Einstein's Relativity

[artisticsolution]

Paranoia?

Who told you I was paranoid?!

I was not trying to exclude anyone, nor would I be a position to do so.

I know...I was just having fun.

So what else does Einstein say? Let's move forward...shall we?

[S G R]

That sentence starts "We are accustomed further to regard three points ...". He seems to be talking about how we casually think, not about how we ought to think.

Richard, I’m afraid I can’t figure out what it is you are trying to point out here. Certainly Einstein isn’t saying anything about ‘ought’ but then again I don’t think I am either???

[Richard Baron]

Hello SGR

I thought that you were challenging Einstein, with your words: "Einstein’s proposal to consider two points on a rigid body has always appeared flawed to me". So I thought it worthwhile to point out that so far as I could see, he was not at that point telling us what he thought, but what people commonly thought. My apologies if I misunderstood you, or Einstein.

[Arising_uk]

Here's how I understand Part 1.1

Euclids geometry does not produce 'true' propositions from its axioms but correct ones, given our ability of deduction and the conceptions associated with the propositions proposed as axioms.

So there is no answer to the question "Are the axioms true?" using only geometry to answer. In fact he says the question is meaningless as Geometry is like Logic in that its concerned with the logical relations(connections) produced by the axioms and not being 'true' in the sense of corresponding with a "real" object of experience.

He thinks why we associated Euclids geometry with being 'true' about the world is a logical mistake for Geometry and one based upon our 'habits of thought', i.e. how we see a "distance" and how we know that if we know that there are three identical things and we see them as one then we know they are on a straight line, etc. but he does say that it is these things that produced Euclid's Geometry in the first place.

So, if we wish to understand the propositions of Geometry as being able to be tested as being true, i.e. true of the experience of reality, then the way to go is to understand that if a "distance" is the habit of "...two marked positions on a practically rigid body" then we could add to Euclid's correct geometry the proposition that "...two points on a practically rigid body always correspond to the same distance(line-interval), independently of any changes in position to which we may subject the body,...". This addition makes this Geometry a branch of Physics as it becomes claims about "...the possible relative position of practically rigid bodies", which we can test, hence all the 'ruler&compass' work some learnt in schoolhood maths.

So far so good to me and I'm intrigued that he ends by saying that since this "truth" is founded upon incomplete experience, he will show later that this version of being 'true' is limited and he will consider size of this limitation.

What I like is that it reminds me of how Descartes changed Euclids Geometry and that this book is not an overtly philosophical one, but a physicists explanation of what he does to what he considers an educated layman.

Hope this helps the discussion.

[Arising_uk]

Einstein’s proposal to consider two points on a rigid body has always appeared flawed to me. First he says three points are on a straight line if one can superimpose them from some position by looking at them through one eye, then he talks about ‘line interval’ upon a rigid body. Unless the rigid body is a perfect plain he is talking about two different examples.

Depends if you allow the "line interval" to flex. As I guess you are saying that the 'perfect plain' could be uneven, so if we take a 'rigid body' as 'distance' and rotate it, it'd not 'fit' the 'perfect plain'? But, I guess, we could allow for 'flex' in the 'rigid body' that still would keep Einsteins idea of a 'line interval' that does not change during rotation?

On order.

In my opinion about the best book written by a physicist about what he does for the layman who is interested in such things.

[Arising_uk]

So what I got from this part was that if an axiom is not true in all situations, then we can say that logic itself is more complex.

I think its that we can say the situation is more complicated AS. That is, we may need more 'names' and hence axioms or that one or more of the axioms do not accuratly 'name' reality as we understand it or some such. Because axioms are 'true' by definition. You can disagree with the grounds for them but you can't argue the logic of the propositions produced by them.

="SGR"]I don’t think so – the logic is just the logic, if it doesn’t hold true it is failing to describe reality. It is not necessarily the case that it needs to be more complex it is just the case that it is an inappropriate description.

So I think we agree but your words sound odd, as Logic does not describe a reality but all reality, what describes our reality is the contingent propositions, as we know all the necessary and contradictory ones.

Does that mean that geometry is untrue or that is is only true on a very small scale because we (humans on Earth) only exist on a tiny dot compared to the universe and if we could see the big picture we could then see the movement?

It means to me that to make geometry true in a sense we can understand on any scale, we first have to agree with Einsteins proposition that there is such a thing as a 'line-interval' that does not alter with rotation, is my thought?

[artisticsolution]

Hi Arising,

A:I think its that we can say the situation is more complicated AS. That is, we may need more 'names' and hence axioms or that one or more of the axioms do not accuratly 'name' reality as we understand it or some such. Because axioms are 'true' by definition. You can disagree with the grounds for them but you can't argue the logic of the propositions produced by them.

AS: Okay...this is going to be a huge barrier for me. It has been all my life because I don't understand the basic reasons for math. Most maths I am only able to understand become someone shows me how to work the problem and I memorize it...I have no idea how it actually works or what it's purpose in life is. So to me, Einstein was making sense in the first 3 paragraphs of part 1 (sorry it wont allow me to cut and paste.) He uses words like "truth" in quotation marks to show truth is relative. And there is a nifty little sentence that goes, "It is not difficult to understand why, in spite of this, we feel constrained to call the propositions of geometry "true."

Also, I looked up axioms on Wikipedia. They had this to say,

"In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths."'

What I am suggesting is that literally "truth" is taken for granted and might not be true at all! For example, who says time is infinite? Just because we take time for granted since it has been around longer than we have is no reason to believe our 'feelings' about time are true.

A:It means to me that to make geometry true in a sense we can understand on any scale, we first have to agree with Einsteins proposition that there is such a thing as a 'line-interval' that does not alter with rotation, is my thought?

AS: Line interval? I can't see how line intervals could remain the same with different people viewing them from points in the universe, at different speeds and then add light to the equation. Light bends right? See...I am at an unfair advantage because I don't know how things work...lol. What makes the sky blue? I am damned and determined to keep up though...so I will continue to ask stupid questions...all of you please answer me when you can...even if you think it's just a given...and it would help if you talk baby talk...lol...I will not be offended.

[artisticsolution]

Hi All,

I was doing a search on related topics in order to understand relativity better and I came across this quote:

Fully 70% of the matter density in the universe appears to be in the form of dark energy. Twenty-six percent is dark matter. Only 4% is ordinary matter. So less than 1 part in 20 is made out of matter we have observed experimentally or described in the standard model of particle physics. Of the other 96%, apart from the properties just mentioned, we know absolutely nothing.

– Lee Smolin: The Trouble with Physics, p. 16

Then I came across this info in wikipedia, about string theory:

"The full theory does not yet have a satisfactory definition in all circumstances, since the scattering of strings is most straightforwardly defined by a perturbation theory. The complete quantum mechanics of high dimensional branes is not easily defined, and the behavior of string theory in cosmological settings (time-dependent backgrounds) is not fully worked out. It is also not clear if there is any principle by which string theory selects its vacuum state, the spacetime configuration which determines the properties of our Universe (see string theory landscape)."

Last but not least I googled 'What are the properties of time?' and 'time' and came up with this little beauty that was very easy and interesting to read. Has this been discussed in the forum yet?

http://plato.stanford.edu/entries/time/#Fat

I believe that if we refuse to consider that our understanding of axioms is flawed then we will only be able to know the universe within a tiny box that we have built around us. Meaning we can go no further than what our minds will allows us to know about "logic." I think it is part of the reason we don't want to think of things such as emotion in logical terms. It frightens us to think about something so wild that it could not be explained by the rules we take for granted.

[Arising_uk]

Okay...this is going to be a huge barrier for me. It has been all my life because I don't understand the basic reasons for math. ...

My apologies AS, as my words were not math but logic from academic philosophy.

I think the reason why so many do not "understand the basic reasons for math" is because of the way it is taught, i.e. without its historical context, and lately even out of historical sequence, e.g. they teach kids Set Theory first as for the Mathematician this is a logical underpinning for the rest of 'math'. Whilst this is fine for the budding mathematician, it can be puzzling to the rest.

My other take is that most get confused when Algebra and Calculus appear.

So, the basic reason for Maths was because people had quantity, shape and size concerns that they needed to record and solve, e.g. temple walls needed to be 90 degrees, recently flooded fields needed to be re-marked by owners as to who owned what, cannonballs needed to break things in the most efficient way, etc. But 'modern' math is split into Pure and Applied, with Pure being Math about Math and Applied being the finding of 'physical' problems that the Pure stuff could help with, or something like this.

If you are interested in how a philosopher can think then I think you could do worse than pick up a book on Propositional Logic. Most would say a beginners book but I'd go for something quite formal, e.g. "Truth-Functional Logic; J. A. Faris" to really start from the ground up. As the experience, I think, will give you an insight into the reason for Math and parts of Philosophy, as pretty much all the great philosophers had a grounding in Logic.

... Most maths I am only able to understand become someone shows me how to work the problem and I memorize it...I have no idea how it actually works or what it's purpose in life is.

What you are doing is what most Engineers do with respect to Mathematics. Although they do think that its purpose is to help them solve their problems

So to me, Einstein was making sense in the first 3 paragraphs of part 1 (sorry it wont allow me to cut and paste.) He uses words like "truth" in quotation marks to show truth is relative. And there is a nifty little sentence that goes, "It is not difficult to understand why, in spite of this, we feel constrained to call the propositions of geometry "true."

Which he says is because we forget that Geometry is like Logic, i.e. about the relationship between its ideas or axioms, and that, Geometry came from 'habits of thought' and the need to solve real world problems.

Here's where my 'academic philosophy' ears prickle, "He uses words like "truth" in quotation marks to show truth is relative", as whilst I agree that this is what he is doing, I'd question what you mean by "...show truth is relative"? Only because this phrase "...is relative" has so many understanding now-a-days.

From my perspective, he is identifying what we need to agree before we can say that something is 'true' or not about what we've agreed. And he is trying to explain how he, as a Physicist, understands how the logical ideas of Geometry are applied in Physics, i.e. Physics can look at Geometry as the movement of a 'rigid body' upon a practically 'rigid body', which is testable by making equivalent bodies(?)

Also, I looked up axioms on Wikipedia. They had this to say,

"In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths."'

What I am suggesting is that literally "truth" is taken for granted and might not be true at all! For example, who says time is infinite? Just because we take time for granted since it has been around longer than we have is no reason to believe our 'feelings' about time are true.

Maybe I can help here. I agree that your thought is a naturally philosophical one. But the idea of Logic is not to tell you whats 'true' or 'false' with respect to the world, but what, if you think the axioms are 'true', what you can then truly say just using those ideas.

A way I was taught to read philosophical books and books from other subjects is, at first, to try not bring any external ideas to the authors words. The idea is to understand what the author says first, to then follow the logic, and if at the end you disagree, to then either find a fault in the logic and if not, the axioms, but you have to go with the axioms first.

And in this case I think Einstein hints strongly that he will be refining truth in an interesting way.

Line interval? I can't see how line intervals could remain the same with different people viewing them from points in the universe, at different speeds and then add light to the equation. Light bends right? See...I am at an unfair advantage because I don't know how things work...lol.

Look at your words, my guess is they are the result of Einsteins thoughts about things and your experience as an artist.

I think his idea of a 'line-interval' is this, if you and I look and place two objects a 'distance' apart, the 'distance' itself, if moved but not moved with respect to its endpoints would be the same wherever we put it. That sound right?

What makes the sky blue? I am damned and determined to keep up though...so I will continue to ask stupid questions...all of you please answer me when you can...even if you think it's just a given...and it would help if you talk baby talk...lol...I will not be offended.

The sky being 'blue' is the result of 'light' scattering-off dust particles, molecules and at bottom, photons and electrons. If you wish a great read about this, try "QED: The Strange Theory of Light and Matter; R.P.Feynman".

[artisticsolution]

A:My apologies AS, as my words were not math but logic from academic philosophy.

AS: Oh good, another barrier in my ability to understand.

A:I think the reason why so many do not "understand the basic reasons for math" is because of the way it is taught, i.e. without its historical context, and lately even out of historical sequence, e.g. they teach kids Set Theory first as for the Mathematician this is a logical underpinning for the rest of 'math'. Whilst this is fine for the budding mathematician, it can be puzzling to the rest.

AS: I can understand the reasons for society to use math. I can't understand it in a way that makes it useful to me. It would be like forcing someone to use a paint brush to make art when they did not see a reason for doing so. So for a person like me to be able to understand math, it would have to be taught using an "art" example.

A;If you are interested in how a philosopher can think then I think you could do worse than pick up a book on Propositional Logic. Most would say a beginners book but I'd go for something quite formal, e.g. "Truth-Functional Logic; J. A. Faris" to really start from the ground up.

AS: Thank you for the tip and I might get the book...my problem is when it comes to things like this usually an actual class helps me better that written word. I remember a thread where you and Richard were having a discussion about logic and I could not keep up with the way the words were being used. I might have kept up if it was in person though.

A:Which he says is because we forget that Geometry is like Logic, i.e. about the relationship between its ideas or axioms, and that, Geometry came from 'habits of thought' and the need to solve real world problems.

AS: Yes, but my thoughts were headed along the lines of a time in history when an axiom which was considered 'true' at the time failed us by comparison to the 'truth' we know today, i.e. when people thought the world was flat. There is no doubt that geometry is useful and logical to what we understand in today's world. What I question is it always going to be true in every scenario? Is it true in alternate universes, the 11th dimension, traveling faster than the speed of light? Could there be a universe that it is just the opposite? Where the rules of logic don't apply?

A:Here's where my 'academic philosophy' ears prickle, "He uses words like "truth" in quotation marks to show truth is relative", as whilst I agree that this is what he is doing, I'd question what you mean by "...show truth is relative"?

AS: By truth is relative I mean this: Saw this show on relativity once that said we are always in motion but on earth we feel like we are standing still. However, if we viewed it from another perspective we could see the earth is actually moving 4000 MPH. (Can't remember the real numbers sorry just giving the gist) however, it's not really moving 4000mph because if we could see it from yet another perspective, we could see that it is also rotating around the sun at 64,000 miles per hour...but again if we were outside the universe we could see it is moving at blah blah....and so on and so on. So just because we feel like we are standing still doesn't make it 'true."

I understand there is logic in our universe. But if the string theory is true and there are alternate universes that me be just the opposite of ours or anything for that matter, then wouldn't it stand to reason what the 'logic' would be different? It is in this respect that I feel our logic holds us back. I am just being stupidly abstract. I admit to not knowing logic at all. I can only relate my understanding of Einsteins words. I am probably making things too difficult and that has always been my problem with math. My fantasy world gets in the way...always and forever...I don't even know how I function most the time. I can only try to understand....but it's soooo hard.

A:From my perspective, he is identifying what we need to agree before we can say that something is 'true' or not about what we've agreed. And he is trying to explain how he, as a Physicist, understands how the logical ideas of Geometry are applied in Physics, i.e. Physics can look at Geometry as the movement of a 'rigid body' upon a practically 'rigid body', which is testable by making equivalent bodies(?)

AS: Yes, that is my understanding too. Except for the last part of your sentence, which I didn't understand. Do you mean he was trying to test it with examples?

A:Maybe I can help here. I agree that your thought is a naturally philosophical one. But the idea of Logic is not to tell you whats 'true' or 'false' with respect to the world, but what, if you think the axioms are 'true', what you can then truly say just using those ideas.

AS: Yes, Okay good...we can agree here. But how much can be known using 'just those ideas' is finite. And if we are trying to prove an infinite time or an alternate universe....then how does using an established axiom help? Don't we have to step outside the box to consider the 'world is not flat'?

A:A way I was taught to read philosophical books and books from other subjects is, at first, to try not bring any external ideas to the authors words. The idea is to understand what the author says first, to then follow the logic, and if at the end you disagree, to then either find a fault in the logic and if not, the axioms, but you have to go with the axioms first.

AS: While I was looking up anything I could get my hands on to make me understand relativity I cam across this video of how relativity is used today. They said the GPS system is one of the ways the theory of relativity is being used. It uses 12 satellites to find your position on earth to within 2 yards? Even when you are in motion. That's a pretty cool use. And it is logical...so of course you are correct. I am just reading more into it as usual. Okay, so what's the next thing? I started looking ahead and the math problems look very ominous...lol

A:]Look at your words, my guess is they are the result of Einsteins thoughts about things and your experience as an artist.

AS: How so?

A:I think his idea of a 'line-interval' is this, if you and I look and place two objects a 'distance' apart, the 'distance' itself, if moved but not moved with respect to its endpoints would be the same wherever we put it. That sound right?

AS: do you mean that if we put 2 object on a line they would look like they were in different positions relative to where we were standing but that they would actually be in the same place?

[artisticsolution]

A:I think his idea of a 'line-interval' is this, if you and I look and place two objects a 'distance' apart, the 'distance' itself, if moved but not moved with respect to its endpoints would be the same wherever we put it. That sound right?

AS: do you mean that if we put 2 object on a line they would look like they were in different positions relative to where we were standing but that they would actually be in the same place?

I've been thinking about your suggestion that if we "moved the distance" but "not moved the distance in respect to its endpoints would be the same no matter where we put it."

Yes, the distance would be the same but not the position of the whole line, if it was in motion. Then the coordinates would change and perhaps, if it was traveling faster than the speed of light, the distance would also change?

Here is the problem I am having, I am not quite sure that 'The distance' of the 2 points would remain the same "no matter where we put it." Suppose we put it at the entrance or inside of a black hole? Would the 'distance' between the 2 points still remain the same or would it stretch and change?

[artisticsolution]

In my quest to understand the simple terminology in Einstein's relativity, I inadvertently was directed to spacetime where I found this Wikipedia explanation about Euclidean Space:

"Our universe, being subject to relativity, is not Euclidean. This becomes significant in theoretical considerations of astronomy and cosmology, and also in some practical problems such as global positioning and airplane navigation. Nonetheless, a Euclidean model of the universe can still be used to solve many other practical problems with sufficient precision."

I understood this but most of my time is spent reading shit I can't understand. I wish I had someone to help me....freaking science makes my brain hurt.

[artisticsolution]

Okay, I am now up to 'space and time and classical mechanics.' I like how honest he is by saying we can't 'form the slightest conception' of space. And replaces the word 'space' with 'motion relative to a practically ridged body of reference.' I can 'see' this example because I can visualize our whole universe in motion.

It's a little harder for me to 'see' the difference between 'body of reference' and 'system of coordinates'...

When he talks about the system of coordinates "Rigidly" attached to the ground vs. the carriage, I take this to mean the system of coordinates are not yet moving (relative to the 'thing' they are attached to) but can and will at a later time in his description of relativity.

Then he says, "With the aid of this example it is clearly seen that there is no such thing as an independently existing trajectory (lit. path curve), but only a trajectory relative to a particular body of reference."

Okay, This is why sometimes language confuses me. Why would he make a point of changing "Body of reference" to a "system of coordinates" and then turn around and use 'body of reference' in a point he was making about Trajectory? Why waste his breath on the whole "system of coordinates" thing? It makes me think I am missing something important about what he is trying to say. I hate when people make it complicated when no such complication exists. And if he does mean the 2 to mean separate things then why not spell it out and then use it in that manner the whole time. Don't say "we are going to call a rose a daisy" and then turn around and call it a rose! WTF? Maybe I am just being impatient...

And this is where he lost me completely...

"Each of the observers determines the position on his own reference-body occupied by the stone at each tick of the clock he is holding in his hand."

Can anyone tell me what this means?

[Arising_uk]

Hi AS,
You raise many points and questions and for once I think the best way for me to reply is to explain my approach to reading this book.

The main thing to remember is that even if we understand what Einstein is saying in this book, most of us will still not understand his Theory of Relativity. Why? Because the actual theory is written in Mathematics and not in a Natural Language, so there will be no "understanding" it in a very real sense.

In the preface he says that what he is trying to do in this book is to give an "insight" to the educated layman of the ideas and issues that led him to formulate the theory in the first place. So I think that if we do understand this book it will at least give us the grounding to decide whether other natural language explanations we hear by other authors are plausible(or make sense) or not.

The thing with reading such a book is that our cultural-world is now replete with metaphors about 'Relativity' and we tend to bring those understandings to the ideas in this book. But the problem is that they come from the ideas in this book in the first place, so are not that useful in understanding it, is my take.

The way I'm approaching it is to assume that Einstein is going to be true to his word and treat the "empricial foundations" in a "step-motherly" way, so the first few chapters are like the axioms that he talks about in Euclids Geometry. I have to make a meaning of them that allows me to accept what he says about them before I can progress to what he says next.

So, I accept that he says that Geometry can be Physics if we accept the idea that a 'distance'(line-interval) is the same as having a rigid-body with two marks upon it. In my earlier reply to you I think I over complicated the idea by making 'distance' sound like an abstraction of some sort, but I think the easiest way to explain his idea is that if we have a practically straight stick and we make two marks upon it, we would agree that we have a 'distance' and no matter how we move the stick about we'll still have the same 'distance'.

If so, then he says you now understand that he understands Physics as the search for practically-rigid bodies and testing if they obey the Laws of Euclids geometry, i.e. he is testing for what the 'geometry' of the real world is.

The next chapter Part 1.2 starts by saying that if you agree to this then we can now start to measure this 'distance', i.e. 'find' its length. We do this by using a set 'distance'(a rod S, obviously smaller than the 'distance' we are measuring) and count how many times this 'distance' fits the original 'distance', this'll be its length. In fact he says this is the basis for all "measurement of length".

He then goes on to talk about the "system of co-ordinates" based upon this idea but I'll stop here as there's a lot I don't understand about this new stuff.

In general I think its useful to remember that this is not a philosophy book, its a book by a Physicist trying to explain how he thinks about Physics and why it led to his theories. As such we need to get his 'axioms' or definitions first.

a_uk

[Eliza]

I have just started reading this book. So if anyone is still out there and up for discussions, I'll certianly join in. I am approaching this from the aspect of attempting comprehesion of his perspective vs. application as inconsistencies can make it difficult to do so.