Miscellaneous Science Questions

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby speising » Tue Mar 31, 2015 9:12 pm UTC

doogly wrote:2) A light ray is a straight line, not a wiggle through space, so there isn't really anything exactly equivalent.

Is that true, though? What about diffraction, double slit and all the other wavey stuff then, how does that work?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Sizik » Tue Mar 31, 2015 9:14 pm UTC

speising wrote:
doogly wrote:2) A light ray is a straight line, not a wiggle through space, so there isn't really anything exactly equivalent.

Is that true, though? What about diffraction, double slit and all the other wavey stuff then, how does that work?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby thoughtfully » Wed Apr 01, 2015 1:32 am UTC

speising wrote:
doogly wrote:2) A light ray is a straight line, not a wiggle through space, so there isn't really anything exactly equivalent.

Is that true, though? What about diffraction, double slit and all the other wavey stuff then, how does that work?

Gravity's special. Certainly when in the famework of General Relativity. That other stuff happens in the context of forces/interactions.

"In free space", light travels in straight lines. It's just that in a 3+1 spacetime, straight is defined as the geodesic, which can seem warped depending on your vantage point in the "just space" part.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Wed Apr 01, 2015 1:44 am UTC

Another thing that helps - light isn't like a wave on a string or the surface of water, where the unit of amplitude would be length - a height of wave.

It's more like a compression wave.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yomcat » Wed Apr 01, 2015 1:32 pm UTC

doogly wrote:Another thing that helps - light isn't like a wave on a string or the surface of water, where the unit of amplitude would be length - a height of wave.

It's more like a compression wave.


It appears most of us are being mislead in these introductory textbooks, online introductions, etc, where every depiction of the electromagnetic spectrum is always stringy

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Wed Apr 01, 2015 1:40 pm UTC

Yes, those suck.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yomcat » Wed Apr 01, 2015 1:48 pm UTC

doogly wrote:1) There's no such thing as slowing down in an absolute sense. What you mean is are they slowed down relative to some other clock. Here, we do see an effect relative to a clock left on the surface --- on the surface, there is gravity! And really, what you want to look at is not gravitational force, but the gravitational potential. If you go down in gravitational potential, the clock frequency goes up.


Looking at gravitational potential and not force seems to be getting away from Einstein's original thought experiment where there isn't a difference between force of gravity and force of acceleration. In most cases potential would be proportional to force, but not inside the mass. From my understanding, gravitational potential is only used after you solve some metric tensor/stress energy/ whatever type stuff for outside the mass (like Swarcheild solution). And even in solving those field equations, there had to be some rounding. So is gravitational potential still a valid indicator for inside the mass?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Wed Apr 01, 2015 1:57 pm UTC

Potential's not proportional to force. You use calculus, not fractions, to go between them.
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Re: Equivalence of Inertial Reference Frames valid?

Postby DR6 » Wed Apr 01, 2015 3:27 pm UTC

yomcat wrote: Does that not contradict the velocity of light not being additive? If I am in a train traveling near light speed (assume the train has a vacuum inside so light is not slowed down), and I aim a flashlight against the opposite wall perpendicular to the motion of the train, shouldn't the light take a path that is strange to me because the velocity of the train is not added to it? Like if 2 rockets are traveling parallel to each other near light speed and one rocket shoots a laser at the other, you wouldn't expect the laser beam to hit the other rocket because the beam wouldn't have the velocity from the rocket. That situation shouldn't change by connecting the rockets with a long tube thereby making them the same reference frame and then shining the light.


No, it doesn't, because the direction the light beam was shot in depends on the reference frame, and due to time dilation the light beam is still traveling at c even if it travels different distances.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Wed Apr 01, 2015 3:35 pm UTC

Right, the direction changes, thus the distance it travels changes, and the time it takes also changes, but the result of all these is that the speed stays constant.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Spinachina » Wed Apr 01, 2015 8:12 pm UTC

I have a basic question about the relativity of time and space. If you walk a 100 metres, it takes more time than if you run the 100 metres. Is this because when you move faster in space (running), you move less in time?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yomcat » Wed Apr 01, 2015 10:25 pm UTC

doogly wrote:Potential's not proportional to force. You use calculus, not fractions, to go between them.


I used the wrong term. You are right. That sentence did not really help me set up my question anyway. So pretend it wasnt there, and I am going to edit it out so someone else doesn't get on me either.

edit: on further thought, I didn't use the wrong term. I just meant a different defintion. I meant the common non mathematical definition. Force of gravity and gravitational potential correspond well, closely related, etc.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Thu Apr 02, 2015 1:51 am UTC

Spinachina wrote:I have a basic question about the relativity of time and space. If you walk a 100 metres, it takes more time than if you run the 100 metres. Is this because when you move faster in space (running), you move less in time?

Not really. It takes longer because you are moving more slowly. Relativity has no significant effect at those scales. I don't think "moving through time" has a clear meaning. Motion refers to a change in position over time.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Qaanol » Thu Apr 02, 2015 6:22 am UTC

Eebster the Great wrote:I don't think "moving through time" has a clear meaning.

Sure it does, that’s the whole point about clocks at different velocities (or gravitational potentials) after all. We may not be able to say in an absolute sense how rapidly your clock is advancing, anymore than we can say in an absolute sense how fast you are moving through space, but we can certainly measure both things relative to any particular observer.

And observers that are stationary relative to the fixed stars (and/or the CMBR) and distant from any massive objects, tend to agree pretty well with each other about how far things have moved and how much time has elapsed. (Or at least we assume they do, not having had many stellar opportunities to travel to such places ourselves.)
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Thu Apr 02, 2015 6:57 am UTC

I mean, you can talk about the rate time advances for one observer relative to another, so if you want to call the ratio of change in time to change in proper time "motion through time," I guess it works. I usually think of motion as involving a change in position pretty much by definition.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yomcat » Thu Apr 02, 2015 2:11 pm UTC

DR6 wrote:No, it doesn't, because the direction the light beam was shot in depends on the reference frame, and due to time dilation the light beam is still traveling at c even if it travels different distances.


Eebster the Great wrote:Right, the direction changes, thus the distance it travels changes, and the time it takes also changes, but the result of all these is that the speed stays constant.


I was assuming the speed of light stayed the same. That was why I questioned the second axiom/postulate/whatever of special relativity. There are many ways of stating the second postulate. One is that you cant tell the speed of a moving reference frame that you are in. From those two axioms, we get time dialation. So you cant use time dialation to prove the axiom.
I am trying to think about it from the beginning when Einstein was first thinking about it before he came up with time dialation. When it was introduced to me in a book, there was a train moving close to the speed of light. A light was shot from the floor at a mirror on the ceiling. It came back exactrly where it was shot from. The outside observer would have seen the light travel faster than the speed of light. So from there, Einstein rederived the Lorenz transformation and got time dialation out of it.
What I am saying is that the scenario where the light returned exactly where it was shot from does not seem plausible. For that to happen, the sideways velocity of the train would have been added to it. What should have happened is the fast moving train would have traveled a little before the light reached the other side and the light would have hit behind a little bit.

And yes we have done many tests to validate the relativity theories. But that doesnt mean there are not other explanations. I don't have access to the data of the experiments and am not familiar with the physics do do anything with the data if I had it.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yomcat » Thu Apr 02, 2015 2:18 pm UTC

Does anybody have any of the data to gravitational lensing observations/studies. Specifically I am wondering if the photosphere/chromosphere/sun's atmosphere/whatever was taken into consideration? I am thinking how light bends when it hits the earth's atmosphere because of the index of refraction of air. Was there a calculation of how much the sun's atmosphere would have bent the light and then subtracted out of the final result?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Quizatzhaderac » Thu Apr 02, 2015 2:47 pm UTC

Spinachina wrote:I have a basic question about the relativity of time and space. If you walk a 100 metres, it takes more time than if you run the 100 metres. Is this because when you move faster in space (running), you move less in time?
In relativity, "time" is broken down into two concepts.

Coordinate time: The amount of time that passes according to the "objective" external observer. For instance measuring the distance and speed of a runner using external clocks
Proper time: The subjective time that passes according to the moving object. For instance a watch carried by the runner.

Walking 1 m/s, it takes exactly 100 seconds of coordinate time to travel 100 meters. Running at 3 m/s it takes exactly 33.3...coordinate seconds to travel the same distance.
Walking 1 m/s, it takes slightly less than 100 seconds of proper time to travel 100 meters. Running at 3 m/s it takes slightly less that a third of the proper time to it took to walk that distance.

General, why people talk about something moving quicker or slower though time, they're referring to the ratio of proper time to coordinate time. One reason people tend to do this is that this "speed" plus (well, Pythagorean summed) with your spatial velocities always equals c.

Just as there is a coordinate and proper time, there are also coordinate and proper velocities (I was using coordinate velocity above). Coordinate velocity nicely relates the positions and coordinate time of objects, and is capped at c. Properly velocity nicely relates to the momentum, kinetic energy, and proper time of the object, and it can go arbitrarily high.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby speising » Thu Apr 02, 2015 3:13 pm UTC

yomcat wrote:A light was shot from the floor at a mirror on the ceiling. It came back exactrly where it was shot from. The outside observer would have seen the light travel faster than the speed of light. So from there, Einstein rederived the Lorenz transformation and got time dialation out of it.
What I am saying is that the scenario where the light returned exactly where it was shot from does not seem plausible. For that to happen, the sideways velocity of the train would have been added to it. What should have happened is the fast moving train would have traveled a little before the light reached the other side and the light would have hit behind a little bit.

from the train's frame, there is no sideways motion, so all works fine. from an outside observer, the train is a bit shorter, and it's time is running a bit slower ("time dilation"), so even though the beam is seen as travelling a farther distance, it has more time to do so on the *observer's* clock, so, again, all works out to the correct speed of c.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yomcat » Thu Apr 02, 2015 4:51 pm UTC

speising wrote:from the train's frame, there is no sideways motion, so all works fine.

That is the concept I have been trying to question all along. Is there really no sideways motion? The reason why Newton thought that is because velocities of every object in the frame is additive to the frame itself so the frames velocity doesnt matter for stuff happening inside the frame. The main thing I am asking: is all that still a valid assumption for light when we specifically know that light's velocity is not additive.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Thu Apr 02, 2015 4:56 pm UTC

In the rest frame of the train, there's no relativity at all, Galilean or Lorentzian. The rest frame is where everything is super simple.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yomcat » Thu Apr 02, 2015 5:30 pm UTC

doogly wrote:In the rest frame of the train, there's no relativity at all, Galilean or Lorentzian. The rest frame is where everything is super simple.


I guess one of the implications of my line of questioning the reference frame thing is there might be an absolute rest frame, albeit really hard to figure out where. And that you cant call a moving frame a rest frame. If this is the case, you could measure how fast your local reference frame is traveling by using the fact the the speed of light is constant. At slow speeds this would be really hard, but at speeds close to the speed of light, you could just shine a light, mark where it hits, and do some trigonometry. If you knew the direction of travel but didn't know the speed you would only have to shine it once. But if you didn't know the direction you would have to shine it 3 times (once along some x, y, and z axis).

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby speising » Thu Apr 02, 2015 5:45 pm UTC

Yeah, no. The whole reason it's called "relativity" is that there is no priviledged frame. If you say "the reference frame is moving", you immediately have to answer "in relation to what?"

As you have intuited, if you have an absolute reference frame, the whole relativity arithmetic just doesn't work any more.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby firechicago » Thu Apr 02, 2015 5:51 pm UTC

yomcat wrote:I guess one of the implications of my line of questioning the reference frame thing is there might be an absolute rest frame, albeit really hard to figure out where. And that you cant call a moving frame a rest frame. If this is the case, you could measure how fast your local reference frame is traveling by using the fact the the speed of light is constant. At slow speeds this would be really hard, but at speeds close to the speed of light, you could just shine a light, mark where it hits, and do some trigonometry. If you knew the direction of travel but didn't know the speed you would only have to shine it once. But if you didn't know the direction you would have to shine it 3 times (once along some x, y, and z axis).


This experiment was first done by Michelson and Morley in 1887, and has been repeated with increasingly sensitive equipment many times since. I suppose you could argue that the universal reference frame just happens to be precisely aligned with the motion of the surface of the earth, but that seems like some very special pleading (not to mention contradicted by measurements from satellites which move in a different reference frame).

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby FancyHat » Thu Apr 02, 2015 6:07 pm UTC

yomcat wrote:I guess one of the implications of my line of questioning the reference frame thing is there might be an absolute rest frame, albeit really hard to figure out where. And that you cant call a moving frame a rest frame. If this is the case, you could measure how fast your local reference frame is traveling by using the fact the the speed of light is constant.

This reminds me of the Michelson-Morley experiment, though that worked differently to what you're imagining.

Suppose, in a very fast train travelling at (cos 30°)c (c being the limiting speed of the universe, the speed of light in a vacuum), which is about 0.866 c (since cos 30° is about 0.866), someone sends a flash of light from one side of the train to the other.

In the rest frame of the train, the flash of light travels along a path perpendicular to the length of the train and the railway track. If the train is two yards wide, it takes just about 6 ns to travel that distance. (Conveniently, light takes just about 1 ns to travel one foot.) The track and the ground are whizzing past at about 0.866 c.

In the rest frame of the track, the train is whizzing along at about 0.866 c. The flash of light travels from one side of the train to the other, but also along the track. The angle between the path of the light and the track is 30°. It travels four yards, taking 12 ns to reach the other size of the train. By that time, the train has moved about 3.4 yards along the track. The flash of light has also moved about 3.4 yards along the track, and two yards across it, so it reaches the part of the train that was originally directly opposite the source of that light.

You can check this with basic trigonometry. Relative to the track, the light travels along the hypotenuse of a right-angle triangle, where the hypotenuse is twice the length of the shortest side, and the smallest angle is 30°.

Relative to the track, clocks travelling on the train will be running at half speed, taking two seconds to count each second. This is consistent with passengers on the train measuring the speed of light to be c when making those measurements and doing those calculations in the train's rest frame.

There is no way to detect absolute motion, or absolute rest, this way.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yomcat » Thu Apr 02, 2015 6:20 pm UTC

speising wrote:Yeah, no. The whole reason it's called "relativity" is that there is no priviledged frame. If you say "the reference frame is moving", you immediately have to answer "in relation to what?"

As you have intuited, if you have an absolute reference frame, the whole relativity arithmetic just doesn't work any more.



The word "priviledged" invokes ideas of geocentrism and a flat earth. That is probably why nobody questions it. But there might be an absolute reference frame or priviledged or whatever you want to call it. So the "in relation to what" would be that absolute privilidged frame. And that little light shine experiment immediately above would tell you how fast and in what direction you were moving. And my assumption with that is that the speed of light is constant relative to that "priviledged frame".

And what are the consequences of the relativity arithmetic not working any more? That's why I suggested a couple posts above that there might be other explanations for things. The answers that I seem to be getting all are along of the lines that it violates special relativity. But if I am questioning one of the assumptions that went into relativity, then that is already a given.

speising wrote:Relative to the track, clocks travelling on the train will be running at half speed, taking two seconds to count each second. This is consistent with passengers on the train measuring the speed of light to be c when making those measurements and doing those calculations in the train's rest frame.

There is no way to detect absolute motion, or absolute rest, this way.


It is true that you couldn't detect the absolute frame if time dialation is true, which is true if special relativity is true, which is true if there are not absolute rest frames. But if there is an absolute rest frame, then special relativity is untrue, and time dialation is untrue, and therefore you should be able to detect it.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby speising » Thu Apr 02, 2015 6:25 pm UTC

Why do you think Einstein came up with relativity in the first place? Because the Michelson Morley experiment failed to show any deviation.
It's a theory, not a hypothesis, meaning that it fits with observations and its predictions have been observed, too.
There is no "assumtion" to question. Relativity is based on empirical fact.
When people say "it would violate special relativity" that is not out of respect for Einstein, but because anything that violates relativity violates what we can observe of the universe.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yomcat » Thu Apr 02, 2015 6:52 pm UTC

speising wrote:Why do you think Einstein came up with relativity in the first place? Because the Michelson Morley experiment failed to show any deviation.
It's a theory, not a hypothesis, meaning that it fits with observations and its predictions have been observed, too.
There is no "assumtion" to question. Relativity is based on empirical fact.
When people say "it would violate special relativity" that is not out of respect for Einstein, but because anything that violates relativity violates what we can observe of the universe.


At first I thought the Michelson Morely experiment only showed velocity of light didn't matter the source. I looked at the experiement again and see why it is used to also show no absolute reference frame. It is very similar to what I was proposing with my x axis y axis crap. But looking at that experiment ( and there might be a more modern version that doesn't have this problem) it compared the time for light to go to a mirror and bounce back with the time it took for light to go perendicular and bounce back. If there was some speed lost/gained on the way down the leg that was parralel to the earth's rotation, it would gain/lose it on the way back cancelling it out. That is my initiial thoughts as I look at that experiment from that line of thinking. I will look at it again to see if I am understanding the experiment differently. And I will look for a more modern experiment.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby gmalivuk » Thu Apr 02, 2015 7:07 pm UTC

yomcat wrote:If there was some speed lost/gained on the way down the leg that was parralel to the earth's rotation, it would gain/lose it on the way back cancelling it out.
No, it wouldn't, because speed is averaged over time, not distance.

If you go 10m at 11m/s and then come back at 9m/s, your will have gone 20m in (10/11 + 10/9) seconds, for an average speed of 9.9m/s. Meanwhile the perpendicular path will be 20m in 2 seconds for an average speed of 10m/s.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby FancyHat » Thu Apr 02, 2015 7:22 pm UTC

yomcat wrote:If there was some speed lost/gained on the way down the leg that was parralel to the earth's rotation, it would gain/lose it on the way back cancelling it out. That is my initiial thoughts as I look at that experiment from that line of thinking.

Such things were taken into account over a century ago. You're really not coming up with anything new here. Not by a long way. It's all been thought of before and worked through thoroughly. And, as gmalivuk points out, the differences in speeds wouldn't fully cancel out.

It turns out that length contraction is part of how absolute motion would be undetectable. There's also relativity of simultaneity, as well. Two clocks can be synchronized in one reference frame while being out of sync in others.

You might find the concept of a 'light clock' helpful. It's two, parallel mirrors, facing each other, with a pulse of light bouncing between them. Each time the light bounces off one mirror, it's a 'tick', and each time it bounces off the other mirror, it's a 'tock'. The frequency of that clock - the rate at which it 'tick-tocks' - is determined by the distance between the mirrors and the motion of the clock. In the clock's rest frame, it's simply the distance between the mirrors and the speed of light that determine its frequency. Otherwise, you need to do a bit of maths to work it out.

If, in some reference frame, the clock is moving in a direction parallel to the mirrors, the pulse of light will trace out a zig-zag pattern between the moving mirrors. But the distance between the mirrors will be the same as in the clock's rest frame. A simple bit of trigonometry is enough to derive time dilation from this.

If, in some other reference frame, the clock is moving in a direction perpendicular to the mirrors, and parallel to the path the pulse of light follows back and forth between the mirrors, the distance between the mirrors has to be contracted so that the clock's frequency is what it should be for the amount of time dilation there will be at that speed. And by taking into account the difference in times and distances from 'ticks' to 'tocks' and from 'tocks' to 'ticks', relativity of simultaneity can also be established.

When you do all that, what you find is that, if Special Relativity is correct (and it agrees amazingly well with much experimental testing), absolute motion would be undetectable. And if absolute motion is perfectly undetectable, then in what real sense would motion even be absolute? It then seems to be a philosophical question, but not a scientific one. If there's no detectable absolute motion, then, in practice, motion is just relative.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yomcat » Thu Apr 02, 2015 8:12 pm UTC

gmalivuk wrote:
yomcat wrote:If there was some speed lost/gained on the way down the leg that was parralel to the earth's rotation, it would gain/lose it on the way back cancelling it out.
No, it wouldn't, because speed is averaged over time, not distance.

If you go 10m at 11m/s and then come back at 9m/s, your will have gone 20m in (10/11 + 10/9) seconds, for an average speed of 9.9m/s. Meanwhile the perpendicular path will be 20m in 2 seconds for an average speed of 10m/s.


That seems to have settled that one as far as I can tell.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby eSOANEM » Thu Apr 02, 2015 8:17 pm UTC

speising wrote:Why do you think Einstein came up with relativity in the first place? Because the Michelson Morley experiment failed to show any deviation.


Nah, Einstein wasn't aware of the Michelson-Morley experiment.

The reason Einstein came up with SR was that Maxwell's EM was not invariant under Galilean transformations but rather Lorentz transformations (which Einstein already knew). Meanwhile, Newtonian mechanics are invariant under Galilean transformations but aren't under Lorentz transformations.

This inconsistency was a major roadblock. SR was one was round it, aether theories were another way (which was discovered earlier). Michelson-Morley was a roadblock for aether theories and not for Maxwell or Newtonian dynamics but one which was also worked around by Lorentz and Poincaré with Lorentz Ether Theory. It was finished a year or so after Einstein published "on the electrodynamics of moving bodies" and so it faded into obsolescence (although it was later proven to produce identical predictions).
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yomcat » Thu Apr 02, 2015 8:23 pm UTC

FancyHat wrote: You're really not coming up with anything new here. Not by a long way. It's all been thought of before and worked through thoroughly. And, as gmalivuk points out, the differences in speeds wouldn't fully cancel out.


I dont think I came across as coming up with anything new. I have had 2 physics classes. I came here with 3 questions and then a 4th one later. 1 of them was immediately answered satisfactorily. Now this one makes 2.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby speising » Thu Apr 02, 2015 9:04 pm UTC

eSOANEM wrote:
speising wrote:Why do you think Einstein came up with relativity in the first place? Because the Michelson Morley experiment failed to show any deviation.


Nah, Einstein wasn't aware of the Michelson-Morley experiment.

The reason Einstein came up with SR was that Maxwell's EM was not invariant under Galilean transformations but rather Lorentz transformations (which Einstein already knew). Meanwhile, Newtonian mechanics are invariant under Galilean transformations but aren't under Lorentz transformations.


Hm, at least the wikipedia says
The inconsistency of Newtonian mechanics with Maxwell’s equations of electromagnetism and the inability to discover Earth's motion through a luminiferous aether led to the development of special relativity
which sounds like M-M to me. Unfortunately, my school physics seems to have taught a rather simplified history.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby eSOANEM » Thu Apr 02, 2015 9:29 pm UTC

Ah, I've misremembered slightly. Einstein was aware of Lorentz's earlier work on LET and the correct Lorentz transformations (which include the γ factor absent in his earlier work but added to agree with MM) so was presumably aware of MM.

That said, my history of physics lectures last year definitely included a quote where he made it very clear that his motivation was solely reconciling the invariances of mechanics and EM (although, the only notes available online are last year's and don't seem to have the quote).
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Fri Apr 03, 2015 12:14 am UTC

SR also has the advantage of unifying the E and B fields into a single tensor.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby eSOANEM » Fri Apr 03, 2015 1:37 am UTC

Oh yeah, looking at the history of the various transformations Lorentz used to arrive at the actual symmetries of Maxwell is painful.

He was only really able to get the first order transformation analytically, after that he just inserted the Lorentz factor because it put predictions in line with Michelson-Morley. It would have been a tremendous achievement to get to the Lorentz transformations from theoretical grounds alone without a tensor formalism.

Once you've got a tensor formalism of course, you just look for something which preserves contractions and that takes you directly to the Lorentz group with no messing around.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby PM 2Ring » Fri Apr 03, 2015 6:48 am UTC

yomcat wrote:
speising wrote:from the train's frame, there is no sideways motion, so all works fine.

That is the concept I have been trying to question all along. Is there really no sideways motion? The reason why Newton thought that is because velocities of every object in the frame is additive to the frame itself so the frames velocity doesnt matter for stuff happening inside the frame. The main thing I am asking: is all that still a valid assumption for light when we specifically know that light's velocity is not additive.


In SR, velocity is not additive for anything, not just light, but for low velocities it's approximately additive. If we use natural units of velocity (so the speed of light is 1), then the SR equation for combining velocities u and v is (u + v) / (1 + uv), so even if u and v are both 0.1 the deviation of SR's true combined velocity from the Newtonian simple additive result is only around 1%.

FWIW, there's another measure of motion called rapidity which is sometimes used. Rapidity of collinear vectors is additive, and it has no upper limit, i.e the rapidity of light is infinite.


eSOANEM wrote:
speising wrote:Why do you think Einstein came up with relativity in the first place? Because the Michelson Morley experiment failed to show any deviation.


Nah, Einstein wasn't aware of the Michelson-Morley experiment.

The reason Einstein came up with SR was that Maxwell's EM was not invariant under Galilean transformations but rather Lorentz transformations (which Einstein already knew). Meanwhile, Newtonian mechanics are invariant under Galilean transformations but aren't under Lorentz transformations.

This inconsistency was a major roadblock. SR was one was round it, aether theories were another way (which was discovered earlier). Michelson-Morley was a roadblock for aether theories and not for Maxwell or Newtonian dynamics but one which was also worked around by Lorentz and Poincaré with Lorentz Ether Theory. It was finished a year or so after Einstein published "on the electrodynamics of moving bodies" and so it faded into obsolescence (although it was later proven to produce identical predictions).


What eSOANEM said. IIRC, according to Pais in Subtle is the Lord Einstein was not concerned about Michelson-Morley when he developed SR, but the fact that SR neatly explains M-M was a handy validation of SR.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Kozmo » Sat Apr 04, 2015 8:42 am UTC

Just noticed this recent discussion, I don't think I have anything particular to add to it, but it's quite in line with something I just wrote a few days back. It's a blog post about where relativity came from, and what it is in its essence. It's basic stuff, but might be interesting for people with not much experience in it. Also, I see lots of people here are quite knowledgeable, should they read and disagree with something, I'd be happy to discuss. Link is in my signature below.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby jewish_scientist » Tue Apr 14, 2015 6:59 pm UTC

Let's imagine that you have 2 invincible atomic clocks that are perfectly synchronized. The first, C1, you lock in a vault; the second, C2, you throw into a super-hot furnace. After a while passes, you compare the 2 clocks. Would the clocks still be synchronized?

Think about this. Every particle of the C2 was heated to a very high temperature, meaning that they are vibrating very fast. I am talking about relativistic speeds. Because every individual particle is moving so fast, every individual particle ages slower (is that the right way to say that) from our point of view. The clock as a whole is not moving, so it ages at the same rate as us from our point of view. So are the 2 clock still synchronized?
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