Nature of Time Dilation and Length Contraction

TOM2:

You are rapidly proving yourself to be a paper tiger.

Do you really want to disapoint your most avid groupie who has called you a really smart fellow?

 

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Again: What?

Your expression "working mechanics of the development of the Lorentz contraction in a contracting body" makes no more sense than Prosoothus' superfluous properties in equations. You are both just making word salad. That's fine, but you shouldn't expect to be understood if you do that.

And no, length contraction is not a bedrock of relativity, it's a consequence of relativity. The postulates form the bedrock of relativity. It is exactly these kinds of misconceptions that I am referring to when I say that I am not inclined to respond to them.

*yawn*

Couldn't care less, buddy.

 

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TomTom is obviously sensitive to, and expert at, playing to an audience. Unfortunately, he does not yet understand that the only listeners who are impressed by his outbursts are even less less intelligent than he is.

The seemingly negative result of the MM science experiments of the 1880s put scientists into a frenzy to explain. Explanations took the form of the Lorentz length contraction. Ring a bell, TomTom? Einstein adopted the Lorentz length contraction in his Electrodynamics of Moving Bodies. Length contraction is bedrock fundamental to the derivation of gamma.

Without the length contraction, there could not be any Relativy. Is it coming back to you now, TomTom?

In a post not long ago, TomTom confided that he did not know, ( even though the mathematical analysis is simpler than dirt ) whether the contraction started at the front or the back or in the middle.

CANGAS is a mathematics expert. But, CANGAS does not know if 1 + 1 = 3, or 4, or 1.5. It may depend on what the meaning of the word is is. Right, TomTom?

 

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Tom2,

I thought my statement was self-explanatory. I guess not. Let me explain it for you:

Let's take the classical formula for gravity:

F=G*m1*m2/r^2

r is the distance between the two masses. It can be expressed in absolute coordinates in Euclidean geometry like this:

r=sqr(((x1-x2)^2) + ((y1-y2)^2) + ((z1-z2)^2))

where x1,y1,z1 are the absolute coordinates of m1 and x2,y2,z2 are the coordinates of m2. So the classical formual for gravity can be rewritten with absolute coordinates like this:

F=G*m1*m2/(((x1-x2) + ((y1-y2)^2) + ((z1-z2)^2)))

The above absolute formula is just as accurate (in Euclidean) geometry as the Newton's gravitational formula. Then why not use the absolute formula instead? Because the force of gravity is influenced only by the distance between the two masses, and not the absolute coordinates of the masses. You can change the absolute coordinates to any values you wish, and the gravitational force will be the same as long as the distance between the masses is the same. This is an example of how absolute values can be superfluous in an equation. That doesn't mean that the two masses don't have absolute coordinates, it only means that their absolute coordinates are superfluous to the gravitational interaction. So, for example, you can say that Newton's formula for gravity is a relative equation in its own way.

Now, when it comes to inertial frames of reference, absolute values (like abslolute coordinates or absolute speed) may under most cases be superfluous as well, but that doesn't mean that they must be in all cases. For example, in an inertial frames of reference, the relative velocities of objects may only be needed to give the correct result for many of the interactions between them, but that doesn't mean that absolute velocity doesn't exist. Nor does it mean that there aren't interactions in that frame that require absolute coordinates or absolute velocity (like the speed of light).

Basically what I'm trying to say is just because most interactions are relative (don't require absolute values) in an inertial frame of reference, doesn't mean that they all have to be. It appears that Einsten didn't agree with me.

Then explain to me why Einstein insisted that the speed of light is constant in all inertial frames of reference based on an experiment done on the surface of the Earth? Why after 100 years of Special Relativity, no one has ever measured the speed of light in an object that is actually moving through a gravitational field? This simple experiment would once and for all prove to all us crackpots that the speed of light is not tied to something that is geocentric (like an aether or the Earth's gravitational field), if it isn't. Even Einstein suggested that the Earth is dragging spacetime around. How was he so sure that the speed of light was not only equal to c relative to this moving spacetime and nothing else?

These are the kinds of questions that make me believe that Einstein was attempting to satisfy one of his desires (the desire that an inertial observer can't perform any experiment that can be used to determine his/her absolute velocity) instead of trying to uncover the true nature of the universe.

 

Can you think of even a single equation or interaction where the absolute coordinates are not superfluous?

-Dale

 

Before chiding others you should be sure of your own facts first.

The Lorentz Contractions as originally derived were mere mathematical "sleight of hand". They were adopted to make the model of an aether fit the observation.

What Einstein did was to show that the same expression could be derived from the two postulates without assuming an aether. He did not adopt Lorentzian Length Contraction, he arriverd at the same expression via a different route and for different underlying reasons. He could have done so even if Lorentz had never delevoped his contraction formula.

So no, length contraction does not form the "bedrock" of Relativity

 

The observer's inertial 'rest' frame. Coordinates and time only change in frames moving relative to this absolute frame of reference, according to relativity.

 

*shrug*

Hey, when you toss a sloppy word salad it reflects badly on you, not me.

Good god you're a moron. If you'd ever actually read the paper you refer to above you would see that Einstein did not assume length contraction. He derived it, just like I said he did.

I confided no such thing. Double your dosage and get a grip.

"Ooga Booga" to you too, sir.

 

But the absolute value didn't go anywhere. All you did was give it a different coordinate representation. If you were given the gravitational force and the masses, you would calculate the same distance between the objects using either system of coordinates. This is not the case with spatial and temporal intervals in relativity. No matter how you write the Lorentz transforms you will predict that spatial and temporal intervals will not be Lorentz invariant.

Why not just start from the equations of relativity? Then you'll see that the invariants are not the ones you would expect, but are rather quantities such as the speed of light, proper time, etc.

It's certainly true that a preferred frame of reference is not ruled out a priori. But then again, physicists don't reject it a priori either. They reject it because no experiment ever performed has detected such a preferred frame.

I already addressed this: There are Lorentz invariants in Special Relativity. They just aren't the ones you would expect from Galilean Relativity.

I'm going to pass on that. I've tried explaining to you before why the postulates of SR are considered necessary, and I've tried referring you to literature that explains it, including Einstein's original paper. I think that any further attempt would be a waste of time on my part. When you have shown that you have made a serious attempt to learn relativity, then we will have something to talk about here.

The speed of light "in an object"? I'm not sure of what that is, but the speed of light from moving sources has been measured.

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

It isn't important for the scientific community to prove anything to crackpots. Questions on the validity (and the limits of validity) of Special Relativity have long since been answered rigorously and satisfactorily by people who understand the larger picture in physics. Physicists don't need to disprove the ad hoc idea that gravitational fields somehow affect the speed of light. None of the research that has ever been done in either electromagnetism or gravitation suggests that such a coupling between the two interactions exists. On the other hand, GR does predict a certain coupling between light and gravity, and those predictions have passed the experimental test with flying colors. Consequently, that is a connection between light and gravity that is worth investigating. That's the difference between a good theory and a vague, ad hoc conjecture.

If crackpots don't get it, then they don't get it. There's certainly no reason for the people who do get it to take the time out to prove something that is already established. This is especially the case when the crackpots who are clamoring for proof steadfastly refuse to lift a finger to educate themselves, but rather expect everything to be spoon fed to them. Their opinion simply doesn't count.

He wasn't sure. He made that perfectly clear in between the time that he proposed Special Relativity and the first experimental confirmations. But he proposed it because it accounted for all of the experimental evidence at the time.

Also, frame dragging is a prediction of General Relativity. No one would expect the predictions of Special Relativity to hold when effects that are uniquely GR-like are manifest.

You can believe whatever you want, of course. But all you ever seem to do is make up your own answers to the questions you raise, so it's not surprising in the least that your beliefs don't match reality. There's no need to guess at why Einstein postulated SR, all you have to do is read his papers.

 

Truth.

More than that, there are good reasons for the people who do get it NOT to take the time to engage in these debates. By now it should be clear that the anti-relativity crackpots are not out to learn anything, but rather to create the illusion that there is some kind of legitimate scientific dissent about relativity by baiting knowledgable people into arguing as if there were.

 

Do you really want to get into all of this again?

There are an infinite number of inertial frames in which any given inertially-travelling object is at rest. These can be derived from one another by arbitrary translations and rotations. The object will remain at rest as long as no boost is applied. Which of these infinite number of coordinate systems is the "absolute" one?

All of that is largely irrelevant to my question to Prosoothus. I am simply asking him if there is any physical phenomenon where the absolute position does not "drop out" as it does for gravity.

-Dale

 

TomTom:

Whether or not you said that you did not understand how the length contraction progressed is of lesser importance than the matter of whether you DO understand, as a bona fide Relativy expert and prophet, how the contraction progresses, according to Einstein Relativy.

Why don't you explain to us, in this thread having some vague relation to length contraction, how a "real smart fellow" who is a self acclaimed Relativy expert, describes the progress of the length contraction in an accelerating body, according to Special Relativity?

As for length contraction not being relevant to Relativy, why don't you also explain to us antirelativy fools how MM, 1880s, and the Einstein derivation of gamma is completely independent of contraction?

 

You use the light clock thought experiment to work out gamma and time dilation (at least that's how its introduced in highschool textbooks), then you work out the lenght contraction and miraculously end up with the same gamma.

Actually I'm not sure why it can't be done differently: Assume that the length is not contracted (or even stretched by some factor), and work out how much time dilation, width stretching, and the magnitude of the relativity of simultaneity effects you need to keep c invariant. This gives an infinite number of possible transforms. I suppose there's only one that's consistent with electromagnetism, though.

 

Given relative velocity of 0.866c, gamma = 2.0000

Distance.

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1..........................................................................P2
A's Frame:0......1......2......3......4......5......6......7......8......9......10
B's Frame:0..............1..............2.............3..............4...............5

Clock Ticks:
A's Frame:0......1......2......3......4......5......6......7......8......9......10
B's Frame:0..............1..............2.............3..............4...............5

Ticks & Distance:
A's Frame:0......1......2......3......4......5......6......7......8......9......10
B's Frame:0......1......2......3......4......5

Ticks/Distance:
A's Frame:0......1......1......1......1......1......1......1......1......1.......1
B's Frame:0......1......1......1......1......1

Clocks are not dilated. Tick rates MUST be the same if you declare spatial contraction.

Likewise if you declare time dilation (tick rate differentials) then distance MUST remain the same.

The interesting feature is that even though clocks remain synchronized tick/tick (no time dilation) at the end of the trip from P1 to P2, B has accumulated less time and is hence younger.

A seemingly physical inconsistanty. On the other hand if you consider that the dilated tick rate of a clock fully accounts for the accumulated time on the clock then there is no room for spatial contraction.

The result is that the moving observer would calculate a higher velocity. If velocity is frame dependant the inconsistancy vanishes. If you mark the course between P1 and P2 by meter markers the moving oberver sees those markers passing by a twice the rate because his clock is ticking only half as fast.

While we have a natural reaction to think that relative velocity MUST be equal it must be remembered that time and distance are physical quantities and velocity is a calculated value of the ratio d/t.

That is what we see is also frame dependant and the thought that velocity is the same in both frames simply does not take into consideration the fact that the moving frame clock (thought process and vision responses) would be slower making it appear things were passing by faster with distance the same but with time dilated.

 

DaleSpam,

Me, and other anti-relativists, believe that the speed of light is tied directly, or indirectly, to gravitational fields. So the speed of light in an inertial frame of reference is not a relative value that is tied to the observer, but is an absolute value that is tied to local gravitational fields. I'm also considering whether magnetic fields are tied to gravitional fields as well. I'm not sure yet because I don't have enough information, but I'm leaning towards the assumption that the strength of the magnetic field created by a moving charge is related to its motion through a gravitational field, and not to it's relative motion to an observer.

 

Tom2,

So let me see, no experiment was ever performed that detected a preferred frame, and that type of experiment will never be performed because the scientific community wouldn't want to prove anything to crackpots. How convenient for the status quo.

I'm suggesting that the speed of light is only equal to c relative to the gravitational field that it is moving through. So if you have a detector that is stationairy in a gravitational field (like on the surface of the Earth), it will always measure the speed of light to be equal to c regardless of whether the light was emitted by a stationairy or a moving source. Only if the detector itself is moving relative to the gravitational field will a change in the speed of light be detected.

Quoted by me:

“Even Einstein suggested that the Earth is dragging spacetime around. How was he so sure that the speed of light was not only equal to c relative to this moving spacetime and nothing else?"

So are you claiming that Einstein proved that the speed of light is not tied to spacetime, or that he just abandoned the idea because he liked Special Relativity better?

 

No, Prosoothus, I didn't say that the experiment you suggested will never be done. I said that I don't know what the speed of light "in an object" is, then I gave you a list of expeirments that have been done. How you arrived at me saying that some experiment will never be done, I do not know.

Yes, that's exactly how scientists decide what research programs to follow. They dilligently look through all the crackpot websites and discussion forums, and they scratch all the experiments that will prove the crackpots right off their list. That way the staus quo gets preserved, and everyone keeps their cushy job.

How deluded.

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I've already responded to this more than once. I don't feel the need to do it again.

http://www.sciforums.com/showthread.php?t=31035

edited to add:

Here's the most relevant text from that thread. It explains that a common piece of everyday technology works because of the principle that there is no difference between the motion of a source and the reciprocal motion of a detector.

Moving on...

No, I'm saying that he had doubts about the veracity of SR until it was confirmed.

 

CANGAS old buddy! I wasn't expecting you to have gotten your foot out of your mouth so soon. It was in there pretty deep!

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Of course it's important that the record be straight on what I said and didn't say. As for me passing your little test, that is not important at all.

I didn't say that I am a "Relativity expert".

No. You aren't going to lead me around by the nose by putting words in my mouth, and then calling me out to answer every claim that you imagined I made. This could go on forever, and it would be a waste of my time. Besides, you said that the mathematical analysis is "simpler than dirt", from which I infer that you already think you know how to do it. No need to pretend that you're actually interested in having a dialog by asking me then.

Again, you are putting words into my mouth. I said that length contraction is not the bedrock of SR. It is a consequence of it. I never used the word "relevant".

No. Read the paper On the Electrodynamics of Moving Bodies, and you can see for yourself how the Lorentz transforms were derived without invoking length contraction.

Here's the paper:
http://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf

See, if you read the paper, one of two things will happen. One, you could understand it, in which case this silly line of questioning will end. Or two, you could either not get it or ignore it, in which case I would expect that you would have done the same with anything I wrote. But at least if you read it yourself then it's your time that's wasted instead of mine, which is a far better thing.

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A question about length contraction from another perspective:

Assume you had a rod made out of unobtainium (unobtainium being perfectly rigid and non-compressable) that was one light year long. No assume an observer one light year away standing equidistant from either end of the rod. If one were to apply a force to one end of the rod along the direction of its length, how long would it take to see the other end move?

I assume that if the rod was perfectly rigid, the minimum amount of time it would take for the other end to move would be 1 year, and if the observer measured the length of the rod (from his vantage point, knowing his distance from the rod) during the interim period, he would measure the rod be shorter?

 

If your unobtanium rod was perfectly rigid, the other end would move instantly, but there's no such thing as an a perfectly rigid rod. I don't think its even theoretically possible. All rods have to be compressible enough such that the other end will move at least 1 year later, but this compression is not the length contraction in relativity.