Hi,

The measurement problem in quantum mechanics does not arise from any experimental limitations. It's inherent characteristic of the theory that a superposition of eigen-states of some operator can give a unpredictable eigenvalue.By unpredictable I mean that their relative weight of occurence is the only thing we can calculate. Special theory of relativity has built in dogmatic viewpoint which gives definite answer to a well posed question. Given some initial condition it's prediction at any later instance is purely deterministic. This way it's obvious that STR does not have any measurement problem.

No-it does define invariant quantities. The fact that the speed of light doesn't depend on the reference frame doesn't mean that it's impossible to define a time-like direction; indeed, in special relativity, such a definition is global. It just means that time, as an individual coordinate, depends on the reference frame.

(Incidentally, there doesn't exist any measurement problem in physics, at all.  It's just that quantities that were thought to be independent of the reference frame, in a certain approximation, turn out not to be, when the approximation is replaced by a more complete description.)

@ All,

I think I have been misunderstood here. Let me explain what I mean by "special theory of relativity (STR) an offshoot of a measurement problem, though of different kind than from quantum mechanics (QM)."

Measurement problem in QM:  As Remi has mentioned,  it refers to an irreducible statistical spread in measurement in QM. And as I understand it is an inherent property of the nature which implies that we cannot observe a system without disturbing it.

Measurement problem in STR: Remember that example of a light pulse bouncing to and fro between vertically parallel placed mirrors. And in horizontal motion the path becomes right angled triangle, Longer path implies more time to bounce off between the mirrors, thus leading to time dilation.

See attached pages from the book of Beiser. 

My question is: 

If time is measured such that it does not depend on light speed, or a photon bouncing off between two parallel placed mirrors, will the different phenomena such as time dilation from special relativity still hold?

Yes. The various ingenious clock designs are only for illustration. An  abstract clock is completely sufficient.

Maybe another angle to explain the problem: Imagine a magnetic field in which an observer moves. If the observer carries a charged particle with him (to measure electric fields), the particle will experience a force, leading the observer to conclude that instead / in addition to the magnetic field, there is an electric field.

However, on the theory side, transforming an electric into a magnetic field is not simple. Even a cursory glance on Maxwell's formulas tells you that they tend to be coupled with different derivatives (time or space). Hence, if you want to make electrodynamics consistent between moving observers, you absolutely must mix time and space coordinates during the coordinate transformation between observers. That is what the Lorentz-transformation does. This is inconsistent with classical mechanics and experience (where time is not transformed), which made Einstein introduce relativistic dynamics. These contain the classical mechanics as the everyday low-velocity limit.

No clock design needed for the whole reasoning.

The premise is meaningless. A photon moves along a light-like path in all frames-that's all that's needed. In the presence of boundaries, however, that break translation invariance, Lorentz invariance is broken and only a subset of Lorentz transformations are symmetries. Time dlation is just the name given to the fact that not all curves, that join two points in spacetme (not space alone), are geodesics. 

There's no problem of principle in computing the trajectory of a photon in the presence of boundaries-it's a standard exercise.  

Another homework ghostwriting assignment... 

@ Nicolis, Could you please explain what you have written in simpler words? I am finding it hard to follow.

What do you mean by "light-like path", "boundaries" (of what type). What sort of symmetry is underlying Lorentz transformations? "Time dilation is just the name given to the fact that not all curves, that join two points in spacetime (not space alone), are geodesics. " ?

Thanks Remi, I am aware of those lecture series and also watched some. Though inspired by Feynman, "If you can't explain something to a first year student, then you haven't really understood it.", I try to understand concepts at a simpler level with intuitive Physics. Mathematics comes after that.

And, that mirror-photon setup has bothered me the most since I had studied it for the first time 12 years ago.  I will definitely look at Landau's and Thorne's book.

@ Remi, I have read most of the Feynman's lectures on Physics (the millennium edition) and thoroughly enjoy them. Also, I guess there is hardly a YouTube video on Feynman which I have not watched. I consider two scientists as my ideal: Feynman and Ramanujan (the Indian mathematician).

Although my PhD research has been on a different topic, the two topics which I have found difficult to digest since my bachelor's education are 1) Theory of relativity (Special and General) and 2) Quantum Mechanics (the probability concepts). I do understand that all these theories are well battle-tested in experiments, still I have  a problem with them. Probably, there is a deficiency in my part (understanding)  which I wish to overcome. Since my PhD is completed now, I am working on to engage my previous love interests of relativity and quantum mechanics, once again.

I agree on the quality of responses from the names that you have mentioned. And I must say I have met some pseudo-scientific scholars and physicists from the so called 1st world, both on RG as well as personally.

Regarding the problem I have asked here on RG, I had contacted some physicists from MIT and Cambridge. And this is what two of them had replied to me,

1) "The time difference only comes when we compare one frame with the other. As for the so called light clock, this is only a symbolic example. The exact mechanism by means of which time is measured is irrelevant -- it could be for example with the vibration of a quartz crystal, rather than a bouncing bit of light. The symbolic example is merely to bring out the difference between a "moving" and "stationary" observer."

2) “We must remember that this is not just a physical effect. Everything – including the chemical, the biological, the physiological and even the psychological – is affected by the difference because time underwrites everything. In other words, your grandfather, stepping off the space ship at the end of the trip, would genuinely feel younger, and you would genuinely feel older!”

However, lets take another example, of making time measurements using a simple pendulum onboard a spacecraft. My first impression says, when viewed from an outside frame (from earth), pendulum will take longer time to reach to one of its extreme position when it is oscillating in the direction of spacecraft's travel direction. In contrast, it will take shorter time to reach to its other extreme position when oscillating in a direction opposite of the spacecraft's travel direction. The gain and loss in time during one complete oscillation would be equal in magnitude and will cancel each other. Thus, no time dilation. 

Am I wrong?

Time dilation has nothing to do with the mechanism of a watch or clock.