Putting numbers in Einstein's thought problem

[JesseM]

When the moving frame is a train car, a boat, or any other means of transportation it seem very odd to pretend that the observer aboard has no means of detecting which one is moving. His very reason for being there automatically tells him what should be moving. He'll demand his money back if he doesn't move.

He is moving relative to the ground of course, but in his inertial rest frame, this is because the train-carriage is at rest while the ground is moving past it. The first postulate of relativity says that the basic laws of physics work the same way (obey the same equations) in all inertial frames, so there is no way to tell whether you are moving in an absolute sense, as opposed to just moving in relation to some other body. The first postulate demands that if the train-carriage is completely sealed off from the outside world so the observer inside can't determine his motion relative to anything outside it, then as long as the carriage is not accelerating, there is no experiment that can be done inside the carriage that will have different results depending on whether the carriage is at rest relative to the ground or in motion relative to the ground.

If light behaved the way you want it to, this basic postulate of relativity would be violated. Suppose there is a laser hanging straight down from the ceiling of the carriage, and a spot has been painted on the floor of the carriage directly under the laser. Your claim is that in the frame of the embankment, the beam will always go straight down, regardless of the motion of the carriage relative to the embankment. So obviously if the carriage is at rest relative to the embankment, you claim that the laser beam will hit the floor right where the spot on the floor is painted. But your claim also implies that, if the carriage is in motion relative to the ground, the laser beam will not hit that spot on the floor, since by the time the photons have traveled from the laser to the floor, in the embankment frame the spot will have traveled forward slightly along with the entire carriage. So, if these photons are still traveling straight down from the laser in the embankment frame, they won't hit exactly the point of the spot on the floor, according to your theory. This means that even if the carriage was completely sealed off from the outside world so the observer on board couldn't tell if he was moving relative to the embankment by looking out a window, he could still perform an experiment inside the carriage to determine whether he was moving or not, by hanging a laser straight down from the ceiling and seeing if it hit the ground at a spot directly below the laser. This also implies that the embankment frame is a preferred frame, since it's the only frame where photons from a laser hanging vertically from the ceiling will always hit the a point on the ground directly below the laser.

I never denied that light moved in "straight line paths", I just said that the angle of the straight line path relative to the angle of the source (assuming the source is an object that points in one particular direction, like a flashlight or laser pointer) as seen in a given frame will depend on the velocity of the source in that frame. If you are claiming that a laser beam will always come out parallel to the angle of a laser pointer in the ground frame, regardless of the velocity of the laser pointer in this frame, then you are simply wrong, and you'd be implying that the ground frame is a preferred frame (because if that were true, we could look at the same laser and laser pointer from the perspective of another frame like the carriage frame, and it would not be true that the laser always comes out parallel to the angle of the laser pointer in this other frame).

So let me get this straight; you believe that the light takes two different paths. One that is parallel to the laser pointer for the guy on the train and one that is propagated at an angle to the pointer for the one on the embankment.

What do you mean by "different paths"? All observers will agree about localized facts about the path of the photons, like what part of the floor of the carriage is struck by the laser. But they will represent the path differently in their different coordinate systems. The path of any slower-than-light object looks different in different coordinate systems, do you disagree? If not, why should light be any different?

My contention is that it only points straight down if the pointer is pointed straight down. The reason the guy traveling with the source sees it differently is a matter of perception created by his extream speed.

But in relativity "speed" is relative rather than absolute, that's why the call it relativity! In one frame the ground is at rest while the carriage is moving forward with extreme speed, but in another frame the carriage is at rest while the ground is moving backward with extreme speed. The whole point of the first postulate of SR is that there is nothing in the basic laws of physics to distinguish these two frames. If there was an absolute truth about which had the greater speed, then that would imply the Newtonian idea of absolute space and time which relativity rejects.

Your thoughts about math and theorums are of course correct from a purely mathematic point of view but the Lorentz Transformations are meaningless unless they are considered in relation to the real physical world they are said to depict.

So do you admit that "from a purely mathematic point of view" there is no doubt that the Lorentz transformation follows logically from the two postulates of SR?

I admit nothing of the kind. What I meant was that there are no purely mathematical contradicitions to be found in the Transformations, they are mathematically consistent and not mathematically contridictory.

But the question is whether they follow from the two postulates of relativity. And the answer to this question is a purely theoretical one, we are asking what mathematical consequences follow if we take the two postulates as starting axioms, regardless of whether those postulates happen to be true in the real world. Do you disagree that in math, determining the logical consequences of axioms has nothing to do with whether the axioms are true in real-world physics? If you disagree with that, then you misunderstand something basic about what mathematicians are doing when they prove theorems. And if you don't disagree with that, then what I'm trying to say is that the question of whether the Lorentz-symmetry of the laws of physics follows from the two postulates is the same sort of question, the answer has nothing to do with any empirical observations about reality. Of course, even if one agrees that Lorentz-symmetry follows from the two postulates, there is then the separate question of whether Lorentz-symmetry is actually true of the real laws of physics that we observe in the real world--it might not be, since it might turn out that one of the two postulates is violated by real-world physics. But if you can't see that these are two separate questions, the first one purely theoretical and the second one involving empirical considerations, then I think you really are confused. Your statement that "the Lorentz Transformations are meaningless unless they are considered in relation to the real physical world they are said to depict" seemed to conflate the two questions, but I may have misunderstood.

I do not agree that they can be derived from the postulates of special relativity though I am certain that is what Einstein believed he had done back in 1905.

But your comments about the laser, and your apparent notion of an absolute truth about "movement", suggests you don't really understand the meaning of the first postulate of relativity. If you still disagree that the first postulate says the basic laws of physics should be the same in each frame, or if you disagree that a consequence of this is that a person sealed in a non-accelerating windowless box will see the same results for any experiment performed in the box regardless of the box's motion relative to other objects like the ground, I can point you in the direction of books and papers confirming that this is how the first postulate is understood by physicists.

There is no supportable reason to invoke different frames of reference in the first place. Everything in all of these thought problems can be described for both observers using a single set of cartisian co-ordinates, in fact the entire universe and all events within it can be described with one regardless of the relative motions of any of the players.

Of course everything can be described using a single frame, the point is to discover a symmetry in how the laws of physics look when described in different frames, which limits the allowable equations that the laws of physics could obey in any one frame (if you write down a candidate equation for the law governing some phenomenon in one frame, it's a purely mathematical calculation to determine whether this equation is a Lorentz-symmetric one, and relativity says that we should look for equations that have this property of Lorentz-symmetry, which so far has led to a lot of successes like quantum field theories). Besides, the first and second postulate refer directly to multiple frames, so if we're dealing with the theoretical question of what consequences follow from the two postulates, you have to consider multiple frames, even if you don't think there is any "supportable reason" for being interested in this question. The question of the usefulness of a theoretical proof deriving consequences from postulates is separate from the question of whether the proof is logically correct in its derivation of consequences, in much the same way that the question of empirical validity of these postulates & consequences is separate from the question of whether the consequences follow from the postulates. If you aren't willing to distinguish between these different types of questions, your argument becomes an incoherent muddle of different unrelated complaints.

 

[Mentz114]

It is the attachment of significance to them that is faulty and I do not agree that they can be derived from the postulates of special relativity though I am certain that is what Einstein believed he had done back in 1905. That the transformations are totally unnecessary to understand what actually is happening to the light in all of these thought problems is the key to my arguments and the frames of reference are the key to understanding what is wrong with Einstein's logic. There is no supportable reason to invoke different frames of reference in the first place. Everything in all of these thought problems can be described for both observers using a single set of cartisian co-ordinates, in fact the entire universe and all events within it can be described with one regardless of the relative motions of any of the players.

That's patent garbage.
If you mean that, I cordially suggest you go and display your arrogance and spout rubbish somewhere else.
You're the n'th person we've had here telling us that we're all wrong and Einstein even wronger. I'm sure you'll feel more comfortable amongst your fellow crackpots.

 

[DanRay]

[

originally by JesseM;2573421] there is no experiment that can be done inside the carriage that will have different results depending on whether the carriage is at rest relative to the ground or in motion relative to the ground.

What you say is of course what Einstein believed and what he tried to demonstrate in section 3 with the rock toss, but he misunderstood how light would behave in your isolated frame or anywhere else for that matter.

Originally by JesseM

If light behaved the way you want it to, this basic postulate of relativity would be violated. Suppose there is a laser hanging straight down from the ceiling of the carriage, and a spot has been painted on the floor of the carriage directly under the laser. Your claim is that in the frame of the embankment, the beam will always go straight down, regardless of the motion of the carriage relative to the embankment. So obviously if the carriage is at rest relative to the embankment, you claim that the laser beam will hit the floor right where the spot on the floor is painted. But your claim also implies that, if the carriage is in motion relative to the ground, the laser beam will not hit that spot on the floor, since by the time the photons have traveled from the laser to the floor, in the embankment frame the spot will have traveled forward slightly along with the entire carriage. So, if these photons are still traveling straight down from the laser in the embankment frame, they won't hit exactly the point of the spot on the floor, according to your theory. This means that even if the carriage was completely sealed off from the outside world so the observer on board couldn't tell if he was moving relative to the embankment by looking out a window, he could still perform an experiment inside the carriage to determine whether he was moving or not, by hanging a laser straight down from the ceiling and seeing if it hit the ground at a spot directly below the laser. This also implies that the embankment frame is a preferred frame, since it's the only frame where photons from a laser hanging vertically from the ceiling will always hit the a point on the ground directly below the laser.

It is not that light behaves "The way I want it to" it is actually the way light does behave. It is not surprising that Einstein didn't realize this fact. After all most of the scientists of 1905 were still trying to defend the ether concept and in fact that is why Lorentz came up with "Lorentz Contraction" (which was for light, not matter) and the Transformations in the first place. Your description of the light hitting behind the spot is right on, though you don't believe it. What isn't right on is your belief that this somehow violates the first postulate of relativity. If light always travels in straight line paths unless it is bent by gravity how does that violate any frame of reference inertial or otherwise?

Originally by JesseM

What do you mean by "different paths"? All observers will agree about localized facts about the path of the photons, like what part of the floor of the carriage is struck by the laser. But they will represent the path differently in their different coordinate systems. The path of any slower-than-light object looks different in different coordinate systems, do you disagree? If not, why should light be any different?

Light should be different because it is different! Those slower-than-light objects that you mention (much slower; our fastest launch rockets only go about 7 miles per second) all consist of matter and they have mass and momentum in proportion to their mass. That is the moving form of inertia and is what carries the stone forward and causes the passengers to lurch forward or backward depending on acceleration or braking. Light photons (any photons) have no mass and are not subject to that form of inertia and I don't even think you can call their motion at c the same as inertia. As I said before photons always move in straight line paths and take off at c without the need to accelerate. All behaviors of photons are vastly different than any that apply to any matter in any situation.

Originally by JesseM

But your comments about the laser, and your apparent notion of an absolute truth about "movement", suggests you don't really understand the meaning of the first postulate of relativity.

The "absolute truth about movement" for light can be demonstrated by considering the movement of the light from the farthest galaxies imaged by Hubble. Light from a galaxy 12 billion light years away was headed straight for the lens of the telescope at least 7 billion years before the sun even formed and it wasn't anywhere near its present location even when it did form. That light was all headed at c from those galaxies toward the point in space that the sun not yet formed and the Earth not yet imagined would eventually come to occupy so that Hubble could "see" it today. What do you want to imagine that light to be relative to? Was it moving at c relative to the point in empty space that the Hubble Telescope would today occupy?

Originally by JesseM

If you still disagree that the first postulate says the basic laws of physics should be the same in each frame, or if you disagree that a consequence of this is that a person sealed in a non-accelerating windowless box will see the same results for any experiment performed in the box regardless of the box's motion relative to other objects like the ground, I can point you in the direction of books and papers confirming that this is how the first postulate is understood by physicists.

Once again, I don't dissagree with anything the postulates say nor do I think light moving in straight line paths from the point of origin violates the postulates in any way. What your arguments allways do is take perception to be the same thing as the reality. It is not the same thing. No two observers in any situation ever see exactly the same light so there will always be observational differences no matter how slight. The laws of physics for light are not the same as the laws of phisics for matter. That is where our ideas diverge.
You have already pointed out many things to try to teach me the basics of relativity, all the time presuming that there is somthing I'm just not getting. I'll say once again that I understood all of it going in. I could write all of your arguments for you.
There is somthing I have avoided saying because it seems so obvious to me. You can imagine all sorts of inertial reference systems but in actual practice there are none. The trains, the ships, rocket ships; none of them can go very far at all without encountering the curvature of the Earth or a bump or a curve in the track or a swell in the ocean. Light and other photons are in fact the only things we know of that always travel in straight paths. All the star systems we know of all exibit curviliner orbits for everything that orbits. Only photons are different and they behave exactly as I have described. If you contemplate a little longer you will see why neither of Einsteins Postulates are violated and why the Lorentz Transformations are unnessary.

Have a good day, DanRay

 

[Doc Al]

Enough already. Please read the sticky at the top of this forum titled "IMPORTANT! Read before posting".