Putting numbers in Einstein's thought problem

[DanRay]

The thought problem in section 7 of “Relativity” is the beginning of Einstein’s rationale for using his version of Lorentz Transformations. He uses a railroad embankment as one “rigid reference-body (frame)”, and a train car on the tracks moving at a constant speed parallel to the embankment as a second (inertial)“rigid reference body”. He has removed the air above the embankment so his “ray of light” will be propagated in a vacuum. He does this is to demonstrate why simple addition of velocities won’t work the same for the light in this thought problem as it did for a man walking along the railroad car in the same direction as the train’s motion in section 6 of “Relativity” where he demonstrated the “theorem of the addition of velocities” in regard to the speed of the man relative the embankment. (W = v + w)

The question posed by Einstein in his section 7 problem is this: “If a ray of light is sent along the embankment, we see from the above that the tip of the ray will be transmitted with the velocity c relative to the embankment. ---” The unknown of the problem is the speed of the tip of the ray relative to a train carriage moving at speed v (relative to the embankment) in the same direction as the light. He sets up an equation using the standard equation for an addition (or in this case, subtraction) of velocities problem with the resultant velocity w as the unknown: w=c-v.

It is Einstein’s next comment that is the beginning of his justification for using the Lorentz Transformations: “The velocity of propagation of a ray of light with respect to the carriage thus comes out smaller than c.” That of course violates the second postulate of Special Relativity and leads him into his famous statement at the end of this same section. “As a result of an analysis of time and space, it became evident that in reality there is not the least incompatibility between the principle of relativity and the law of propagation of light,----”

And we’re off Galilean/Newtonian Universe out; Time dilation, rod shortening, speed limits and eventually the curving space-time continuum in.

Some time ago I began to wonder what would happen if I put actual numbers into Einstein’s section 7 problem. This is what I found: a light flash begins from a source situated 100 meters away from a point (A) on the embankment at the moment a mirror on the back of the carriage aligns with point A. The carriage is moving 100km/h. It will take the “tip of the ray” 1/3rd of a microsecond (333ns)to reach point A on the embankment but the train will only have moved .00925 millimeter in that time. The “tip of the ray” will cover that extra distance in .030833ns. Obviously these are distances and intervals far too small for human observers to perceive.

But what if the speed of the carriage is 200,000km/sec. (2/3 c). As before the tip of the ray of light will reach point A on the embankment in 1/3rd microsecond in which time the train will have moved a very perceptible 66.6 meters. The light will catch up to the observer on the train in just 1 microsecond from its starting point at a point 200 meters from the observer on the embankment. Though a human observing from Einstein’s omnipotent point of view would clearly see the 200 meter difference, he would not likely be able to perceive a time difference of only 1 microsecond. (Light traveling at c moves 300m/microsecond.). So it would appear to the observer that the light arrived at both the point on the embankment and the mirror on the train 200 meters down the track simultaneously. If the reflected light from the mirror is accurately timed it will be back at the source exactly 2 microseconds from when it began and if you could substitute an accurate measuring device for the mirror it would be measured as exactly c.

I don’t think there is a problem here for either of Einstein’s Special Relativity postulates but for me it puts up a big question mark about the rationale for his use of the Lorentz Transformations and all of the phenomena that derive from. That doesn’t necessarily prove that none of those are true, it just seems to negate Einstein’s pathway to them. The Lorentz Transformations are the only math Einstein used in relation to Special Relativity.

Am I missing something here? Please tell me the flaw in my reasoning.

 

[JesseM]

Some time ago I began to wonder what would happen if I put actual numbers into Einstein’s section 7 problem. This is what I found: a light flash begins from a source situated 100 meters away from a point (A) on the embankment at the moment a mirror on the back of the carriage aligns with it.

The mirror aligns with point A, or the mirror aligns with the source? I assume from the later comments you probably mean that the mirror is aligned with A...

But what if the speed of the carriage is 200,000km/sec. (2/3 c). As before the tip of the ray of light will reach point A on the embankment in 1/3rd microsecond in which time the train will have moved a very perceptible 66.6 meters. The light will catch up to the observer on the train in just 1 microsecond from its starting point at a point 200 meters from the observer on the embankment.

1 microsecond in the embankment frame, yes. But you don't appear to be considering the time it takes the light to go from the source to the back of the train in the train's own rest frame, or the distance the light travels in this time in the train frame, and wasn't that the whole point of Einstein's thought-experiment, to compare the speed of a ray of light in two different frames?

Though a human observing from Einstein’s omnipotent point of view would clearly see the 200 meter difference, he would not likely be able to perceive a time difference of only 1 microsecond.

"Observation" does not literally mean what you see with your unaided eyes, it refers to what you measure using equipment which is at rest in your frame. You're allowed to use cameras and precise clocks and the like.

(Light traveling at c moves 300m/microsecond.). So it would appear to the observer that the light arrived at both the point on the embankment and the mirror on the train 200 meters down the track simultaneously. If the reflected light from the mirror is accurately timed it will be back at the source exactly 2 microseconds from when it began and if you could substitute an accurate measuring device for the mirror it would be measured as exactly c.

Again, you're sort of missing the point of the thought-experiment if you don't figure out what the speed would be when measured by equipment at rest relative to the train. Obviously since you assume in your calculations that the light moves at c in the embankment frame, it's necessarily going to be true that the light takes 1 microsecond to travel 100 + 200 meters to catch up with the back of the train, and another microsecond to travel 300 meters back, since all these measurements are themselves specific to the embankment frame.

 

[DanRay]

1 microsecond in the embankment frame, yes. But you don't appear to be considering the time it takes the light to go from the source to the back of the train in the train's own rest frame, or the distance the light travels in this time in the train frame, and wasn't that the whole point of Einstein's thought-experiment, to compare the speed of a ray of light in two different frames?

"Observation" does not literally mean what you see with your unaided eyes, it refers to what you measure using equipment which is at rest in your frame. You're allowed to use cameras and precise clocks and the like.

Again, you're sort of missing the point of the thought-experiment if you don't figure out what the speed would be when measured by equipment at rest relative to the train. Obviously since you assume in your calculations that the light moves at c in the embankment frame, it's necessarily going to be true that the light takes 1 microsecond to travel 100 + 200 meters to catch up with the back of the train, and another microsecond to travel 300 meters back, since all these measurements are themselves specific to the embankment frame.

Dear Jesse M,
Thanks for your reply. However I must take exception to all that you say. Section 7 of Relativity is Einstein's 1916 explanation of the reasoning path he took to discovering all of the things you are talking about. You are wanting me to accept that Einstein should have used time dilation to prove time dilation. You have to accept that at some point he didn't know what he would discover and if you read Section 7 you will see that the whole point of it and this problem is to explain what led him to use the Lorentz Transformations. Sections 8 through 10 are also part of this reasoning journey. He introduces Lorentz and time and space variations in Section 11. My point about my findings is that there is nothing in this problem that justifys the introduction of the transfprmations in the first place and although I didn't mention it before if you look at the two examples I gave and any others you care to examine the difference that satisfies the addition of velocities problem is always in the different arrival time of the "tip of the ray" first to point A then the carriage.

Simply you can't use a conclusion to prove itself!

And by the way Einsteins observer in this case and I think in all cases in this book is the human mind he doesn't invoke any instrumentation at all.

 

[Ich]

DanRay,

I can't make sense of you first post. As JesseM put it, you seem to be completely missing the point.
Your answer to JesseM also seems to have nothing to do with what he said.
And this is simply wrong:

And by the way Einsteins observer in this case and I think in all cases in this book is the human mind he doesn't invoke any instrumentation at all.

Maybe you can formulate a specific question or claim, which can then be discussed.

 

[yuiop]

Section 7 of Relativity is Einstein's 1916 explanation of the reasoning path he took to discovering all of the things you are talking about. You are wanting me to accept that Einstein should have used time dilation to prove time dilation.

I do not have the book you mention, but I assume Einstein demonstrated time dilation is a consequence of the constant speed of light postulate and the light clock thought experiment before he gets to the train thought experiment. In the latter experiment, he demonstrates that what appears simultaneous to one observer, does not appear simultaneous to anotyhe observer with relative motion to the first observer.

My point about my findings is that there is nothing in this problem that justifys the introduction of the transfprmations in the first place...

The justification is that without the Lorentz transformations the postulates of the constant speed of light and the laws of physics being equal in all inertial reference frames are violated.

 

[DanRay]

DanRay,

I can't make sense of you first post. As JesseM put it, you seem to be completely missing the point.
Your answer to JesseM also seems to have nothing to do with what he said.
And this is simply wrong:


Maybe you can formulate a specific question or claim, which can then be discussed.

Dear Ich,

Thanks for your concern. Everything I put in quotes is from Einsteins 1916 book "Relativity" and the problem I am dealing with is Einstein's own. I simply put numbers in where he had none and kept it true to his original. In this book Einstein is explaining the reasoning he used to develop his Special Relativity conclusions all of which are based on Lorentz Transformations (other than the two postulates themselves). My specific claim is that I can't see a reason to apply Lorentz Transformations to this problem without using the conclusions he (Einstein) seeks to prove by using them. This problem was meant to establish Einstien's logic for using the Transformations in the first place.

I would hope that anyone who wants to understand my point would actually read this book. The section on Special Relativity is only 64 pages long in the copy I have so it is an easy read if you quickly comprehend what he wrote.

 

[Mentz114]

DanRay

... a light flash begins from a source situated 100 meters away from a point (A) on the embankment at the moment a mirror on the back of the carriage aligns with point A.

1. Is the light source on the embankment or the train ?
2. see bold - whose frame ? There is no absolute simultaneity between spatially separated events.

Your obsession with this is puzzling. Putting numbers into the formula cannot say anything different from what the formulae say.

Also, we're discussing principles here, so it's absurd to think that 1 sec interval is different from a 1 nano-sec interval in relativity.

 

[Ich]

In this book Einstein is explaining the reasoning he used to develop his Special Relativity conclusions all of which are based on Lorentz Transformations (other than the two postulates themselves).

There is nothing based on Lorentz Transformations. Einstein uses the postulates to derive the transformation.
Transformations are used to get from one coordinate system to another. As JesseM rightly said, all your quotes and numbers are dealing with only one coordinate system. So it is absolutely impossible that the reasoning so far could be based on a certain transformation. Therefore your answer to JesseM doesn't make sense.
Then, I don't see at all what you're getting at with the numbers. They seem correct, and irrelevant.
Further, your comment I quoted could be read as a claim that all of SR is based on the inability of a human observer to resolve short timescales. I can't imagine anyone seriously claiming such things, so there must be a misunderstanding.

Again, could you provide us with a clue as to what you're trying to convey? If you believe to have spotted an error in Einsteins popular account, could you point us to it?

 

[sylas]

I would hope that anyone who wants to understand my point would actually read this book. The section on Special Relativity is only 64 pages long in the copy I have so it is an easy read if you quickly comprehend what he wrote.

You can get the book online, in a pdf of an English translation, at relativitybook.com.

Meaning no offense, but your points are incoherent; and in so far as they are comprehensible, they are incorrect and show that you have not understood the book.

As others have said, the issue is not about measurement accuracies. Einstein shows in the book a popular exposition of how to get the Lorentz transformations, using simple language and the basic assumption of constancy of the speed of light for all observers. You can assume all times and distances are known to complete accuracy.

Cheers -- sylas

 

[JesseM]

Dear Jesse M,
Thanks for your reply. However I must take exception to all that you say. Section 7 of Relativity is Einstein's 1916 explanation of the reasoning path he took to discovering all of the things you are talking about. You are wanting me to accept that Einstein should have used time dilation to prove time dilation. You have to accept that at some point he didn't know what he would discover and if you read Section 7 you will see that the whole point of it and this problem is to explain what led him to use the Lorentz Transformations. Sections 8 through 10 are also part of this reasoning journey. He introduces Lorentz and time and space variations in Section 11. My point about my findings is that there is nothing in this problem that justifys the introduction of the transfprmations in the first place and although I didn't mention it before if you look at the two examples I gave and any others you care to examine the difference that satisfies the addition of velocities problem is always in the different arrival time of the "tip of the ray" first to point A then the carriage.

Simply you can't use a conclusion to prove itself!

I didn't say that he would have "used time dilation to prove time dilation", I was just saying that the point of the thought-experiment in section 7 was to compare the distance/time measured in the embankment frame with the distance/time measured in the train frame, so if your own problem doesn't even refer to the train frame it kind of misses the point. Looking on section 7 of this 1920 edition of the book online, you can see that Einstein doesn't derive any specifics about time dilation or length contraction in section 7, his point in section 7 is just that if you assume rulers and clocks work the same way they do in classical Newtonian physics (no time dilation, length contraction, or disagreements about simultaneity) then you'd reach the conclusion that the train observer would measure the light to travel at w = c - v, and he points out that this is in contradiction with the assumptions of relativity. So, he's using this section just to show the negative conclusion that rulers and clocks cannot work the same way in relativity that they do in Newtonian physics, but he doesn't derive how they actually do behave until later. Your own numbers do not even show what speed the train-observer would measure for the light using Newtonian assumptions, so like I said, missing the point.

And by the way Einsteins observer in this case and I think in all cases in this book is the human mind he doesn't invoke any instrumentation at all.

That's wrong, in early sections of the book he makes clear that whenever he talks about "systems of coordinates" or "rigid reference bodies", they are ideally to be defined by noting positions on a system of rigid rods (see section 2) and clocks (see the last paragraph of section 3). So, for example, when he says "People traveling in this train will with advantage use the train as a rigid reference-body (co-ordinate system)" in the opening of section 9 where he talks about the relativity of simultaneity, he is referring to measurements made on such a system of rigid rods and clocks. Also note that in section 8 when introducing simultaneity, he talks very specifically about measuring the time of events on a system of clocks, and defining the time of an event in terms of the reading on the clock that was in the event's immediate vicinity when it happened:

It is clear that this definition can be used to give an exact meaning not only to two events, but to as many events as we care to choose, and independently of the positions of the scenes of the events with respect to the body of reference 1 (here the railway embankment). We are thus led also to a definition of “time” in physics. For this purpose we suppose that clocks of identical construction are placed at the points A, B and C of the railway line (co-ordinate system), and that they are set in such a manner that the positions of their pointers are simultaneously (in the above sense) the same. Under these conditions we understand by the “time” of an event the reading (position of the hands) of that one of these clocks which is in the immediate vicinity (in space) of the event. In this manner a time-value is associated with every event which is essentially capable of observation.

The importance of defining time in terms of readings on clocks which have been "synchronized" using the assumption that light travels at c in the clock's own rest frame (this is known as the Einstein synchronization convention) is also given central importance in Einstein's 1905 paper where he first introduced special relativity--take a look at section 1 of that paper, "Definition of Simultaneity".

 

[DanRay]

Most of you seem to think I don't understand what I'm talking about or you think everything I have said is obvious. I do know that Einstein had already developed and had many discussions about time dilation and foreshorting etc. What I also know is that in these early sections of his book "Relativity" he is trying to demonstrate his reasoning path to using the Lorentz Transformations and all that stems from them. And I am also well aware that Einstein could have put these or any numbers into this thought problem and determined the correct answers. My original thought was that it would be obvious from my demonstration that the only thing that would perceptively vary would be the arrival distance differences and the time of arrival for the "tip of the ray" (Einstein's own term) to the point on the embankment and then the very fast moving carriage. We all agree and of course Einstein already knew that the speed of light would be measured the same in both places. I believe that it was invalid for him to put c into a standard addition of velocities problem that he knew requires the possibility of variance for any value in the problem. The differences I refer to for time of arrival and position relative to the embankment at arrival of the tip of the ray can only be observed once for any continuous ray of light. From then on the speed (and perhaps a red shift) are the only thing that can be measured.

Here is a side issue that I think is related to this thought problem. Did anyone ever wonder why only one of the changes indicated by the Lorentz Transformations can happen with each permutation and which phenomena (time dilation, forshortening, apparent speed) is indicated is dependent on which value is the unknown. Can anyone explain why only one is true at a time within the same set of facts?

 

[DanRay]

By the way, that 1920 on line version of relativity I'm sure reads the same as these sections in my 15th addition version which is still in print, copyright 1961 by the Estate of Albert Einstein. My copy is a paperback Published by Three Rivers Press ($8.95 US). The 15th edition first appeared in 1952 and has a fifth appendix titled "Relativity and the Problem of Space" which was new in this edition. If you haven't read that I think you would all find it very interesting. I don't know which appedicies appear in the 1920 version, I have yet to check that.

 

[sylas]

... My original thought was that it would be obvious from my demonstration that the only thing that would perceptively vary would be the arrival distance differences and the time of arrival for the "tip of the ray" (Einstein's own term) to the point on the embankment and then the very fast moving carriage. ...

The things that depend on the observer -- that vary depending on who is measuring -- include

• The distance from the location where the tip of ray starts out to the the location where it is observed.
• The time it takes from when the tip of the ray starts out to the time when it is observed.
• The time showing on the passenger's watch at the instant when the ray starts out.

These things are respectively

• The relativity of distances.
• The relativity of elapsed times.
• The relativity of simultaneity.

These differences are nothing to do with measurement accuracies. They are all a consequence of the Lorentz transformations. They are explained in the chapters 8, 9 and 10, after the chapter 7 which first shows that the conventional Galliean transformations are inadequate. In chapter 11 the Lorentz transformations themselves are introduced.

As Einstein shows, the Lorentz transformations be shown to follow by accepting that the speed of light is a constant, and that there is a linear transformation between times and distances in two frames. The book basically shows how this works, without using too much maths, because it is intended for teaching relativity to interested novices. The mathematical derivations of the Lorentz transformations is in appendix 1.

Cheers -- sylas

 

[JesseM]

Most of you seem to think I don't understand what I'm talking about or you think everything I have said is obvious. I do know that Einstein had already developed and had many discussions about time dilation and foreshorting etc. What I also know is that in these early sections of his book "Relativity" he is trying to demonstrate his reasoning path to using the Lorentz Transformations and all that stems from them.

But in section 7, he is not actually giving the reasoning that leads to the specific equations of the Lorentz Transformation, he is just making the negative argument that if we assumed that the train observer's rulers and clocks bore the same relation to the embankment observer's rulers and clocks as they do in standard Newtonian physics, then if the embankment observer measured the light to move at c in his frame, the train observer would measure it to move at w = c - v in his own frame, which would contradict one of the basic assumptions of relativity which Einstein had mentioned earlier. Do you disagree that he was just making this type of negative argument (a sort of proof-by-contradiction that Newtonian assumptions must be wrong if the basic assumptions of relativity are correct) in section 7?

I believe that it was invalid for him to put c into a standard addition of velocities problem that he knew requires the possibility of variance for any value in the problem.

c appears in classical electromagnetism as the speed of all electromagnetic waves, it already had a known value. But classical physicists assumed that the equations of classical electromagnetism could only work precisely in one preferred frame (the rest frame of the luminiferous aether), and that anyone moving at velocity v relative to this preferred frame would measure electromagnetic waves to travel at c+v or c-v relative to themselves. Einstein was exploring what conclusions would hypothetically follow if we instead started out with the assumption that the laws of classical electromagnetism must work precisely in every inertial frame, so that every frame would measure an electromagnetic wave to move at c (then once he had found out what conclusions would hypothetically follow from this starting assumption, it would of course be an experimental matter to see whether the conclusions match up with what is actually seen in nature). Since this is his basic starting assumption, it doesn't make much sense to say that he should have considered "the possibility of variance" in c.

 

[DanRay]

The things that depend on the observer -- that vary depending on who is measuring -- include

• The distance from the location where the tip of ray starts out to the the location where it is observed.
• The time it takes from when the tip of the ray starts out to the time when it is observed.
• The time showing on the passenger's watch at the instant when the ray starts out.

These things are respectively

• 
  [*]The relativity of distances.
  [*]The relativity of elapsed times.
  [*]The relativity of simultaneity.

As Einstein shows, the Lorentz transformations be shown to follow by accepting that the speed of light is a constant, and that there is a linear transformation between times and distances in two frames. The book basically shows how this works, without using too much maths, because it is intended for teaching relativity to interested novices. The mathematical derivations of the Lorentz transformations is in appendix 1.

Cheers -- sylas

Sylas, you are alway kind to my misteps and I appreciate that. I am keenly aware of everything that you say, but you are attempting to introduce the conclusion as the reason to head toward it. All three of the things you mentioned are as you have said yourself derived from the results of the Lorentz Transformations and I think therefore cannot be used as an argument for employing them before thay are introduced. That is where we are with Einstein's section 7 problem. Please think about what I said about putting a constant into an equation that is designed for variables. In this old standard equation and it's variations anyone of the values can be the unknown and each one varies acording to the combined values of the other two. We know Einstein already knew that c was invariable so I think he should have known that it didn't belong in the addition of velocities problem as a presumed variable.

Do you have any thoughts about why you can only derive each of the things you mentioned from one variation or other of the Transformations. In other words if the unknown is the speed there is no dilation or forshortening,you use the measured values for those two and end up with your "Relativistic speed". If the unknown is the distance you use the measured speed and and time and the result is "relativistic distance". If the unknown is the time you use the measured values for the other two and you have "relativistic time". And this can all be for the same event in the same frame with three different observers with the different combinations of information mentioned.

Cheer to you too. DanRay

 

[Mentz114]

DanRay,
have you read 'On the Electrodynmaics of Moving Bodies' ? Length contraction and time dilation are shown to be a consequence of the invariance of the speed of light.

I have to say I find it difficult to interpret this

... putting a constant into an equation that is designed for variables.

 

[sylas]

All three of the things you mentioned are as you have said yourself derived from the results of the Lorentz Transformations and I think therefore cannot be used as an argument for employing them before thay are introduced.

That's actually backwards. All the three things mentions are consequences of the invariance of the speed of light for all observers.

That is why they are introduced where they are introduced, to motivate the subsequent derivation of the Lorentz transformations. The argument for relativity of time, or distance and of simultaneity stands quite apart from the transformations, and that's partly why you will have problems putting numbers to chapters 7 to 10.

The way Einstein develops the explanation here doesn't depend on specific numbers. You can put them in, of course, but you don't have all the tools to give numbers for the train passenger given numbers for the observer on the embankment.

Do you have any thoughts about why you can only derive each of the things you mentioned from one variation or other of the Transformations.

The book itself shows that you derive each of the three points without using the transformations at all. You only need that the speed of light is constant for all observers.

Given this, you can show that time must be relative, and that distance must be relative, and that simultaneity must be relative, simply by showing that they cannot be equal for the two observers. In these initial chapters, that is done without transformations and without calculating actually HOW MUCH difference there is.

Felicitations -- sylas

 

[DanRay]

DanRay,
have you read 'On the Electrodynmaics of Moving Bodies' ? Length contraction and time dilation are shown to be a consequence of the invariance of the speed of light.

I have to say I find it difficult to interpret this

Yes I read it a long time ago but I don't currently have it. It may be online, I haven"t checked. I am currently reading Poincare's "Science and Method" first published in 1908. He also used Lorentz Transformations in ways simular to Einstein but he never did give up the ether concept. However he did deal with the changes derived from the transformations with conclusions much like Lorentz's own.

Your answer to me suggests that like the others you suspect I am either mad or not fully grasping what you all know so well. None of you are willing to accept that there might be some reason to take another look at Einstein's reasons for using Lorentz Transformations. I suspect that most of you have never examined any of it from any point of view other than learning it as part of a physics course as settled Science. I am aware that Relativity and Lorentz Transformations are taught in basic physics classes. I helped my own daughter understand all of these things (from the point of view that it is all settled science) for her High School Physics class in the mid 1980s. She got A+ routinely in High School and As in physics in College as well. I think she was probably more intelligent than me but unfortunately she passed away from cancer in 1994. The toughts in this thread originally came to me from her and it caused me to reread and think about this book and many others not from a try to understand it point of view but from a questioning point of view. I already understood all of it pretty well but I had never questioned any of it. I do that all the time now with everything I read. It has given me some insights and some misteps.

By the way I believe if Einstein were still with us he would have a sense of humor about my approach even if he thought it was comical and futile. He welcomed debate and opposing theories and never debased those who disagreed with him. And if you think my thoughts are an attack on Einstein and Relativity, think again. As far as I am concerned his 1905 achievements still rank as the single most amazing thing that any human has ever acomplished and probably will stand for a long time to come if not forever.

 

[chronon]

There are two things I would mention
1) Science works along the lines of:
Devise a theory (somehow), make predictions from the theory, see whether these agree with experiment. The fact that the derivation of the predictions may depend on the theory doesn't matter.

However, if you try to derive the theory from observations or from basic principles, then you are likely to get into arguments about whether the derivation depends on the theory.

2) The train thought experiment is one dimensional, and I doubt whether it is possible to untangle the effects of length contraction from those of time dilation - to do that you also need a light beam going perpendicular to the direction of motion

 

[sylas]

None of you are willing to accept that there might be some reason to take another look at Einstein's reasons for using Lorentz Transformations.

You seem unwilling to accept that you haven't yet actually given any reason to think you have some new insight that everyone here has missed.

Your latest post adds absolutely nothing to the substance of discussion; only lots of private reasons why we should all take you seriously, and unjustified false assumptions about everyone being refusing to consider new ideas. But I am taking you seriously. I do that by dealing with the actual substance of your points. But your latest post doesn't say anything of interest to the actual point.

The fundamental premise of special relativity is that light moves in straight lines at the same speed, for all observers. You appear to accept that. The Lorentz transformations follow from this.

Real science is perfectly allowed to question the hypothesis that the speed of light is constant for all observers. But you don't seem to be doing that. Is that right?

If so, there's a problem; because the Lorentz transformations follow as a mathematical consequence of the invariance of lightspeed for observers in Euclidean 3D space.

And a second post...

2) The train thought experiment is one dimensional, and I doubt whether it is possible to untangle the effects of length contraction from those of time dilation - to do that you also need a light beam going perpendicular to the direction of motion

The various simple thought experiments with the train go into all three spatial dimensions, and the derivation I cited derives the full Lorentz transformations in 3D space from these thought experiments.

Cheers -- sylas

 

[JesseM]

Yes I read it a long time ago but I don't currently have it. It may be online, I haven"t checked.

Did you read my previous post to you? (you never responded to it...) I gave you a link to the 1905 paper online at the end.

Your answer to me suggests that like the others you suspect I am either mad or not fully grasping what you all know so well. None of you are willing to accept that there might be some reason to take another look at Einstein's reasons for using Lorentz Transformations.

And what is that reason?? You certainly haven't given any clear summary of what your objection is. Do you understand that in the book you refer to Einstein was not trying to prove that relativity must actually be true in the real world--instead he was just exploring the logical consequences that would follow if the basic postulates of relativity (namely, the postulate that all inertial frames see the same laws of physics, and the postulate that all inertial frames measure light to move at c) were true? Once he has shown what consequences would follow if that were true, then of course it becomes a matter of experiment to check if those consequences actually match up to what we see in the real world.

 

[DanRay]

Your latest post adds absolutely nothing to the substance of discussion; only lots of private reasons why we should all take you seriously, and unjustified false assumptions about everyone being refusing to consider new ideas. But I am taking you seriously. I do that by dealing with the actual substance of your points. But your latest post doesn't say anything of interest to the actual point.

The fundamental premise of special relativity is that light moves in straight lines at the same speed, for all observers. You appear to accept that. The Lorentz transformations follow from this.

Real science is perfectly allowed to question the hypothesis that the speed of light is constant for all observers. But you don't seem to be doing that. Is that right?

If so, there's a problem; because the Lorentz transformations follow as a mathematical consequence of the invariance of lightspeed for observers in Euclidean 3D space.



Cheers -- sylas

I apologize for the personal digression about my Daughter. I spent the day today at the funeral of a dear friend and and at such times my daughter's untimly death and thoughts of her loom heavy in my mind.

I do not agree that the Lorentz Transformations follow in the manner you say. I am well aware that they were formed by Lorentz for a different purpose than Einstein adapted them for use with special Relativity. Lorentz and Irish Physicist Fitzgerald both tried to explain away the ether experiment of Michelson and Morely by postulating that "each body of light foreshortens when it moves against the stationary ether" when the instrument is set up to measure light parallel to the Earth's movement in orbit. Einstein with his new insights into light rejected the concept of an ether and Lorentz's idea of foreshortening and adapted the equations to a different purpose. Poincare did some of that too but he actually believed in the ether to the end of his life and had different reasoning for both relativity and the Lorentz Transformations.

I have no argument with Einsteins two Special Relativity postulates I think they are among the most brilliant of scientific insights ever. But I don't think you can get to the three main consequences by reasoning alone. I believe Einstein derived them from the Lorentz Transformations applied to problems just like this one. It is easy to see from the equations themselves that if they are valid then all of these things are also true.

My original point with this problem was that if you could demonstrate with a different approach to it that the speed of light is actually measurabe as c (the mirror gives you a two way trip from the source to the carriage and back to the source) and from that and from the
known distance to the back of the train derived from its speed, you can by simply timing when it gets back to the source calculate that it did the round trip at exactly c. You then have the answer to Einstein's question with that addition of velocities problem whether you accept my statement that Einstein misused it or not by putting what he knew was a constant into a problem that required it to be variable. If there is any doubt that you should know where the mirror would be when "the tip of the ray" hits it then you are ignoring that the constancy of the speed of light is one of the most accurate measuring devices for distance known to man. The timing itself will verify that your expectations of where that will be are correct.

 

[JesseM]

My original point with this problem was that if you could demonstrate with a different approach to it that the speed of light is actually measurabe as c (the mirror gives you a two way trip from the source to the carriage and back to the source) and from that and from the
known distance to the back of the train derived from its speed, you can by simply timing when it gets back to the source calculate that it did the round trip at exactly c.

But Einstein's point was not about experimental confirmation, it was about the logical consequences if it is true that light moves at c in every frame (once we have derived these logical consequences, only then do we turn to the experimental question of whether the derived predictions actually match with experimental data). Actually performing the experiment is irrelevant here. What's more, you once again ignore the issue of what would be measured for the speed of the same light ray in the train's rest frame, and the whole point of section 7 was that if the train observer's rulers and clocks were unchanged as observed by the embankment observer (as in Newtonian physics), and if the embankment observer measured the light to move at c and the train to move at v, then this would logically imply that the train observer would measure the light to move at c-v.

Do you understand what a proof by contradiction is? If so, you can see that this is a proof by contradiction that the assumption of the train observer's rulers and clocks being unchanged as measured by the embankment observer is not compatible with the postulate that light moves at c in every frame. That was the entire point of the train example in section 7, and your example ignores the train observer's measurements entirely, so you miss the point.

 

[DanRay]

Did you read my previous post to you? (you never responded to it...) I gave you a link to the 1905 paper online at the end.

And what is that reason?? You certainly haven't given any clear summary of what your objection is. Do you understand that in the book you refer to Einstein was not trying to prove that relativity must actually be true in the real world--instead he was just exploring the logical consequences that would follow if the basic postulates of relativity (namely, the postulate that all inertial frames see the same laws of physics, and the postulate that all inertial frames measure light to move at c) were true? Once he has shown what consequences would follow if that were true, then of course it becomes a matter of experiment to check if those consequences actually match up to what we see in the real world.

Sorry JesseM, I tried to reply to you earlier and had problems with my internet service and today I have been otherwise occpied. I haven't yet tried to use your link but I have read all of it before. I think Einstein gives a very good accounting of all of his Relativity thinking in this book. I do realize that he always called it a theory until the day he died but he defended it passionately as well. It only gained inflexible status in the hands of later proponents. Einstein loved to debate and did it often with humor and grace along with his brilliance and insight. If you read the answer I posted earlier to Sylas you will get a better idea of where I'm coming from.

So to be clear I don't have a bit of doubt about the validity Einstein's postulates. I do have serious doubt about the validity of the Lorentz Transformations and I have reasons that I will attempt to demonstate for anyone who is interested that apply to several other thought problems that use them but I can't do it until later. I must get some sleep now and I will be busy all weekend so it might be next week before I can post much more. Regards; DanRay

 

[sylas]

I do not agree that the Lorentz Transformations follow in the manner you say.

That's why everyone is sure you haven't understood this yet. This is not a matter for informed disagreement; it stands as a mathematical theorem.

The scientific questions are still open, but the mathematical ones are not. You can never prove a scientific theory is correct; you can prove a mathematical theorem. And it has all the status of a theorem that the Lorentz transformations follow from the postulates.

I have no argument with Einsteins two Special Relativity postulates I think they are among the most brilliant of scientific insights ever. But I don't think you can get to the three main consequences by reasoning alone. I believe Einstein derived them from the Lorentz Transformations applied to problems just like this one. It is easy to see from the equations themselves that if they are valid then all of these things are also true.

The very book you are citing shows the relativity of time, of distance and of simultaneity follow from the postulates by reasoning alone; and without even using the Lorentz transformations. That is the whole points of chapters 7 through 10, which establish that the postulates require the relativity of time, distance and simultaneity. THEN you get to chapter 11, which introduces the Lorentz transformations.

My original point with this problem was that if you could demonstrate with a different approach to it that the speed of light is actually measurabe as c (the mirror gives you a two way trip from the source to the carriage and back to the source) and from that and from the known distance to the back of the train derived from its speed, you can by simply timing when it gets back to the source calculate that it did the round trip at exactly c. You then have the answer to Einstein's question with that addition of velocities problem whether you accept my statement that Einstein misused it or not by putting what he knew was a constant into a problem that required it to be variable. If there is any doubt that you should know where the mirror would be when "the tip of the ray" hits it then you are ignoring that the constancy of the speed of light is one of the most accurate measuring devices for distance known to man. The timing itself will verify that your expectations of where that will be are correct.

This still appears to miss the whole point of the chapter, which is to compare measurements of the two different observers, and show that they must give different results for durations, and distances and simultaneity. It also still appears to mix up the notion of accuracy of measurement with the derivation of qualities being measured. Measurement accuracy has nothing to do with it; this is a distraction. The point is the thing being measured, which we can assume is measured as accurately required... just like we can assume trains moving at 60% light speed.

Cheers -- sylas

 

[DanRay]

That's why everyone is sure you haven't understood this yet. This is not a matter for informed disagreement; it stands as a mathematical theorem.

The scientific questions are still open, but the mathematical ones are not. You can never prove a scientific theory is correct; you can prove a mathematical theorem. And it has all the status of a theorem that the Lorentz transformations follow from the postulates.

Sylas, thank you for trying to set me straight. Once again I am not repentant. I have tried to assure you that I knew Einstein’s (and Science’s) position on all of this when the discussion began. This is not a theorem of mathematics in the traditional sense. Theorems and what they signify are all verifiable by measurement and experience. The Lorentz Transformations are not. If misconceptions are contained in the thought problems used to confirm LTs and the effects they are said to prove then I see nothing that upholds them. I know that you are well versed in all of the accepted scientific points of view. But I doubt you have ever considered that there might be a problem with the Lorentz Transformations. I’m trying to give you a reason. Hardly a month goes by that I don’t see a question like “Was Einstein Wrong?” (Scientific American March 2009). Yet it seems nobody wants to actually take a look at the beginning of Einstein’s Theories and the math he used. I don’t get that.

No one has answered my two main questions;
1. Why would you need any transformations if you could answer Einstein’s section 7 question without them? Presumably you all believe that the mirror wouldn’t be where a standard vt would calculate it to be.
2. Why is it acceptable to put a constant, c, into any math problem that requires a variable term where it is used in the problem?

The Lorentz Transformations are full of terms like (c-v) (c+v) that taken by themselves seem improper, what makes them proper within these problems?

There is a ubiquitous light/thought problem that appears in physics texts and encyclopedias, with varying specifics, that are all based on the Galileo’s ship problem. They are used to demonstrate time dilation according to the Lorentz Transformations in a simple straightforward way. The trouble with all such problems is that they imagine that the light beam follows forward with the momentum of the ship. They state that the “light path” observed from the shore is longer than the straight down beam observed from the ship and therefore that observer’s clock will say the light took longer to hit the deck. The fact is that it doesn’t matter how fast the ship is going the light does not move with the momentum of the ship but takes a straight down path from the point of propagation and looks like a straight down beam to the shore observer. It will hit the deck behind the mast not in front of it. From the point of view of an observer on board the light seems to angle back by the same amount that it is usually imagined that it angles forward for the observer on shore. But he will measure the time it takes to hit the deck exactly the same as the guy on shore. No transformations are necessary to establish that. Einstein’s second postulate, the independence of light from its source, demands my point of view not the common one that requires transformation.

There is another type of thought problem that involves 2 observers moving away from each other on a single straight line. When the LTs are applied to that type of situation they give you the universal speed limit. The problem here is that the LTs keep the light tied to the source in these problems in an inappropriate way. The light signals always originate from the point in space occupied by the observer at the moment it is sent and heads from that point to the other observer at c and can easily catch up even if both observers are moving at some large fraction of c.

My objections all require a reexamination of the significance of independent “frames of reference” as Einstein developed the concept in Section 3 of relativity. When Einstein drops the rock out of the window he has put it into the reference frame of the observer on the path but he could have just as easily dropped it inside the carriage and nothing would change if the guy on the path could see it. Both observers would see it exactly as before. The parabolic path is real and is the result of the combined effects of the rocks forward momentum and gravity. These differences between observations are always a matter of perspective. But a light ray from a source on the ceiling of the train car doesn’t follow with the momentum of the train. It takes a straight down path the moment it is propagated from the place the light occupied at the moment of propagation. To imagine otherwise is to give special status to the moving one. Everything occurs in both frames not just the one the light source is anchored to.
Have a good day. DanRay

 

[JesseM]

This is not a theorem of mathematics in the traditional sense. Theorems and what they signify are all verifiable by measurement and experience.

No, a mathematical theorem is verified simply by doing the appropriate calculations, in math "measurement and experience" are irrelevant. One can easily prove mathematical assumptions that involve starting axioms that don't appear to actually apply in the real world (axioms about the geometry of space for example, or the number of dimensions, or the laws governing dynamics of moving bodies).

Hardly a month goes by that I don’t see a question like “Was Einstein Wrong?” (Scientific American March 2009).

If these questions are in mainstream publications (as opposed to crackpot websites), you can bet that none of them are saying he might have been "wrong" in his theoretical derivations, they are only questions about whether the theories provide accurate descriptions of the laws of physics that govern real-world situations.

No one has answered my two main questions;
1. Why would you need any transformations if you could answer Einstein’s section 7 question without them? Presumably you all believe that the mirror wouldn’t be where a standard vt would calculate it to be.

As I explained to you before, Einstein's section 7 question was about what speed would be measured in the train-observer's rest frame, not about what would happen in the embankment frame, if you disagree then you've just totally missed the point of the section. There is absolutely no question whatsoever about where both the mirror and the light would be at any given time in the embankment frame, since Einstein starts out from the assumption that we know the mirror's velocity v and the light's velocity c in this frame.

2. Why is it acceptable to put a constant, c, into any math problem that requires a variable term where it is used in the problem?

Where do you get the idea that the math problem "requires a variable term" there? Einstein is doing a theoretical derivation of what must be true in relativity given certain axioms, one of which is the axiom that the speed of light is a constant c in every inertial frame. Again it seems you may be confused about how mathematical derivations of the consequences of axioms work.

The Lorentz Transformations are full of terms like (c-v) (c+v) that taken by themselves seem improper, what makes them proper within these problems?

The Lorentz transformation does not contain any terms like that. The Lorentz transformation equations just tell you the coordinates (x',y',z',t') of an event in the primed frame if you already know that event's coordinates (x,y,z,t) in the unprimed frame:

x' = gamma*(x - vt)
y' = y
z' = z
t' = gamma*(t - vx/c^2)

where gamma = 1/sqrt(1 - v^2/c^2)

In any case, nothing in relativity says that terms like (c-v) are "improper" unless they are meant to refer to the speed of a light ray in an inertial frame, which (according to the basic starting assumptions or axioms) must always be exactly c. You can certainly use (c-v) to refer to some other speed besides the speed of a light ray as seen in an inertial frame.

There is a ubiquitous light/thought problem that appears in physics texts and encyclopedias, with varying specifics, that are all based on the Galileo’s ship problem. They are used to demonstrate time dilation according to the Lorentz Transformations in a simple straightforward way. The trouble with all such problems is that they imagine that the light beam follows forward with the momentum of the ship. They state that the “light path” observed from the shore is longer than the straight down beam observed from the ship and therefore that observer’s clock will say the light took longer to hit the deck. The fact is that it doesn’t matter how fast the ship is going the light does not move with the momentum of the ship but takes a straight down path from the point of propagation and looks like a straight down beam to the shore observer.

Nope, you forget the other basic axiom of relativity, namely that the laws of physics must work the same way in all inertial frames. So, if you have two windowless rooms moving inertially at different speeds, one on the ship and one on the ground, any experiment done in both rooms must give the same result in both rooms--there should be no experiment an observer in either room can do to determine whether he is at rest relative to the ship or at rest relative to the ground (again assuming the ship and ground are both inertial and not accelerating). This means that if a flashlight's beam extends parallel to the direction the flashlight is oriented in the ground frame when the flashlight is at rest relative to the ground, it must similarly be true that the beam extends parallel to the flashlight in the ship frame when the flashlight is at rest relative to the ship. If this weren't true, it would violate the first postulate of relativity which says the laws of physics work identically in all inertial frames.

Einstein’s second postulate, the independence of light from its source, demands my point of view not the common one that requires transformation.

Einstein's second postulate only says the speed of a light beam is independent of the speed of its source, it does not say the observed direction of a light beam relative to its source is independent of the source's speed relative to the observer.

There is another type of thought problem that involves 2 observers moving away from each other on a single straight line. When the LTs are applied to that type of situation they give you the universal speed limit. The problem here is that the LTs keep the light tied to the source in these problems in an inappropriate way. The light signals always originate from the point in space occupied by the observer at the moment it is sent and heads from that point to the other observer at c and can easily catch up even if both observers are moving at some large fraction of c.

It's actually irrelevant where the observers are located in space, in fact you can ignore their location altogether and just consider the point the light was emitted as measured by both observers' ruler/clock systems, and the point where the light was received as measured by both observers' ruler/clock systems. Remember, Einstein makes clear that the coordinates of any event in a given frame are ideally to be established by local measurements on a system of rulers and synchronized clocks at rest in that frame, like the ones I illustrated in this thread.

My objections all require a reexamination of the significance of independent “frames of reference” as Einstein developed the concept in Section 3 of relativity. When Einstein drops the rock out of the window he has put it into the reference frame of the observer on the path but he could have just as easily dropped it inside the carriage and nothing would change if the guy on the path could see it. Both observers would see it exactly as before. The parabolic path is real and is the result of the combined effects of the rocks forward momentum and gravity. These differences between observations are always a matter of perspective. But a light ray from a source on the ceiling of the train car doesn’t follow with the momentum of the train. It takes a straight down path the moment it is propagated from the place the light occupied at the moment of propagation. To imagine otherwise is to give special status to the moving one.

Wrong, it is your idea that gives special status to the observer at rest relative to the ground, since it says that if different observers take flashlights and aim them straight down at the ground, only the observer whose flashlight is at rest relative to the ground will see the beam extend straight down parallel to the flashlight, while other observers like the carriage observer will see it extend down at an angle in their own frame (since you assumed that the beam would continue to extend straight down in the ground frame). If we assume the laws of physics work the same way in each frame, then any observer who aims a flashlight straight down (with the flashlight at rest in their own frame) should see the beam extend straight down in their own frame, so no frame can have a special status.

 

[DanRay]

Nope, you forget the other basic axiom of relativity, namely that the laws of physics must work the same way in all inertial frames. So, if you have two windowless rooms moving inertially at different speeds, one on the ship and one on the ground, any experiment done in both rooms must give the same result in both rooms--there should be no experiment an observer in either room can do to determine whether he is at rest relative to the ship or at rest relative to the ground (again assuming the ship and ground are both inertial and not accelerating). This means that if a flashlight's beam extends parallel to the direction the flashlight is oriented in the ground frame when the flashlight is at rest relative to the ground, it must similarly be true that the beam extends parallel to the flashlight in the ship frame when the flashlight is at rest relative to the ship. If this weren't true, it would violate the first postulate of relativity which says the laws of physics work identically in all inertial frames.

Einstein's second postulate only says the speed of a light beam is independent of the speed of its source, it does not say the observed direction of a light beam relative to its source is independent of the source's speed relative to the observer. --- (end quote)

Pardon me for not responding sooner. My sattalite internet service has been down due to weather conditions. I stand by my original statement that the idea of refrence frames must be reexamined. It is one thing to restate "facts" that one has learned and quite another to think and reason. One thing that you seem to be unaware of is that the ship or the carriage doesn't leave the stationary frame of reference just because you declare that there is another frame of reference attached to the moving one. Everything that occurs in the one frame occurs in the other as well. The only difference is one is moving and one is not. There is absolutely no doubt that light always propagated in straight line paths from the point in space where it originates and is not tied to the source throught angular momentum. It is true that Einstein may not have been aware of that fact in 1905 or maybe not even in 1955, but that doesn't mean it isn't true.

By the way I listed earlier the peridicals I read and this is the only internet sight that I have ever visited that has to do with physics so your inference that perhaps I read "crackpot internet sites" for my ideas is way off base. My thooughts are my own and they come by way of years of actually thinking about these things. I still do however weigh every counter thought carefully and think before I respond. Someone asked if I have ever read "On The Electrodynamics of Moving Bodies". I said yes, long ago, but I have since downloaded it and studied it thouroughly. Considering what Einstein had to build on I think it is still one of the most amazing science papers ever published, but nothing that is in it changed my mind in any way.

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.

Have a good day DanRay

 

[JesseM]

One thing that you seem to be unaware of is that the ship or the carriage doesn't leave the stationary frame of reference just because you declare that there is another frame of reference attached to the moving one. Everything that occurs in the one frame occurs in the other as well.

I am quite aware that all physical events can be described from the perspective of any frame, if you think something in my post implied otherwise you must be misunderstanding something.

The only difference is one is moving and one is not.

In relativity there is no frame-independent definition of "moving" or "not moving". In the carriage frame, the embankment-observer is moving, while in the embankment frame, the carriage is moving; both are equally valid perspectives in relativity.

There is absolutely no doubt that light always propagated in straight line paths from the point in space where it originates and is not tied to the source throught angular momentum.

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).

It is true that Einstein may not have been aware of that fact in 1905 or maybe not even in 1955, but that doesn't mean it isn't true.

If you are indeed claiming it's "true" that a laser will always come out parallel to the angle of the laser pointer as seen in some preferred "not moving" frame, what is your basis for believing this to be true? Can you point to any textbooks or experiments that support the notion that the angle a light beam comes out relative to the source is independent of the velocity of the source?

By the way I listed earlier the peridicals I read and this is the only internet sight that I have ever visited that has to do with physics so your inference that perhaps I read "crackpot internet sites" for my ideas is way off base.

In that case, I think perhaps you have gotten confused about the difference between suggesting Einstein was "wrong" in his mathematical derivation of the consequences of various postulates, such as deriving the Lorentz transformation from the two basic postulates of SR, and suggesting he might have been "wrong" in the sense that some of these postulates might not actually be true in the real world. You may find mainstream publications discussing the second possibility, but no mainstream publications will argue that his mathematical derivations might be flawed.

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? And thus that the only way the Lorentz transformation could fail to apply to actual measuring-devices in the real world would be if there were experimental situations where we could see violations of one of the two postulates in the real world? (i.e., either an inertial measuring-system finding the speed of a light in a vacuum to be different from c, or different inertial measuring-systems finding that the laws of physics don't obey the same equations in their respective frames, like one preferred frame finding that lasers are always emitted parallel to laser pointers while other frames measuring the same lasers to be emitted at an angle relative to the same laser pointers)

 

[DanRay]

In relativity there is no frame-independent definition of "moving" or "not moving". In the carriage frame, the embankment-observer is moving, while in the embankment frame, the carriage is moving; both are equally valid perspectives in relativity.

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. I realize that it makes no diference to the math but it does make a difference that the train has an engine that must constantly consume fuel to produce and maintain the motion. So the special case that Einstein creates is to deny the obvious.

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. 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. It is the paralax view. It amounts to the same thing as why he can't perceive the parabolic curve of the rock in Einstein's section 3 example whether it is dropped inside or outside the train car.

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? And thus that the only way the Lorentz transformation could fail to apply to actual measuring-devices in the real world would be if there were experimental situations where we could see violations of one of the two postulates in the real world? (i.e., either an inertial measuring-system finding the speed of a light in a vacuum to be different from c, or different inertial measuring-systems finding that the laws of physics don't obey the same equations in their respective frames, like one preferred frame finding that lasers are always emitted parallel to laser pointers while other frames measuring the same lasers to be emitted at an angle relative to the same laser pointers)

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 consistant and not mathematically contridictory. 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.

Have a great day, DanRay

 

[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 consistant 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".