Implications of Einstein's Theories

[JimiJams]

What little I've read about Einstein, out of a textbook, regarded his theories on motion at the speed of light. I'm not sure if this is general or special relativity, but it involved observations such as time dilation and length contraction, as well as changes to momentum and energy.

I realize his whole theory, just about, rests on the premise that light will move at the speed of light regardless of your reference frame's velocity. This is a very counter-intuitive notion, when we think of this in terms of classical/Newtonian physics. My question is, does his observations of time dilation and length contraction, or any other observations/realizations he made, serve to explain just why and how light always moves at the speed of light? I mean just thinking about traveling at the speed of light right next to a photon, how can it be that that photon still appears to be moving away at the speed of light while you're traveling at the same speed? Again, does time dilation or anything in his theory at all clarify these observations?

 

[Drakkith]

First, you cannot have an inertial frame of reference that moves at the same speed as a photon. Light always moves at c with respect to any inertial frame.

Second, length contraction, time dilation, and other effects are all interrelated. They are a consequence of the various rules of nature, one of which is that light always moves at c in a vacuum. There is no underlying reason, that we know of, that light always travels at c when viewed from any inertial frame. It is simply what we observe.

 

[JimiJams]

Realistically, no, you can't have an inertial reference frame that moves at the speed of light. But, hypothetically, if you were to move at the speed of light or .9c, whatever makes you more comfortable, light will appear to move at the speed of light.

The classic example of the photon emitting at an angle and reflecting off a mirror back towards a sensor hypothesizes an observer traveling alongside that photon (and the photon appears to move up and down in a straight line rather than any angle...).

Even if you want to entertain the thought of traveling parallel to a photon at .9c, the photon will apear to move away at c rather than c-.9c. I was wondering if anywhere in his theories he can explain how this phenomenon takes place. Does time dilation, length contraction, space-time stretch etc.. serve to explain how light always appears to move away at the speed of light, even if you're traveling at .999999999c?

 

[Simon Bridge]

What little I've read about Einstein, out of a textbook, regarded his theories on motion at the speed of light.

Um - almost. Relativity applies for all speeds - not just the very fast ones. At light-speed is not covered (except for light) and it is always the other guy who is moving and not oneself.
It takes a bit of practisce to get used to this way of thinking.

I'm not sure if this is general or special relativity, but it involved observations such as time dilation and length contraction, as well as changes to momentum and energy.

If it involves gravity, then it is general relativity, otherwise it is normally special relativity.

I realize his whole theory, just about, rests on the premise that light will move at the speed of light regardless of your reference frame's velocity.

your reference frame is always stationary with respect to you. Get used to always talking about who is doing the observing in specific terms - it helps a lot.

The postulate is that all observers will measure the same speed for light in a vacuum.
It does not matter that they may have different velocities with respect to each other.

This is a very counter-intuitive notion, when we think of this in terms of classical/Newtonian physics. My question is, does his observations of time dilation and length contraction, or any other observations/realizations he made, serve to explain just why and how light always moves at the speed of light?

It doesn't.
The postulate was just that if c is invarient, then that results in a bunch of math that makes sense of a lot of other stuff. It does not explain why the invariant speed has to be c or why light should travel at that speed.

I mean just thinking about traveling at the speed of light right next to a photon, how can it be that that photon still appears to be moving away at the speed of light while you're traveling at the same speed?

The situation you described is impossible of course - you cannot travel along next to a photon - and the "frame of reference of a photon" is a meaningless concept in relativity.

Again, does time dilation or anything in his theory at all clarify these observations?

Imagine that Alice and Bob measure the speed for the same light beam.
Alice is holding the light source while Bob takes off along the beam to do his measurement.

But we realize that, according to regular (Galilean) relativity, if Alice measure Bob's velocity to be $v$, then Bob measures Alice's velocity to be $-v$. By the same relativity, when Alice measured $c_a$ she expected that Bob would measure $c_a-v$ (since he was traveling along the beam in the direction of propagation). Similarly, Bob would expect Alice to measure $c_b+v$. Instead they got $c_b=c_a=c$.

How do you normally measure speed? Why, by timing the thing you want the speed of over a fixed distance. But Alice points out that Bob's rulers are length contracted and his clocks are time-dilated ... when she checks she finds out that they are time dilated by the exact amount needed to make the speed of light come out the same as her's every time.

Bob also noticed that Alice's time was dilated and her lengths were contracted in the same ratios so no wonder she gets the same speed as him.

The time dilation and length contraction relations are what you need to happen for the speed of light to be measured the same by all observers.

 

[Simon Bridge]

The classic example of the photon emitting at an angle and reflecting off a mirror back towards a sensor hypothesizes an observer traveling alongside that photon (and the photon appears to move up and down in a straight line rather than any angle...).

In this example the observer is NOT "travelling alongside the photon".
If you have a reference that says this, then the reference is WRONG.

If you and I stood next to each other, and, on your signal, I walked to the far wall and back again while you stayed put ... you would not describe yourself as "moving alongside" me would you?

In "the classic example", you, the observer, are standing in a box with some equipment.
You throw a switch and the equipment emits a pulse of light, and starts a stopwatch. The light reflects of the ceiling and returns to the box, which detects it and stops the stopwatch.

Someone else outside the box has a means to tell when the light was emitted and when it was detected - which is recorded on their own stopwatch.

You and the other person compare notes later.

Thing is that the other guy says you were going amazingly fast while the experiment took place - some 0.9c. But according to you, they were the ones going really fast, the other way. Who's right?

Each of you has a different time for the period between throwing the switch and the pulse returning.
But if you crunch the numbers, the times you get are consistent with the speed of light being the same to both of you.

 

[JimiJams]

How do you normally measure speed? Why, by timing the thing you want the speed of over a fixed distance. But Alice points out that Bob's rulers are length contracted and his clocks are time-dilated ... when she checks she finds out that they are time dilated by the exact amount needed to make the speed of light come out the same as her's every time.

Bob also noticed that Alice's time was dilated and her lengths were contracted in the same ratios so no wonder she gets the same speed as him.

The time dilation and length contraction relations are what you need to happen for the speed of light to be measured the same by all observers.

Thank you Simon!, This answered just what I was too lazy to do the math to figure out. I learned about time dilation and length contraction but they struck me as only a bizarre phenomenon, I failed to realize that they also explain just WHY light always travels at the speed of light regardless of the observer's velocity.

By the way, I didn't explain very well but the example I was referring to when I said "traveling alongside the photon", is a thought experiment regarding a light box (I think that's what it's called) that was in the same text. It goes; there's a box with a photon emitter in a lower corner, and a mirror on the top of the box inside, and a photon sensor in the other lower corner. If you are standing still observing this box you would see a photon come out at angle theta relative to the ground of the box, hit the mirror and reflect towards the sensor in the other corner at the same angle relative to the ground of the box. Let's say the photon traveled a total 2 meters in time t.

Now, if you hypothetically traveled alongside the photon the very instant it was emitted the photon's path would look like it went straight up and then straight down, rather than at angles. If you do the trigonometry this equates to the photon traveling less of a distance in the same amount of time t than it did when you were standing still. From this, his time dilation and length contraction hypotheses can be surmised.

If you've already heard this example before I'm sorry if I bored or offended you.

 

[JimiJams]

Just to correct myself in my last post, the time is obviously not the same when standing and observing the photon and its distance, and traveling alongside the photon and observing its distance. The distances the photon traveled in both instances are different (for each observer), and the speed of a photon is always c, the speed of light. From that, we can calculate that there is a time difference taking place between the two observers.

 

[Simon Bridge]

Now, if you hypothetically traveled alongside the photon the very instant it was emitted the photon's path would look like it went straight up and then straight down, rather than at angles. If you do the trigonometry this equates to the photon traveling less of a distance in the same amount of time t than it did when you were standing still. From this, his time dilation and length contraction hypotheses can be surmised.

The way this is written misses out a very important bit of information - the second observer has to be moving horizontally along with the photon ... i.e. must be traveling at $v=c\sin\beta$ along the floor of the box. We'd normally set up the experiment the other way round since it is easier to think about that way.

Have a look through the FAQ here:
http://www.physicsguy.com/ftl/

 

[JimiJams]

Good point Simon, I should have clarified a horizontal movement by the observer.

 

[JimiJams]

Not to stray off topic, but does Einstein's General Relativity paint a clearer portrait of time dilation and length contraction? I know he developed the theory of space-time and I'm guessing it can be tied into time dilation, length contraction and why observers will experience these events while moving at the speed of light. Something to do with the fabric of space being made of space-time and a certain give and take relationship between the two (time and space).

I would like to get a good book on GR and a supplementary book on the mathematics needed to understand GR, can this be recommended? I've heard Taylor and Wheeler have a good one but it's light on the math. I want something with the math so I can get a clear understanding. It seems Schutz (A First Course in General Relativity), Hartle (Gravity: An Introduction to Einstein's General Relativity) and Carroll (Spacetime and Geometry: An Introduction to General Relativity) all have well-reviewed books on the topic on Amazon, does anyone know which contain the supporting math?

 

[WannabeNewton]

Not to stray off topic, but does Einstein's General Relativity paint a clearer portrait of time dilation and length contraction?

No. Kinematical time dilation and length contraction are effects that come about due to local Lorentz boosts from one local Lorentz frame to another so even in curved space-times it's still analyzed within the framework of SR, GR doesn't offer anything novel there. It just restricts the analysis to local regions of space-time because space-time is locally Minkowski. However GR does introduce the notion of gravitational time dilation.

I would like to get a good book on GR and a supplementary book on the mathematics needed to understand GR, can this be recommended?

Peruse the textbook subforum because there have been tons of people who have asked the same thing in the recent past: https://www.physicsforums.com/forumdisplay.php?f=21

 

[JimiJams]

Thanks for the clarification Newton, even though my math studies never took me into local Lorentz boosts or local Minkowski it sounds like there's no tying correlation between time dilation/length contraction and spacetime. Also thanks for the helpful link. Can you by any chance tell me what kind of math text I should look for to supplement study of general relativity?

 

[WannabeNewton]

How much math do you know already? You'll learn about local Lorentz boosts when you study GR so don't worry about that.

EDIT: Also I just saw that you're a Hendrix fan, awesome :)

 

[JimiJams]

I've taken three semesters of college level calc, differential equations, and discrete math fwiw.

Yeah huge Hendrix fan and Page for that matter too, as I'm sure you are haha. You a guitar player?

 

[Integral]

A simple answer to your basic question: Does relativity say anything about why light travels at the speed of light.

No. A constant speed of light is ASSUMED in the postulates. So relativity examines the result of a fixed light speed but does not delve into why it is so.

 

[WannabeNewton]

I've taken three semesters of college level calc, differential equations, and discrete math fwiw.

Learn linear algebra and you'll be all set!

Yeah huge Hendrix fan and Page for that matter too, as I'm sure you are haha. You a guitar player?

Haha yeah Jimmy Page is my god. And yeah I play guitar.

 

[JimiJams]

sweet, I'll have to grab a good linear algebra text.

Nice, obviously Hendrix is my anointed guitar god, I've been playing for 12 years now. You really can't go wrong looking up to either one though, they are the best in my opinion.

 

[phinds]

... I learned about time dilation and length contraction but they struck me as only a bizarre phenomenon, I failed to realize that they also explain just WHY light always travels at the speed of light regardless of the observer's velocity.

No, they most definitely do not explain why light always travels at the same speed regardless of the observers velocity. They are a RESULT of that fact, not an explanation for it. As Simon said we do not have an explanation for it. It just IS and we make use of it. Time dilation / length contraction show up as a result.

 

[JimiJams]

phinds, I mean time dilation and length contraction explain how it's possible for something to appear to be moving at a constant speed even if you're moving at close to the same speed. I don't mean they are the cause, only the result, which helps me to better understand just how an observer would interpret a photon as staying at constant speed c. Sorry for the confusion, I may have been confused myself when I posted that, admittedly.

 

[Nugatory]

phinds, I mean time dilation and length contraction explain how it's possible for something to appear to be moving at a constant speed even if you're moving at close to the same speed.

They don't, unless you also consider relativity of simultaneity.

 

[phinds]

phinds, I mean time dilation and length contraction explain how it's possible for something to appear to be moving at a constant speed even if you're moving at close to the same speed. I don't mean they are the cause, only the result, which helps me to better understand just how an observer would interpret a photon as staying at constant speed c. Sorry for the confusion, I may have been confused myself when I posted that, admittedly.

Yeah, I should have added that actually I THOUGHT you were getting idea right by now, but that you had poorly described what you thought was going on. My experience has been that sloppy use of terminology ties directly to sloppy thinking so I just wanted to make sure you were clear.

 

[PAllen]

They don't, unless you also consider relativity of simultaneity.

If you model measuring one way speed, this is true. If, instead, you model a moving apparatus measuring two way light speed you find that:

- you expect it to measure speed of light as (c^2 - v^2)/c

- but if you assume someone moving with the apparatus has measured its length as L$\gamma$, and time as t/$\gamma$, then you figure they would measure a speed $\gamma$^2 times what you expect. Then:

((c^ - v^2)/c) * $\gamma$ ^2 = c

I believe this is how earliest analyses of the MM experiment explained the negative result with length contraction and time dilation without yet realizing relativity of simultaneity.

 

[JimiJams]

I'm not sure what relativity of simultaneity is, how would that have an effect on how the observer sees the photon moving away at c? This might be too large a can of worms to open here, but if it pertains or if you have links I'd be interested.

 

[Chronos]

The speed of light is another one of the poorly understood facts of nature. It can be derived from the values assigned to vacuum permeability and permittivity, but, that is an incestuous relationship.

 

[ghwellsjr]

I'm not sure what relativity of simultaneity is, how would that have an effect on how the observer sees the photon moving away at c? This might be too large a can of worms to open here, but if it pertains or if you have links I'd be interested.

The best thing you can do to grasp what's going on with Special Relativity (where gravity is ignored) is to learn what the Lorentz Transformation is and one of the easiest ways to do that is to draw spacetime diagrams. I use a simplified version of the LT where the value of c is 1 so that it drops out of the equations and I like to use units of feet and nanoseconds and define c to be 1 foot per nanosecond. I also like to limit all motion and activity to the x-axis so that we only have two equations (plus the calculation of gamma, γ) to deal with. I also use speed as a fraction of c and we call that beta, β, which is equal to v/c. As is customary, I use the primed variables for the coordinates of the transformed frame and the unprimed variables for the coordinates of the original frame. And we always use inertial frames (non-accelerating). So here are the three equations:

γ = 1/√(1-β²)
x' = γ(x-βt)
t' = γ(t-βx)

There are certain values of β that make γ come out as a rational number and one of them is 0.6 where γ=1.25. So that's what I'm going to use in the following example.

You mentioned earlier a light box so that's what I'll use for my example. Consider a box with two mirrors on opposite sides spaced 3 feet apart. We start two photons (or flashes of light) going back and forth between the mirrors such that they cross paths in the middle of the box. Then we draw a spacetime diagram to depict this scenario:

Hopefully this diagram makes sense to you. The dots represent 1-nanosecond increments of time along the two worldlines for the ends of the box where the mirrors are. Each dot is a separate "event" with its own x and t coordinates. (It also has y and z coordinates but we set them equal to zero and they remain zero even after transformation.) Note that since the light travels at 1 foot per nanosecond, it follows the thin lines drawn at 45-degree angles.

Also note that an observer at the blue end of the box can only see what is going at x=0. So he can see that a flash of light reflects off his mirror every 3 nanoseconds. And since he knows that there are two flashes of light, he knows that it takes 3 nanoseconds for each flash to make the round trip. And since he defines the speed of light to be 1 foot per nanosecond in his rest frame, he declares that the two flashes of light hit the opposite mirrors at the same time, in other words simultaneously, although he cannot see this happening. That's what we show in the diagram. Every 3 nanoseconds, there is a flash of light reflecting off of each mirror.

Now we transform from the blue observer's rest frame to one that is moving at -0.6c. This will make it look like the light box is moving to the right at 0.6c:

Now, all of a sudden, we see Time Dilation, Length Contraction and Relativity of Simultaneity. But first, let's make sure you know how the LT works. Pick any dot. Let's start with the blue one at the top. It's coordinates are x=0 and t=18 in the original frame. So we plug those numbers into the LT equations, one at a time:

x' = γ(x-βt) = 1.25(0-0.6*18) = 1.25(0.6*18) = 13.5
t' = γ(t-βx) = 1.25(18-0.6*0) = 1.25(18) = 22.5

As you can see on the transformed diagram, the top blue dot has coordinates matching those values. You can continue with all the other dots. Or you can cheat and just do it for the top two and bottom two dots and then just fill in the remaining dots by proportionally spacing them.

OK, now that we're clear you know how to do the LT, let's look at the coordinates of some of the events shown as dots on the diagram in the two diagrams. First, we note that the Coordinate Time increment for the dots is spaced farther apart in the second diagram. That is what we mean by Time Dilation, a stretching out of the Proper Time (depicted by the dots) for a moving clock or observer. Note that the stretching out factor is equal to γ, in this case 1.25.

Second, we note that the distance between the two worldlines is closer together. Look at the spacing between the blue and red lines at t=5 and you'll see that it is about 2.4 feet. This is what we mean by Length Contraction and it is equal to the Proper Length (from its rest frame) divided by γ, in this case, 3/1.25 which equals 2.4 feet.

Finally, we note that the two events of the flashes of light reflection off both mirrors at the same time is no longer true. There is a difference of over 2 nanoseconds between what used to be simultaneous events. This, of course, is demonstrating the Relativity of Simultaneity, which doesn't have any special factor like LC and TD.

Here is another very important observation to make and that is that each observer in a scenario, sees, measures, and observes everything in exactly the same way in each reference frame. The blue observer continues to see a flash every 3 nanoseconds according to the Proper Time on his clock or watch. So to answer your question, Relativity of Simultaneity has no effect on how the observer sees the photon moving away because he cannot see the propagation of light. LC, TD and RoS are all coordinate effects and not directly observable by any observer unless he takes extra effort to actually collect a lot of data, apply Einstein's second postulate and draw his own spacetime diagram.

Now you have had a crash course on the most important aspect of Special Relativity, the Lorentz Transformation.

Does this all make perfect sense to you? Can you see how it relates to all the previous answers you have been given? Any more questions?

 

[A.T.]

I'm not sure what relativity of simultaneity is, how would that have an effect on how the observer sees the photon moving away at c?

Try this video:

https://www.youtube.com/watch?v=C2VMO7pcWhg

Relativity of simultaneity, time dilation and length contraction are just aspects of the same thing, the Lorentz-Transformation that relates reference frames, and replaced the Galliean-Transformation. The Lorentz-Transformation was designed such that it keeps light speed invariant, because that is what is observed.

 

[ghwellsjr]

The Lorentz-Transformation was designed such that it keeps light speed invariant, because that is what is observed.

No, the invariant speed of light is Einstein's second postulate, not an observation or measurement.

 

[A.T.]

No, the invariant speed of light is Einstein's second postulate, not an observation or measurement.

He postulated it because it fitted the observation.

 

[ghwellsjr]

He postulated it because it fitted the observation.

What observation?

 

[A.T.]

What observation?

https://www.physicsforums.com/showthread.php?t=229034

 

[ghwellsjr]

Of course Einstein's second postulate fits all observations in that there is no observation that is in conflict with his idea that we can define the speed for light to propagate in all directions to be invariant, but that's different than what I though you meant in your first comment that we could observe the invariant speed of light. Remember, you were quoting JimiJams when he asked "how the observer sees the photon moving away at c?" And I had just responded to the same question by saying "he cannot see the propagation of light".

 

[Naty1]

Hello Jimi:

My question is, does his observations of time dilation and length contraction, or any other observations/realizations he made, serve to explain just why and how light always moves at the speed of light?

As already answered, no, it's kind of a mystery.

And it is counterintuitive, seems like Einstein first thought about it around age 16...even took HIM a while to figure out...The greatest minds of the 1920's were flummoxed by time dilation and length contraction...[Lorentz and Fitzgerald couldn't quit figure it out, for example] searching for a 'luminiferous ether' as a possible explanation.

It took an Einstein to make a further step in understanding. It was his keen ability at physical insights rather than extrordinary mathematical ability that led him. That's why flat spacetime is called MINKOWSKI spacetime rather than EINSTEIN spacetime [LOL]; Minkowski was his former professor and it was Minkoswki who first realzed Einstein's new theory of special relativity should be reformulated in four dimensions...three space, one time.

It turns out that in our everyday low speed environment, space and time are mostly fixed and unchanging...time tick, ticks along at a steady pace, space remains fixed. It turns out that is true only locally, right where you stand, or move. As soon as you look further out with relatively high speeds between observer and observed, our everyday intuition fails: space and time are not what they appear. Lorentz transforms rule the day! Space and time 'conspire' so as to keep the speed of light constant.

One good 'rule' to remember: Your own clock, carried with you, always ticks at the same steady pace. Thats YOUR 'proper time'. And you own local ruler, right there with you, never 'changes length'. You can trust your local instruments accuracy! The other guy as a distant observer may see your clock tick differently than his, and your ruler different than his ruler, but you can be sure yours is fixed and accurate.


Also, it is helpful to know before you get into lots of details, which can get confusing,
that while SR shows us space and time are relative, GR tells us that in addition, changes in gravitational potential show further changes in the pace of time. So in a sense, SR weakens our everyday notions of fixed space and time and GR weakens those notions further.

PS: Another guru here plays guitar, if I recall, sophiecentaur...we recently had a discussion on the natural frequency of wood and electronic instuments...I'll send you a private message if I can find it.

edit: You should search 'guitar' in these forums yourself if interested...I did not realize there were so many prior discussions...

 

[JimiJams]

Well, it seems Lorentz transformations are the next thing I'll have to learn to get an even clearer picture. They may have even been in the text I read all this SR stuff in. I suppose from the observer's point of view, though, the photon would not appear to be moving away at the speed of light. There would be no 'moving away' it seems like the speed differences we experience in our everyday existence (ie a faster car passing you on the highway). Instead the length of space that the photon is traveling through would completely contract and your watch would be ticking just slow enough so that, if calculated, that photon would still appear to be moving at C, but without an appearance of 'moving away'.

This is surreal, even by today's standards. It's very Kubrick-ian. And Einstein doesn't seem like the type to have such a strange imagination when you look at him. Anyway, these results are reached mathematically under the assumption that light will always move at the speed of c relative to the observer's velocity. But just how did they ever prove that light does in fact always move at c relative to the observer? The text basically said many experiments proved this, but it failed to go into any detail at all. The only experiment I ever heard mentioned to corroborate Einstein's theories was when they sent a plane into flight with an atomic clock, and the airport also had an atomic clock. When the plane arrived the clocks were off by the expected amount, but considering it was a minute fraction of a second, couldn't there have been a mechanical error or something? And don't clocks eventually fall in synch again, just like the twin paradox? If so, the two clocks shouldn't have had any difference in what time they were showing.

By the way Naty, the physics of instruments and their materials sounds interesting. Thanks for referring me, I'll definitely have a look at that discussion.

 

[Simon Bridge]

Well, it seems Lorentz transformations are the next thing I'll have to learn to get an even clearer picture. They may have even been in the text I read all this SR stuff in. I suppose from the observer's point of view, though, the photon would not appear to be moving away at the speed of light. There would be no 'moving away' it seems like the speed differences we experience in our everyday existence (ie a faster car passing you on the highway). Instead the length of space that the photon is traveling through would completely contract and your watch would be ticking just slow enough so that, if calculated, that photon would still appear to be moving at C, but without an appearance of 'moving away'.

You need to be more clear with your terminology. you never experience any length contraction or time dilation - that is what happens to other people from where you are standing.
As far as you are concerned, light always moves away from you at the same speed.
It's not a trick.

But just how did they ever prove that light does in fact always move at c relative to the observer?

By having lots of observers measure the speed of light of course.

The text basically said many experiments proved this, but it failed to go into any detail at all. The only experiment I ever heard mentioned to corroborate Einstein's theories was when they sent a plane into flight with an atomic clock, and the airport also had an atomic clock. When the plane arrived the clocks were off by the expected amount, but considering it was a minute fraction of a second, couldn't there have been a mechanical error or something?

No. The minute amount of discrepancy was still bigger than the random variations due to mechanical error.
To make sure - you don't just do the experiment once.

And don't clocks eventually fall in synch again, just like the twin paradox? If so, the two clocks shouldn't have had any difference in what time they were showing.

No. In the twin paradox, the clocks do not "fall into sync" by themselves. The clock that undergoes the accelerations is the one that shows an earlier time when the two clocks are eventually compared.

Mostly the postulate is supported by the consequences being a better match to reality than other theories.

eg. The one that tends to get shown to students is the Mt Washington muon experiment which you can find on youtube.

There are a great many experiments corroborating SR.
See Experimental Basis for Special Relativity FAQ - spec. S3.
What is especially compelling is that the researchers in the best cases have deliberately set out to disprove it. The strength of SR, as with any scientific theory, rests not on the experimental verification so much as the cleverness of the many failed attempts at disproof.

 

[JimiJams]

Hey Simon, yes I fully understand that the length contraction and time dilation is only observed by the observer. My wording may sometimes be unclear to some, but I understand there are different experiences for both the observer and the observed, and the observer sees length contraction and his watch shows a slower time if it were at all possible to compare to the observed.

I can see measuring the speed of light as a straightforward task, but my question is, how would they be able to tell that the observer will always experience the 'object' moving away at the speed of light? How do they know it's not the same as our everyday experience of (object A's velocity) - (object B's velocity)? Just because light always moves at c doesn't mean that an observer will always see it moving at c. Just like if someone were obsessed with driving 40 mph all the time, any observer standing still would observe him moving at 40 mph but if they were going 30 mph he would appear to be going 10 mph. What experiment did they do to conclude that light always appears to move at the speed of light regardless of the observer's velocity?

I was under the impression that in the twin paradox there is no difference in aging which would imply their clocks manged to sync up again by the time the cosmonauts returned. I've heard this has something to do with the acceleration when the rocket turns around. Sorry for the vagueness.