Is "length contraction" an illusion?

[BiGyElLoWhAt]

No that is the equation for length contraction which is a purely relativistic effect and is a result of space-time geometry. Length dilation on the other hand, by which I presume you mean the lengthening of objects relative to certain moving observers, is an optical effect. It is not clear to me whether you're trying to derive the former or the latter.

At this point I don't feel I have a strong enough conceptual understand to derive either. I'm trying to figure out what relativity is. This post was titled as such because that was my first thought when I decided to make this post.

Via your answer, I am reaching a conclusion that I stated earlier: that the "dilation" is always less than 1. However, this was based purely on a geometric equation posted by another user, not a conceptual deduction.

 

[BiGyElLoWhAt]

Another question that I feel is important to my conceptual understanding of relativity.

Can theses conclusions (relativity) be reached a "Doppler effect" method?

In this case (which encompasses all previous attempts) the only variation in length is due to the speed of the object being measured with respect to the speed of light for an object and an observer traveling along the same axis.

But when we offset our observers path (even if the motion is parallel wrt to the objects path) the length variation becomes reliant upon the rate of change of distance from our observer to one end of our object wrt the other end of our object... or is this the optical effect I keep hearing referenced in this thread?

 

[bhobba]

So from where I'm sitting, there are two sides to this coin. Either c is not fixed, or you compensate by saying that time is dilating. What results/concepts favor time dilation over a variable speed of light?

You really are getting yourself in a knot.

Please do read the link I gave.

The speed of light can't be variable because we are dealing with inertial frames. By definition (it may not be the definition you are used to, which usually is along the lines of frames moving at constant velocity wrt each other, but it is the correct one) inertial frames are frames where each point in space, each instant of time and any direction are equivalent. That they must move at constant velocity wrt each other is a simple consequence of this. If the speed of light varied the frame would not be inertial.

The core of SR is frames like that, to a high degree of accuracy, actually exist, but aside from that its conceptually a very very intuitive idea. We don't really expect the laws of nature to depend on man made things like exactly what point we call our origin, or what time we call zero, or how we orientate our coordinate system. Everyday experience strongly speaks to it doesn't matter.

Thanks
Bill

 

[bhobba]

Can theses conclusions (relativity) be reached a "Doppler effect" method?

You are tying yourself in unnecessary mental knots.

Its about symmetry. When you grasp that it all falls into place.

There was this program called the Erlangen program:
http://en.wikipedia.org/wiki/Erlangen_program

The key to geometry is symmetries and group theory. SR is simply the geometry of space-time as determined by the symmetries imposed by the Principle Of Relativity.

Symmetry is the guiding principle of much of modern day physics:
http://www.pnas.org/content/93/25/14256.full

This was the import and revolutionary view Einstein engendered with relativity.

Thanks
Bill

 

[WannabeNewton]

Can theses conclusions (relativity) be reached a "Doppler effect" method?

Yes this is Bondi's K-Calculus that pervect alluded to earlier and known more colloquially as the "radar echo" method.

But I must agree with bhobba, you are really tying yourself into unnecessary knots by trying to learn all over the place. At this point it's not even clear to me what you're looking for in this thread.

If there's anything that I've learned in my 2 years as a physics major it's that trying to figure things out yourself without any logical foundation will be a mess and will lead to more unnecessary confusion rather than any kind of conceptual understanding.

 

[BiGyElLoWhAt]

@ bill

Is your like a spoiler? Because, if so, it defeats exactly what I'm trying to accomplish here. I don't want someone to hold my and and say this is how you do it, this is what it and this is why it is.

I want someone to say, what about this? Explain this.

 

[BiGyElLoWhAt]

Link *

 

[bhobba]

But I must agree with bhobba, you are really tying yourself into unnecessary knots by trying to learn all over the place.

Indeed.

Learn, and understand, the very elegant standard modern view, then branch out.

You can then relate variations on the theme to that for deeper understanding if that's your wont, but its wise to learn the standard way first.

Thanks
Bill

 

[stevendaryl]

This feels weird to me. If the mirrors only need to be adjusted while accelerating, then this implies that either c is changing or you're losing light. Look at one ray bouncing between two mirrors. Give the mirrors a velocity and eventually the ray bounces off of the mirrors and is not rebounded by a mirror (the mirrors have moved past the the path the light is traveling on)

Right. While the mirrors are accelerating, the angle of the mirror has to be adjusted slightly so that the light is aimed ahead of the current location of the other mirror. When the mirrors have stopped accelerating, they can return to being perpendicular to the direction of motion.

If this is not the case, I have to ask one question, how can we measure something accurately enough to verify this phenomenon? If the mirrors only need to be adjusted while accelerating, then the motion of the light (c) is relative to its source,

What do you mean? Light always travels in a straight line at a constant speed. But think about it: If I aim a light toward a mirror, and while the light is traveling, the mirror moves, then the light will miss the mirror. In order for the light to hit the mirror, I have to aim slightly ahead of where the mirror is.

So from where I'm sitting, there are two sides to this coin. Either c is not fixed, or you compensate by saying that time is dilating. What results/concepts favor time dilation over a variable speed of light?

The constancy of the speed of light is both experimentally verified, and is predicted by the equations describing light (Maxwell's equations).

 

[bhobba]

I want someone to say, what about this? Explain this.

OK - what about viewing it as the result of symmetry?

Its very very elegant that way.

Thanks
Bill

 

[bhobba]

Link *

This link:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Relativity from symmetry and group theory.

I am also having difficulty understanding what you are driving at.

If its - how about this or that, has this been tried, what about this idea, I can tell you that process will be immeasurably enhanced when you understand the modern conceptual core.

Thanks
Bill

 

[BiGyElLoWhAt]

I'm not trying to come up with anything new.

When I started this thread, I was looking for some answers/input as to my methods. I got what seems like contradicting responses.

At this point what I would really like is someone who understands relativity well to play devil advocate with me to try to help me understand/figure out the fundamentals of relativity.

 

[WannabeNewton]

At this point what I would really like is someone who understands relativity well to play devil advocate with me to try to help me understand/figure out the fundamentals of relativity.

That's not how this forum works. We don't play devil's advocate here. If you have a well-formed question to ask then you should go ahead and ask it. If you want us to play a guessing game so that you can sate your desire to somehow understand relativity without first going through a proper textbook on the subject and acquiring well-formed questions about concepts regarding it then we can't help you here.

 

[stevendaryl]

Another question that I feel is important to my conceptual understanding of relativity.

Can theses conclusions (relativity) be reached a "Doppler effect" method?

Well, there is an interesting connection between relativity and the nonrelativistic Doppler shift.

Suppose that we have two observers, Alice, who is at rest in some frame, and Bob, who is moving at speed $v$ away from Alice, according to that frame. Let Alice send a light signal to Bob. Let $f_A$ be the frequency of the light as sent by Alice, and let $f_B$ be the frequency of the light as received by Bob. Using the nonrelativistic Doppler shift formula, we find:

$f_B/f_A = 1 - v/c$

Now, suppose that Bob sends a light signal toward Alice. Let $f_B'$ be the frequency as sent by Bob, and let $f_A'$ be the frequency as received by Alice. Then the Doppler shift formula is:

$f_A'/f_B' = 1/(1+v/c)$

They aren't the same formulas. So if the nonrelativistic Doppler shift formula were correct, then you could tell whether it was Alice or Bob who was really moving. That would violate the principle of relativity.

But now, let's introduce a time dilation factor $F$. Assume that, from the point of view of Alice's rest frame, Bob's clock is running slow by a factor of $F$. Then when Bob receives a light signal from Alice, it will seem to have a higher frequency by a factor of $F$. Why is that? Because the measured frequency is the number of oscillations in one second. If Bob's clock is running slow by a factor of $F$, then that means that what he thinks of as one second is actually $F$ seconds. So he'll measure $F$ times as many oscillations. So, instead of

$f_B/f_A = 1 - v/c$

we'll have

$f_B/f_A = F (1-v/c)$

Now, if Bob is the sender, then signals from Bob will have a lower frequency because of time dilation, by the same factor $F$. So instead of

$f_A'/f_B' = 1/(1+v/c)$

we'll have

$f_A'/f_B' = (1/(1+v/c))/F$

Now, if the time dilation factor $F$ just happens to be the right amount, it's possible to make those two ratios equal (and so it would be consistent with relativity--it wouldn't matter whether it was Bob who was moving, or Alice).

$f_A'/f_B' = f_B/f_A$

To get this to work out, it must be that

$F (1-v/c) = (1/(1+v/c))/F$

or

$F^2 = 1/(1-v^2/c^2)$

So if the time dilation factor $F$ is $\gamma = 1/\sqrt{1-v^2/c^2}$, then the principle of relativity is satisfied by Doppler shift, and it's impossible to determine from Doppler shift whether Alice or Bob is at rest.

 

[D H]

I'm not trying to come up with anything new.

No, you're not. Others before you have done much the same. Those others are crackpots. Do you want to join that crowd? You are free to join that crowd; we cannot stop you. But you cannot do this at this site. We do not countenance psychoceramics here.

Being very blunt, you are on the verge of being banned from this site.

You have been supplied with multiple posts that explain the mathematics and physics of relativity. I strongly urge you to pay close attention to those posts and the links within them.

 

[BiGyElLoWhAt]

Being very blunt, you are on the verge of being banned from this site.

Seriously?

That seems rather extreme; I don't see how I'm in any violation of any rules. I didn't start this thread with the desire for someone to play devils advocate, that desire merely emerged as a result of the responses.

But the fact that I feel like I can gain more from understanding the method of deduction that comes from deriving at least a conceptual understanding of relativity rather than having someone walk me through it makes me a crackpot? Really.

That's interesting D H, and not something I would expect from a mentor. I'm sorry for having the desire to work through a problem and not be spoon-fed the answer, then the proof, then have someone say "Hey, now that you know this because we told you so, what's the answer to this question" (as is the method with most textbooks in my opinion).

I'm sorry I asked this forum for help.

Lock this thread D H, because it's clear you think this thread is in some way, shape, or form, in violation of the forum rules (which I have read and don't believe it is [maybe it evolved to be more relevant in the HW questions... beside the point]), but I don't think it is, and I'm not really looking to get banned because I had a question that I asked, got answers that (to my understanding) aren't necessarily in coincidence with each other, and that arose to new questions and an evolution of this thread.


Peace out
-Tyler

 

[BiGyElLoWhAt]

Also, before this thread gets locked down, I want to add one thing.

Nobody HAS to respond to this thread, if you don't want to respond, don't.

But to everyone that has sincerely responded, I want to thank you, because at the very least you got me thinking, and that is precisely what I was looking for upon starting this thread (and ultimately joining this forum) and I thought that we had (for the most part) a good discussion going.

@stevendaryl, I want to point out that somethings you say seem to agree with what I have been trying to do, and some things disagree. It is very likely that this stems from my broken understanding of relativity (a broken understanding of almost nothing hehe). So I want you call you out in particular and thank you.

@pervect, I'm sorry for confusing you about what I was after with this, I do, however, appreciate your help, you've (perhaps indirectly or unintentionally) played the "devil's advocate" roll I was looking for, and at the very least given me a few good topics to research without looking up a detailed explanation of relativity (which is my whole goal with this, in case you haven't caught on).

To everyone else who helped, WannabeNewton, bhobba, and others, I'm sorry if you got left out. Thank you.

So I leave this thread with this: to MOST, I thank you.

 

[BiGyElLoWhAt]

I know I've already thrown in my last words, but...

Right. While the mirrors are accelerating, the angle of the mirror has to be adjusted slightly so that the light is aimed ahead of the current location of the other mirror. When the mirrors have stopped accelerating, they can return to being perpendicular to the direction of motion.

accelerating or moving?

What do you mean? Light always travels in a straight line at a constant speed. But think about it: If I aim a light toward a mirror, and while the light is traveling, the mirror moves, then the light will miss the mirror. In order for the light to hit the mirror, I have to aim slightly ahead of where the mirror is.

yes

The constancy of the speed of light is both experimentally verified, and is predicted by the equations describing light (Maxwell's equations).

just for my knowledge, do you have any experiments that I could look at that demonstrate the constancy of the speed of light within a greater accuracy than a $\delta$ equal to a relevant fraction of the speed of light relative to the velocity of the objects involved in the experiment (I hope that makes sense, I wasn't really sure how to word it)...
I'm sure there is a margin of experimental error in the speed of light. What I'm curious of is this: is the margin of error proportional (or approximately proportional) to the velocity of the objects used in the measurements. I'm sure this has all been thought of before, but again, I'm really trying to see if I can reach certain conclusions deductively.

I know everything that I'm trying to do has been done before.

I'm not trying to come up with any new theories.

I'm not trying to debunk any existing theories.

Where I'm coming from is this: At one point in time, these theories were not established nor conceived. At some later point in time they were. That was done through logical deduction, experimentation, and analysis of the results.

I feel I have more to gain by learning the method rather than learning the theory. (however, learning the theory is a consequence of learning the method)

After all, (in my opinion) being a successful physicist is less about what you know and more about how you think. I'm trying to improve the latter.

 

[Nugatory]

just for my knowledge, do you have any experiments that I could look at that demonstrate the constancy of the speed of light within a greater accuracy than a $\delta$ equal to a relevant fraction of the speed of light relative to the velocity of the objects involved in the experiment (I hope that makes sense, I wasn't really sure how to word it)...
I'm sure there is a margin of experimental error in the speed of light. What I'm curious of is this: is the margin of error proportional (or approximately proportional) to the velocity of the objects used in the measurements.

In a classical Michelson-Morley experiment, we measure the difference in travel time for light traveling crosswise to the Earth's motion through space and parallel to it. We use an interferometer to measure this difference, and the margin of error is independent of the speed of light or the speed of the earth.

 

[Dale]

Where I'm coming from is this: At one point in time, these theories were not established nor conceived. At some later point in time they were. That was done through logical deduction, experimentation, and analysis of the results.

It sounds like you are asking a historical question. The problem is simply that most people on this forum, including myself, consider the historical account of little direct value. People went through several dead-ends and wrong turns and even once they were on the current road they wandered a bit.

I heartily agree with bhobba's recommendation to think about it from a symmetry perspective. Modern physics is built on symmetry, it is an incredibly powerful means to understand.

You can also understand it from Einstein's postulates, which I think remain valuable despite the existence of more elegant formulations.

You can understand it in terms of experimental results, which is an approach that I like also.
http://authors.library.caltech.edu/11476/1/ROBrmp49.pdf

With that, I think that it is time to close the thread. There are many ways to understand relativity, but devil's advocate is not one of them. Also, it is difficult to learn the basics from a forum since you will continually run into what seem like contradictions. Sometimes they are actual contradictions because one or more of the respondents are wrong, but more often they are not contradictions at all either because they are talking about different things or because you have a conceptual error. In either case, a more coherent presentation from a single source will be more likely to help you understand.