# Leave the science to Scientists. Just tell me what is SR.

## Summary:

Accept what science say, or become one yourself.

## Main Question or Discussion Point

I had this notion that it would be very easy to learn and understand Special Relativity, especially Time dilation.
Well, I was wrong.
1. First it will take the general history and philosophy of what Time Dilation is and how it works.
2. Then it takes Mathematical calculations.
3. In the end it takes a visual perception of incidences where one can visualise what is happening in different time frames.

1. Well, I understand the history and philosophy of what Time dilation is. (although I would like to go through it step by step and get confirmatin that what I undrstand is 100% correct.
2. I learned the formulas and calculations, even though there are a few steps which I do not understand why it is done this way, but this is purely to my poor mathematical capability. I am still continuing to play, memorise, and studying it hoping that in future I will know how the calculations works.
3. The visual perception is not so difficuilt. If one keeps in mind that physics remain the same in all timeframes, it is understandable and I can grasp what it is.
Now, this forum has many posts with incredibly nice insight, and the more I read, the more I learn. Therefore, I will continue to do so.

I decided to hinder you guys with my negligible posts one final time, because I need to confirm that my Historical and Philosophical understanding is correct.
• Michelson and Morley devised the inferometer to determine if there is an Aether wind to allow light waves to "travel" in space.
• The device had a source of yellow light beamed to a splitter mirror which splits the light beam in a 90 degree angle to each other.
• one beam will be set up to "travel" in the direction of the anticipated aether wind arriving at the inferometer from space, the other beam will travel perpendicular to the first.
• We will call the first mentioned beam, "Horisontal", and the second "Vertical" to imagine their entry into the Aether wind.
The expectation by Michelson and Morley was:
• The Vetical light beam will travel a longer distance from the splitter "UP" and back "Down", than the horisontal beam travelling "To" and "Fro" from their respective reflector mirrors.
• The inferometer was set up on Mercury to enable it being swung 360 degrees with great acuracy not to distort the 2 light beams on its travlling path
• By looking at the light beams fringe when it arrived back to a point of observation, one will see an interferance when moving the inferometer around where the "Horisontal" beam and "Vertical" beam exchanges their position.
• If the one beam travelled a longer distance, it will now exchange its position and would travel a shorter distance, and vice versa.
Michelson and Morley did not measure any differences, and therewith proved that aether wind does not exist.
However, what about the earth's speed around the sun or its equator? (A question asked by Einstein)
• This made Einstein think about why if this inferometer travelled through space, and the Earth's speed at the equator, or even the earth's speed through space around the Sun will not show any difference?
• He thought about this and eventually came to the conclusion that it does not matter where, how, or when you measure the speed of light, you will not find c slower than c. If you travel next to a light beam at half c, you will still measure the light beam at c, and not at half c as you would if you were overtaking a vehicle travelling at half your speed.
This was groundbreaking stuff because Special relativity were formulated from this insight.
• Scientists uses a beautiful thought experiment to demonstrate the theory of SR. (I am not sure if this was one used by Einstein, I will go back to his book to freshen up)
• A train has a 'light clock where a light beam travells to the ceiling and back at one second.
• Another light clock is "Stationary" in relation to the Train travelling say, to the right of the stationary clock.
• If the train and the ground clock was stationary relative to each other, both will observe the light beams of the other moving up and down at the same rate.
• If the Train was in Motion relative to the stationary clock, the ground observer will see the train's clock move slower, due to the ceiling moving away from its original position, and as the ceiling bounces the light beam back to the floor, the reflector of the floor also moved "forward" from its original position. This will constitute a triangular path which is longer than the original .
• Therefore, for the ground observer the clock on the train moves slower due to the Light beam having to travel further in a triangular fashion. But the ground observer sees his clock is stil running as usual.
• Now, for the observer on the train, His clock will seem to be running as normal, but if he observes the ground clock, He will observe it to be running slow.
Einstein gave an explanation and said,
• The speed of light will always be measured at c.
• and because Distance = Time multiplied with Rate
• in this instance light did not travel faster but Time slowed down
• And if Time did not slow down, Length contracted, but C still remained at c.
Then we get to Lorentz. His calculations took the 2 observers, and the movement of 2 flashes travelling in relation to these points, and of these 2 beams, and he created a mathematical formula to show the difference between the observers.
This is where I am in a bit of a grey area of understanding.
What does Lorentz's calculation show?

Is it possible to tell me in the fashion I did in the above setp by step analysis?

Last edited by a moderator:

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anuttarasammyak
Gold Member
Summary:: Acceptwhat science say, or become one yourself.

Then we get to Lorentz. His calculations took the 2 observers, and the movement of 2 flashes travelling in relation to these points, and of these 2 beams, and he created a mathematical formula to show the difference between the observers.
This is where I am in a bit of a grey area of understanding.
What does Lorentz's calculation show?
Now you understand SR including rather simple derivation of "Lorentz contraction" by Einstein, I think you do not have to go into detail of pre-SR theories that were revealed not comprehensive. If you are a science historian, disregard me.

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vanhees71
Ibix
If you want to understand SR then the way we discovered it is not the best way to learn. It's full of blind alleys, sudden jumps, and fifty-something years of confusion. For example, Lorentz discovered the transforms that bear his name years before Einstein, and Poincare wrote down the complete maths of what we now call special relativity a year before Einstein. But neither realised the full implications of what they wrote - both thought they were fixing Maxwell's equations, while Einstein realised they were fixing Newton. And Einstein himself didn't realise that he'd implied the existence of spacetime - Minkowski did that on seeing Einstein's work.

So the question is, what do you want to understand? If you just want to understand time dilation, I'd go with the geometric picture in Orodruin's Insight article. Time dilation comes from the fact that spacetime is a thing and two observers in relative motion are defining "time" to be slightly different directions in spacetime, and the Lorentz transforms are how we relate one observer's definition of "space" and "time" to the other. On the other hand, if you want to understand how we got to the concept of time dilation then you need to go into the history. And you seem to have that in slightly the wrong order - Lorentz's work predates Einstein, for one.

You definitely don't need the history to understand relativity. I think a brief overview is worth having just to know how we got here from there. But ultimately the justification for relativity is that its predictions match reality, not the history of its development.

DrClaude
vanhees71
Gold Member
2019 Award
Now you understand SR including rather simple derivation of "Lorentz contraction" by Einstein, I think you do not have to go into detail of pre-SR theories that were revealed not comprehensive. If you are a science historian, disregard me.
Indeed, it's most easy to first learn a subject from a good modern textbook not using the historical approach. Usually in physics the concepts gets more and more clarified the longer physicists use the theory. My favorite example is relativistic thermodynamics and statistical physics. I'd not recommend to learn it from sources older than the 1970ies, because only then a clear formulation has been reached.

Nevertheless, to learn about the history of the subject afterwards also leads to a better understanding of the subject, and it's very interesting anyway how the present knowledge came to be. The problem often is that the history of science written by historians lacks an understanding of the physics and history of science written by scientists often are telling stories rather than history. There are of course exceptions, and one should look for these exceptions. E.g., if it comes to the history of Einstein's science, I think the book by Pais, Subtle is the Lord, is still the best one you can read.

robphy
Homework Helper
Gold Member
Leave the science to Scientists.
If you want to understand SR then the way we discovered it is not the best way to learn.
[snip]
You definitely don't need the history to understand relativity.
Indeed, it's most easy to first learn a subject from a good modern textbook not using the historical approach.

The title of the OP's thread inspired me to recall
one of my favorite quotes, which applies to this thread. (Bolding below is mine.)
• JL Synge Relativity: The Special Theory (1956) p. vii said:
To understand a subject, one must tear it apart and reconstruct it in a form intellectually satisfying to oneself, and that (in the view of the differences between individual minds) is likely to be different from the original form. This new synthesis is of course not an individual effort; it is the result of much reading and of countless informal discussions, but for it one must in the end take individual responsibility. Therefore, I apologise, if apology is necessary, for departing from certain traditional approaches which seemed to me unclear, and for insisting that the time has come in relativity to abandon an historical order and to present the subject as a completed whole, completed, that is, in its essentials. In this age of specialisation, history is best left to the historians.
--J.L. Synge
Synge's relativity books were one of the first relativity textbooks that made use of the spacetime diagram.
https://archive.org/search.php?query=synge relativity
(Synge's books are not introductory level.)

While the history and pseudo-history of relativity tells a nice story,
[as others have said,] it is not the best way to learn the subject of relativity.

In my opinion, the history and pseudo-history [presented in textbooks]
tries to lead one through the various conceptual gotchas and puzzles to get to and get through
the "equations".
If one can't make it through this rough road, one is stranded... with the impression that relativity is incomprehensible [or just plain wrong].
If one manages to get through it, it likely doesn't really resonate... one can solve some textbook problems and that's it.

As others have said, newer viewpoints emphasizing on what's really going on (like geometrical methods, spacetime diagrams, 4-vectors, etc.... introduced appropriately to the target audience) are
better for getting to the physics. (In my opinion, I think these methods are not found in typical introductory physics textbooks because they are "too mathematical" (as is occasionally claimed, as Einstein himself initially claimed when Minkowski reformulated relativity geometrically).

For introductory presentations, I strongly advocate for Bondi's Relativity and Common Sense
https://archive.org/details/RelativityCommonSense
(also see my Insight https://www.physicsforums.com/insights/relativity-using-bondi-k-calculus/ ).
The Lorentz transformations (in the standard form) are not used explicitly in the development of the relativity... they appear in standard form later on, for those interested.

atyy and Ibix
vanhees71
Gold Member
2019 Award
Well, what I found annoying as a student was that somehow the apparent "paradoxes" of relativity were more discussed than the theory itself. Of course, there are no real paradoxes, and as soon as you have learnt the theory you really quickly understand all these apparent paradoxes as stemming from non-realtivistic thinking, which is not adequate for relativity and thus not adequate for a full description of phenomena. That's why relativity was discovered by many scientists at the end of the 19th and begining 20th century and finalized by Einstein in 1915. So why not first learning, how the theory works and then discuss the historical paradoxes, when it is easy to see, where the wrong thinking goes in to produce these paradoxes? Almost always it's not considering the "relativity of simultaneity".

I like Synge's books (despite the fact that there are too many "relativistic masses" around ;-) and thus his treatment of continuum mechanics is rather overcomplicated, starting with introducing three notions of "mass density", only one of which you really need and which is a scalar field, namely the invariant mass per volume in the rest frame of the fluid cell), but the first spacetime diagrams I'm aware of in the literature are indeed in Minkowski's famous talk of 1908 introducing what's rightfully called Minkowski space and also Minkowski diagrams. As far as I'm aware this is one of the rare cases where the common name to a concept is really due to the scientist who first discovered them ;-)).

atyy and robphy
Staff Emeritus
2019 Award
despite the fact that there are too many "relativistic masses" around ;-)
Too many? That would be 1?

robphy and vanhees71
vanhees71
Gold Member
2019 Award
And, horribile dictu, also too many ##\mathrm{i} c t##'s...

Nugatory and robphy
Ibix
And, horribile dictu, also too many ##\mathrm{i} c t##'s...
...and even -1 of them is too many.

Nugatory and robphy
Staff Emeritus
2019 Award
also too many ict's...
¡ i , caramba!

vanhees71 and Ibix
robphy
Homework Helper
Gold Member
Yes, Synge’s textbooks would not be a good starting point for today’s students, although at the time of its publication around 1960 (before I was born), it featured the at-the-time-modern geometric Spacetime viewpoint. It seems relativity texts back then were more about obtaining [in some set of coordinates], then solving differential equations resulting from solutions to the field equations.

Other books that emphasized Spacetime appeared later: Taylor and Wheeler’s Spacetime Physics in 1963 and Misner, Thorne, and Wheeler’s Gravitation in 1973.
(For context... Bergmann 1942, Landau 1951&1962, Rindler 1969, Hawking and Ellis 1973, Wald 1984, Schultz 1985, d’Inverno 1992, Hartle 2003, Carroll 2004,

ict, relativistic-mass,
and maybe someday coordinates will be another abandoned or de-emphasized concept.

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vanhees71
pervect
Staff Emeritus
Einstein gave an explanation and said,
• The speed of light will always be measured at c.
• and because Distance = Time multiplied with Rate
• in this instance light did not travel faster but Time slowed down
• And if Time did not slow down, Length contracted, but C still remained at c.
This is fine as far as it goes, but you are missing one of the more subtle and confusing thing that Einstein showed. While it is subtle and confuses many, it is very important to understanding special relativity. This is "the relativity of simultaneity".

You can find one of Einstein's more popular discussions of this issue in chapter 9 of "Relativity, the special in general relativity", the chapter of which is entitled "The relativity of Simultaneity". The key thought experiment is known as "Einstein's train".

See for instance https://www.bartleby.com/173/9.html

Length contraction and time dilation are not enough, you need also the relativity of simultaneity to have a consistent theory. This, in my opinion, was the biggest breakthrough that Einstein made that earlier writers did not make.

Discussions of the relativity of simultaneity tend to be rather long, and people struggle with it. My main purpose in point. It's not fair to just drop the name and leave, so, while I can't give a long treatment of the issue, I'll give a reference (which I did a above), and a very brief pointer at the math. Hopefully this will give you a place to start if you investigate it more, which I would encourage.

Going to the mathematics, a straightforwards mathematical description of length contraction and time dilation would be:

$$x' = \gamma (x - vt) \quad t' = \gamma t$$

##\gamma## is the factor that causes time to dilate and length to contract, and we know that when x' = 0, x=vt by the definition of the moving frame.

The Lorentz transform, though is something different. It says

$$x' = \gamma(x - v t) \quad t' = \gamma(t - vx/c^2)$$

The mathematical term vx/c^2 in the transformation of t' can be identified as the term in the transformation that causes the relativity of simultaneity.

So the goal is to understand the physical significance of this extra term. Since you have a historical bent, I have referred you to Einstein on that, though some modern studies in how to best teach the subject have shown that Einstein's exposition is resisted even by science students.

I'll refer you to a paper by Scherr , et all, " The challenge of changing deeply held student beliefs about the relativityof simultaneity", http://www.physics.umd.edu/perg/papers/scherr/ScherrAJP2.pdf on that point.

vanhees71
PAllen
2019 Award
And, horribile dictu, also too many ##\mathrm{i} c t##'s...
It boggles my mind that one of the physicists I most respect insists to this day on the utility of ict: Gerard t’Hooft.

vanhees71
Gold Member
2019 Award
Really? Must be inherited from his PhD advisor ;-)).

atyy and Nugatory
Why is ict so bad? It seems like a visual indicator that space and time are not identical even if they are parts of the same four dimensional thing. Is it that the imaginary number is taken too literally? Is is supposed to be?

robphy
Homework Helper
Gold Member
ict hides the causal structure of Spacetime.

Grasshopper
Nugatory
Mentor
Why is ict so bad? It seems like a visual indicator that space and time are not identical even if they are parts of the same four dimensional thing. Is it that the imaginary number is taken too literally? Is is supposed to be?
The disadvantages become more apparent when you move on to general relativity. The ##ict## formalism loses the distinction between vectors and one-forms and messes up some otherwise straightforward coordinate transformations. And the claimed advantage, even in special relativity, is small.

Grasshopper
PeterDonis
Mentor
2019 Award
the claimed advantage, even in special relativity, is small
In classical SR, yes. But in quantum field theory, ##i c t##, at least to a fairly large group of physicists, has a big advantage: it allows analytic continuation to Euclidean spacetime, where lots of things in QFT become much easier to do. When quantum field theorists talk about things like "Wick rotation", they are talking about this advantage.

Whether this QFT advantage actually amounts to anything as far as actual physics (as opposed to mathematical convenience) is concerned is, as far as I can tell, a matter of opinion and depends on which physicist you talk to.

anuttarasammyak
Gold Member
Why is ict so bad? It seems like a visual indicator that space and time are not identical even if they are parts of the same four dimensional thing. Is it that the imaginary number is taken too literally? Is is supposed to be?
It may seem unnecessary and annoying efforts to introduce Three things,e.g. Two ( covariant and contravariant ) vectors and One metric, in stead of One vector of Minkowsky for SR.

As an example
$$x^2+y^2+z^2+(ict)^2= - \sum_{\mu=0}^3 x_\mu x^{\mu} =-\sum_{\nu=0}^3 \sum_{\mu=0}^3 g_{\mu\nu}x^\mu x^\nu$$
with reinterpretation of
$$i\cdot i = 1 \cdot -1 = -1 \cdot 1 \cdot 1$$

GR is described using these three things. I am not sure whether GR is also described by ict Minkowsky vector and am curious to learn it if it exists.

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Grasshopper
Summary:: Accept what science say, or become one yourself.

I had this notion that it would be very easy to learn and understand Special Relativity, especially Time dilation.
Well, I was wrong.
1. First it will take the general history and philosophy of what Time Dilation is and how it works.
2. Then it takes Mathematical calculations.
3. In the end it takes a visual perception of incidences where one can visualise what is happening in different time frames.

1. Well, I understand the history and philosophy of what Time dilation is. (although I would like to go through it step by step and get confirmatin that what I undrstand is 100% correct.
2. I learned the formulas and calculations, even though there are a few steps which I do not understand why it is done this way, but this is purely to my poor mathematical capability. I am still continuing to play, memorise, and studying it hoping that in future I will know how the calculations works.
3. The visual perception is not so difficuilt. If one keeps in mind that physics remain the same in all timeframes, it is understandable and I can grasp what it is.
Now, this forum has many posts with incredibly nice insight, and the more I read, the more I learn. Therefore, I will continue to do so.

I decided to hinder you guys with my negligible posts one final time, because I need to confirm that my Historical and Philosophical understanding is correct.
• Michelson and Morley devised the inferometer to determine if there is an Aether wind to allow light waves to "travel" in space.
• The device had a source of yellow light beamed to a splitter mirror which splits the light beam in a 90 degree angle to each other.
• one beam will be set up to "travel" in the direction of the anticipated aether wind arriving at the inferometer from space, the other beam will travel perpendicular to the first.
• We will call the first mentioned beam, "Horisontal", and the second "Vertical" to imagine their entry into the Aether wind.
The expectation by Michelson and Morley was:
• The Vetical light beam will travel a longer distance from the splitter "UP" and back "Down", than the horisontal beam travelling "To" and "Fro" from their respective reflector mirrors.
• The inferometer was set up on Mercury to enable it being swung 360 degrees with great acuracy not to distort the 2 light beams on its travlling path
• By looking at the light beams fringe when it arrived back to a point of observation, one will see an interferance when moving the inferometer around where the "Horisontal" beam and "Vertical" beam exchanges their position.
• If the one beam travelled a longer distance, it will now exchange its position and would travel a shorter distance, and vice versa.
Michelson and Morley did not measure any differences, and therewith proved that aether wind does not exist.
However, what about the earth's speed around the sun or its equator? (A question asked by Einstein)
• This made Einstein think about why if this inferometer travelled through space, and the Earth's speed at the equator, or even the earth's speed through space around the Sun will not show any difference?
• He thought about this and eventually came to the conclusion that it does not matter where, how, or when you measure the speed of light, you will not find c slower than c. If you travel next to a light beam at half c, you will still measure the light beam at c, and not at half c as you would if you were overtaking a vehicle travelling at half your speed.
This was groundbreaking stuff because Special relativity were formulated from this insight.
• Scientists uses a beautiful thought experiment to demonstrate the theory of SR. (I am not sure if this was one used by Einstein, I will go back to his book to freshen up)
• A train has a 'light clock where a light beam travells to the ceiling and back at one second.
• Another light clock is "Stationary" in relation to the Train travelling say, to the right of the stationary clock.
• If the train and the ground clock was stationary relative to each other, both will observe the light beams of the other moving up and down at the same rate.
• If the Train was in Motion relative to the stationary clock, the ground observer will see the train's clock move slower, due to the ceiling moving away from its original position, and as the ceiling bounces the light beam back to the floor, the reflector of the floor also moved "forward" from its original position. This will constitute a triangular path which is longer than the original .
• Therefore, for the ground observer the clock on the train moves slower due to the Light beam having to travel further in a triangular fashion. But the ground observer sees his clock is stil running as usual.
• Now, for the observer on the train, His clock will seem to be running as normal, but if he observes the ground clock, He will observe it to be running slow.
Einstein gave an explanation and said,
• The speed of light will always be measured at c.
• and because Distance = Time multiplied with Rate
• in this instance light did not travel faster but Time slowed down
• And if Time did not slow down, Length contracted, but C still remained at c.
Then we get to Lorentz. His calculations took the 2 observers, and the movement of 2 flashes travelling in relation to these points, and of these 2 beams, and he created a mathematical formula to show the difference between the observers.
This is where I am in a bit of a grey area of understanding.
What does Lorentz's calculation show?

Is it possible to tell me in the fashion I did in the above setp by step analysis?
I believe the place to start in appreciating SR is in recognizing the problem of making observations using our eyes recognizing that light has a finite speed. This is not so much for measurements made on earth in a lab, but astronomical ones. I believe this is the problem Lorentz grappled with. Once you start applying the transforms to astronomical problems, you end up with the same conclusions Einstein did.

A.T.
I believe the place to start in appreciating SR is in recognizing the problem of making observations using our eyes recognizing that light has a finite speed.
That light has a finite speed was known for centuries, and is not what made SR necessary.

vanhees71
Gold Member
2019 Award
In classical SR, yes. But in quantum field theory, ##i c t##, at least to a fairly large group of physicists, has a big advantage: it allows analytic continuation to Euclidean spacetime, where lots of things in QFT become much easier to do. When quantum field theorists talk about things like "Wick rotation", they are talking about this advantage.

Whether this QFT advantage actually amounts to anything as far as actual physics (as opposed to mathematical convenience) is concerned is, as far as I can tell, a matter of opinion and depends on which physicist you talk to.
It's a great disadvantage in QFT either. Time is real, and the analytic continuation to imaginary time is a mathematical trick to prove some theorems in renormalization theory more easily. The devil is of course doing the analytic continuation back to real time.

Another application is the Matsubara formalism in equilibrium many-body QFT, which uses a finite interaval in imaginary time, ##\tau \in [0,-\mathrm{i} \beta]##.

In the general many-body real-time formalism, also valid for off-equilibrium situations you have a time contour running back and force along the real-time axis. In the real-time formalism of equilibrium you can combine this with the Matsubara formalism by just adding the vertical part at the end of the real-time contour.

In short: The ##\mathrm{i} c t## formalism is very confusing in all these cases, where you extend time to the complex plane or rather contours defined in the complex plane.

That light has a finite speed was known for centuries, and is not what made SR necessary.
The speed of light often influences how we perceive the truth of observed events and our response to those observations. "for centuries" is not accurate. It was recognized as being finite in the 17th and identified in the 19th. It does not go as far back as Aristotle who laid ground rules for physical observations. His perceptions were earth, water, air and fire which continuing research revealed were the 3 basic states of matter and the means to change those states, energy. He was not wrong from a standpoint of metaphor.