Implications of Einstein's Theories

[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.

 

[Drakkith]

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?

Plenty of examples in this article: http://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation

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.

That is incorrect. The returning twin will have aged less than the twin who stayed on Earth.

 

[JimiJams]

Drakkith, all those experiments came long after Einstein's theory. Were they able to prove that photons always appear to move at the speed of light regardless of the observer's velocity before Einstein began work on his theory? If not how did they come to that conclusion before experimentation?

 

[Simon Bridge]

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,

It is really really important to avoid incautious wording when you are learning SR. There are established ways to talk about it that you should learn so people will understand you.

i.e. in this bit:

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.

... it sounds like you just said that the observer's watch was slow. This is not the case - it is everybody else's (everybody with a non-zero relative velocity) watch that is slow.

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.

Measuring the speed of light is how you observe it moving at a particular speed. In this case the word "observe" is used in the sense of detecting or measuring something.

"Observing" light in any other way doesn't make sense.

Note: we cannot prove that all observers will always measure the same speed for light.
Nobody can - it is only possible to disprove it.

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?

The FAQ I liked to has many such experiments in it - go look.

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.

That impression is incorrect.
The earlier relativity and FTL FAQ I linked to has a detailed description of the Twin's Paradox.
tldr: the traveling twin returns younger.

the "paradox" of the title is that, from the POV of the traveling twin, it is his brother on Earth who is moving. Therefore, he argues, it is the Earthbound twin who should stay younger. What's wrong with the argument?

You are asking for a ot of information that requires a lot of writing. That is why you are directed to read some references ... which makes for a lot of reading for you but that cannot be helped.
The best way for you to get answers right now is to go read those references - I've tried to make them as accessible as I can while still answering the questions.

The relativity & FTL FAQ is very accessible and introduces you to the main tools you need to understand SR as well as a discussion about FTL that should be a nice break. The evidence FAQ itself is easy-ish to read, but the papers linked to are not so much which is tough. But at least you won't have to take my word for it that many experiments have been done.

Here's those links again:
http://www.physicsguy.com/ftl/
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

 

[Simon Bridge]

Drakkith, all those experiments came long after Einstein's theory. Were they able to prove that photons always appear to move at the speed of light regardless of the observer's velocity before Einstein began work on his theory? If not how did they come to that conclusion before experimentation?

I've already answered these questions.
Section 2 of the evidence faq I have repeatedly tried to get you to read, that I linked to in my last post, includes details of experiments before 1905. Please go read the references.

 

[JimiJams]

Simon, thanks for those links, I usually try to get an answer out of someone else though, but in this case I see I'll need to read more first.

Thanks for clarifying the clock situation haha. So the observer would see the the other's clock moving more slowly than his own. So for Einstein's formulas to make sense of light's constant speed of c regardless of observer's velocity, then the non-observer's time observed by the observer and the observed surrounding space outside the observer's reference need to be used for calculations. And length contraction will take place wherever the observer looks outside his reference frame, not just in the non-observer's reference frame, correct? Sorry for the lack of terminology, this is my last question before I read through those links tonight and perhaps the text again...

 

[Drakkith]

Simon, thanks for those links, I usually try to get an answer out of someone else though, but in this case I see I'll need to read more first.

Thanks for clarifying the clock situation haha. So the observer would see the the other's clock moving more slowly than his own. So for Einstein's formulas to make sense of light's constant speed of c regardless of observer's velocity, then the non-observer's time observed by the observer and the observed surrounding space outside the observer's reference need to be used for calculations. And length contraction will take place wherever the observer looks outside his reference frame, not just in the non-observer's reference frame, correct? Sorry for the lack of terminology, this is my last question before I read through those links tonight and perhaps the text again...

Let's use Observer A and Observer B instead of Observer and Non-Observer.

Observer A and B are in spaceships moving relative to one another. Observer A sees B's clock as moving slower than his own and also sees B as being length contracted. Observer B sees A's clock as moving slower than his own and also sees A as length contracted. So BOTH observers see the other person experiencing time dilation and length contraction but not themselves.

 

[JimiJams]

Does observer A see the space around observer B also length contracted?

 

[Drakkith]

Does observer A see the space around observer B also length contracted?

No, as you cannot see space.

 

[JimiJams]

Suppose space was a visible substance, a contracted B would appear like he was moving slower than the speed of light (if A intuitively knew what the speed of light looked like). But when he sees how slowly B's watch is ticking he is then able to validate that B is moving at the speed of light. So mathematically it seems like there is some type of proportionate relationship between the amount of length contraction and the amount of time dilation. My head hurts and I feel like I keep heading down the wrong path here. The link I went to just didn't clarify these questions of mine enough when it discussed length contraction and time dilation and they might not get cleared up until I get to Lorentz transformations I'm guessing.

 

[Drakkith]

Suppose space was a visible substance,

It is not, therefore anything said about visible space is pure speculation.

a contracted B would appear like he was moving slower than the speed of light (if A intuitively knew what the speed of light looked like). But when he sees how slowly B's watch is ticking he is then able to validate that B is moving at the speed of light.

This is wrong. No observer is ever able to move at the speed of light.

So mathematically it seems like there is some type of proportionate relationship between the amount of length contraction and the amount of time dilation. My head hurts and I feel like I keep heading down the wrong path here. The link I went to just didn't clarify these questions of mine enough when it discussed length contraction and time dilation and they might not get cleared up until I get to Lorentz transformations I'm guessing.

I believe the two are exactly proportional.

 

[JimiJams]

It is not, therefore anything said about visible space is pure speculation.

I'm just being reasonably hypothetical to gain a better understanding. Imagining a visible space won't skew any conclusion we come to from my specific question.

This is wrong. No observer is ever able to move at the speed of light.

Then call it a photon with a watch if it makes you happier.

 

[A.T.]

So mathematically it seems like there is some type of proportionate relationship between the amount of length contraction and the amount of time dilation.

The relationship between the length contraction and time dilation can be visualized in a space-propertime diagram:
http://www.adamtoons.de/physics/relativity.swf

 

[Drakkith]

I'm just being reasonably hypothetical to gain a better understanding. Imagining a visible space won't skew any conclusion we come to from my specific question.

Attempting to imagine space as a visible substance is fundamentally wrong and will only lead to confusion.

Then call it a photon with a watch if it makes you happier.

Photons do not have inertial frames of reference, so we cannot use them as observers. An inertial frame of reference is one in which light will be observed to travel at c. Plugging in c as the velocity of an observer makes our math turn out nonsense, indicating that we cannot do it.

 

[mathskier]

Of course, if you consider two observers, one in frame S and the other in frame S' (moving at .99c relative to S), BOTH observers see the photon move at speed c... But the observer in S will see the person in S' move at nearly the same speed. That is, in S' the distance between the person and the photon after time t is ct (and the same can be said about the distance between the person in S and the photon, as measured in S), while in S the distance between the person in frame S' and the photon is only .01ct. Cool stuff!

As long as you stay in one inertial frame, your ordinary intuitions always work.

 

[Simon Bridge]

Suppose space was a visible substance,

You are persisting in imagining things that are unhelpful - things that you'd be steered away from if you had read the references. This leads us to suspect that you are not serious about learning and only want to contemplate artistic imagery.

For the kind of visualization you are contemplating, you need to pick a reference frame and them find a way to mark out a grid ... say: make the void dusty and have a grid of laser beams for objects to fly through.

a contracted B would appear like he was moving slower than the speed of light (if A intuitively knew what the speed of light looked like). But when he sees how slowly B's watch is ticking he is then able to validate that B is moving at the speed of light.

If B is moving at speed v<c in A's reference frame, then in what reference frame is B moving at c? There is no such frame. The observation of B's watch, by A, only confirms the relative speed of v.

This is what we and all the references are telling you about there being no preferred reference frame but you are still writing as if there is one. Get rid of that idea. It is nonsense. You need to start doing the math.

So mathematically it seems like there is some type of proportionate relationship between the amount of length contraction and the amount of time dilation.

Of curse, the amount of each depends on the relative speed.

You are having trouble with it because you failed to define you terms.
What do you mean by the amount of time dilation" and "the amount of length contraction"?

i.e. Alice and Bob both carry standard meter rulers with them.
When the rulers are at rest wrt to each other, the measure the same.
When Bob is moving at speed v in Alice's frame, Alice notices that Bob's ruler is shorter than her's.

It is shorter by $100(L_A-L_B)/L_A$ percent.

Alice could also use her watch to time how link a single tick (1s) on Bob's watch takes.

If you keep thinking in concrete terms like this you won't get quite so confused.
You should have noticed that the references are all full of those sorts of statements.
One of the things you learn with relativity is just how vague common ways of talking about lengths and time actually are. You have to get really specific about describing your ideas if you want to make sense. It's a pain, but, after a while, you get used to it and you stop needing to be quite so pedantic - but when you are learning it is essential.

 

[JimiJams]

I just wrote out an entire response, and just now deleted it. I would have to discuss this face to face with someone because I feel I'm failing to adequately state my question through this medium. I also think my hypothetical scenarios are being taken too literally. You need to imagine things when working with anything in science, just as most scientists have a clear image of what they believe may be taking place and then attempt to validate it through the mathematics. The spacetime grid is a great example of a visual aid that helps to understand a theory better. That's all I'm doing by saying visualize a measurable space. Thanks for any help with this, and I'm sorry if I failed to soak in anyone's attempt at clarifying things, as always I learn best through a book so I'll revisit my text regarding SR as it has been a while.

 

[Drakkith]

I just wrote out an entire response, and just now deleted it. I would have to discuss this face to face with someone because I feel I'm failing to adequately state my question through this medium. I also think my hypothetical scenarios are being taken too literally. You need to imagine things when working with anything in science, just as most scientists have a clear image of what they believe may be taking place and then attempt to validate it through the mathematics. The spacetime grid is a great example of a visual aid that helps to understand a theory better. That's all I'm doing by saying visualize a measurable space. Thanks for any help with this, and I'm sorry if I failed to soak in anyone's attempt at clarifying things, as always I learn best through a book so I'll revisit my text regarding SR as it has been a while.

You misunderstand. There is no reason to even visualize a spacetime grid because in SR spacetime never changes. So visualizing a spacetime grid and asking what happens to it is pointless, as the answer is nothing. The motions of objects has no effect on spacetime.

 

[TumblingDice]

That's all I'm doing by saying visualize a measurable space.

And everyone's trying to guide you away from "heading down the wrong path" as you've said yourself.

Can we just visualize a room or the old classic train car? Go ahead and give them the dimensions you want in their own inertial rest frames. You can even draw lines on the walls to define a ruler framework. We can do all of this to define a physical object with dimensions.

Just don't start visualizing space, because it's only math and geometry.

 

[Simon Bridge]

I would have to discuss this face to face with someone because I feel I'm failing to adequately state my question through this medium.

That may help - but they would still give you the same notes we have.

I also think my hypothetical scenarios are being taken too literally.

You should not be talking metaphorically about this stuff while you are still wrestling with the concepts.
You absolutely must must must be careful to state exactly what you mean.
It is difficult enough without using artistic language.

You need to imagine things when working with anything in science, just as most scientists have a clear image of what they believe may be taking place and then attempt to validate it through the mathematics. The spacetime grid is a great example of a visual aid that helps to understand a theory better. That's all I'm doing by saying visualize a measurable space. Thanks for any help with this, and I'm sorry if I failed to soak in anyone's attempt at clarifying things, as always I learn best through a book so I'll revisit my text regarding SR as it has been a while.

As already observed, movement through space does not affect space, in SR.
There is no movement in space-time.

But space-time grids are useful - scientists do use them - they are the lines in a space-time diagram that you find in the references we have given you and demonstrated in other posts.

You can also set up a grid of space points in some reference frame and then see what that looks like to observers moving wrt the grid.

But you have to set these things up carefully otherwise you will end up talking nonsense.

If you get nothing else from this discussion - take away the idea that you absolutely must use clear terms and clear language when talking about relativity. Intuitive concepts will just not work.

 

[JimiJams]

Drakkith, to put it simply and briefly, length contraction intuitively to me seems to conflict with calculations that show an observed object always moving at c regardless of observer's speed. Because the object would appear to contract or get smaller, so if the space (measurable space, imagine a uniform grid) it's traveling through does not contract it would appear to cover less distance in a given time.

I understand time dilation steps in and corrects this, but it would make more sense to me if the object appeared to grow larger as the observer's speed increased so it would appear to be covering more distance in a given time.

This is all I'll say for now because every time I try to expound on this I find it very difficult to get across on here and end up deleting it. What I typed above is purely from an intuitive standpoint. If length and time are compromised for something to always appear to be moving at c regardless of an outside observer's motion it would make more sense to me intuitively that time would slow and length would elongate. If something's traveling at c and the observrer at .9c then the object should appear to move at .1c. Length and time appear to alter in order for it to still appear to be moving at c, but you would think to make up the difference of .9c (mathematically) that length would not contract but elongate. But it contracts, so time dilation must really make up the bulk of that difference, mathematically.

I hope this is clear, and I'm sure it's wrought with errors, but without getting into mathematical detail this is the best I can do to describe what I would INTUITIVELY think would take place.

 

[TumblingDice]

JimiJams: You've mentioned objects moving at c several times now. For the purposes of this discussion, the only thing that travels at c is light. Nothing with mass ever travels at c.

Can we visualize a room or train car as I suggested in my post #53? The thought experiments you want to do right now should always involve rulers and/or clocks, depending on what you want to focus on in each 'experiment'. Train cars or rooms can be used if you need to establish a framework for your inertial reference frames (observers).

 

[TumblingDice]

If length and time are compromised for something to always appear to be moving at c regardless of an outside observer's motion it would make more sense to me intuitively that time would slow and length would elongate.

You have the slower clock correct, because that allows more 'time' for light to travel at c relative to this observer. Making objects longer however would work against the slower clock, making light have to travel further. It needs to travel 'less' to maintain the locally observed speed of c.

Edit: What I wrote is a bit over-simplified. I hope it paints time dilation and length contraction a bit more intuitively to help you move forward.

 

[JimiJams]

Tumbling, you just clarified it for me. Measuring light inside a reference frame from another reference frame, it certainly would make sense that length contracts along with time dilation.

I misinterpreted what was meant by, "light always travels at c regardless of the observer's velocity."

So to go back to how I kept mistakenly visualizing this, if I was following behind a photon at .9c then it would actually appear to me to be moving away from me at .1c, correct? This seems to be unrelated to relativity because this example does not involve reference frames or any observers.

 

[Drakkith]

So to go back to how I kept mistakenly visualizing this, if I was following behind a photon at .9c then it would actually appear to me to be moving away from me at .1c, correct? This seems to be unrelated to relativity because this example does not involve reference frames or any observers.

If you are moving at 0.9c with respect to a stationary frame and traveling parallel to a light ray, then to the observer in the stationary frame the distance between you and the light will increase at 0.1c. However, in your frame the light moves away at 1.0 c.

 

[TumblingDice]

if I was following behind a photon at .9c then it would actually appear to me to be moving away from me at .1c, correct?

As Drakkith pointed out, light *always* is measured at the speed of c, to all observers.

This seems to be unrelated to relativity because this example does not involve reference frames or any observers.

Ah! Notice that Drakkith also mentioned you moving at .9c relative to a stationary reference frame. (Perhaps an observer on Earth, but could be anywhere relative to your .9c speed. You want to get into the habit of, whenever you mention moving at such-and-such speed, to always add, "relative to X". And in most cases you'll have at least two 'observers' moving relative to each other. Either one can validly take the perspective that their frame is 'at rest'.