I bet you can keep on going like that and still end up with loopholes. To me, this situation reminds me of Godel's theorems in logic. No finite set of axioms can be free from paradoxes :). $\endgroup$ – TryingHardToBecomeAGoodPrSlvr Jul 15 '18 at 23:07
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    $\begingroup$ You can't make statements like these and expect to be taken serious. $\endgroup$ – my2cts Jul 15 '18 at 23:51
  • $\begingroup$ Not every derivation of the Lorentz transformations is mathematically rigorous. The best way is to start from the assumption of the uniformity and homogeneity of space and time. It is a natural intuitive assumption based on the universal symmetry. Then the constancy of the speed of light follows as a logical consequence (along with the other postulate). Also, you are misinterpreting the uncertainty principle. The state of a particle is uncertain not because we don't know it, not because it changes in the process, but because a particle does not have a certain state. $\endgroup$ – safesphere Jul 16 '18 at 1:41
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    $\begingroup$ @TryingHardToBecomeAGoodPrSlvr - I suspect you aren't parsing safesphere's comment that "not every derivation of the Lorentz transformations is mathematically rigorous." You also appear to have a misunderstanding of Godel's theorems. $\endgroup$ – David Hammen Jul 16 '18 at 15:51

So the basic approach with these thought experiments is to define the situation and then see what measurements observers wold actually make. This allows a relation to be drawn between the actual and the observed.

He constructs a hypothetical scenario with K amd K', then teases out what our observer will actually measure. Same for both questions.

  • $\begingroup$ Thanks for the response. But specifically, don't you think that assuming, that velocities of one reference frame with respect to the other, can be measured, is a big assumption? I am being critical here because Einstein is being critical himself about neglecting the effects of light (like its finite speed etc). So why stop there? Why not also try and "figure out" the answers to more fundamental questions like "is it even possible to accurately measure velocity or space/time of any matter -- owing to finite speed of light"? $\endgroup$ – TryingHardToBecomeAGoodPrSlvr Jul 15 '18 at 23:12
  • $\begingroup$ Let me be very specific. Concept of velocity seems to depend on speed of light. But then, he uses the word "speed" in the context of speed of light. Isn't that circular logic? $\endgroup$ – TryingHardToBecomeAGoodPrSlvr Jul 15 '18 at 23:13
  • $\begingroup$ If you can't measure it, it isn't "physics". So basically, you are proposing that "motion is not part of physics" because you believe you can't measure it? $\endgroup$ – alephzero Jul 16 '18 at 0:44
  • $\begingroup$ Forget relativity. If I have a car moving at 50mph, and I'm telling you in this problem I am setting it is moving at 50mph, then I can measure it by whatever process and theorise if that should give an answer of 50mph or something else, and if not 50mph then I can theorise why it is not 50mph. $\endgroup$ – JMLCarter Jul 16 '18 at 0:49
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    $\begingroup$ In a thought experiment a person can assume whatever they find useful to explore the problem. $\endgroup$ – JMLCarter Jul 16 '18 at 21:56

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