Relativity and simple algebra II

ralfcis:

Your analysis is not correct here, but it would take me another lengthy post to do a full derivation to show clearly what you did wrong. Remember that when we're dealing with the length of anything, including a measured length a "start" line and a "finish" line for some journey, two spacetime events are involved when we're just dealing with one reference frame, corresponding to the locations in space of the two lines and the simultaneous time that those two locations are measured. If we then want to look at the same journey in a different frame, then a third spacetime event usually needs to be introduced, because the events that simultaneously mark the locations of the "start" and "finish" lines in one frame will not be simultaneous in the different frame. Therefore, the two frames will not agree on the "length" of the journey, or on the time taken for a spaceship, say, to make the journey.

In the Alice/Bob example of Alice taking a trip, relativity shows that, during the trip, if Bob says that Alice's spaceship is travelling at constant velocity v at all relevant times, then Alice will say that Bob is travelling at velocity -v at all relevant times.

Don't be silly. It was me who pointed out exactly what the difference is, in the first place. You're responding to my post #98, where I explained exactly what the difference is, and even put a label on the quantity $\gamma v$.

Don't try to put words in my mouth, please.

I have no problem with "proper velocity" or "celerity" or whatever you want to call it being valid in relativity, as long as we all understand what we're talking about when we use that concept. That is, as long as you accept the definition in post #98, I have no problem with it at all.

As for me being previously unaware of it, that's not true. I was a little silly in that I didn't think of it previously. That was probably because it came up in this thread in an unusual context. In the general theory of relativity - or in the 4-vector formulation of special relativity - proper velocity is important in defining a number of important physical quantities, which relativistically preserve certain important types of conservation laws and the like.

I have never heard it referred to as "Brehme velocity" before. I've never heard of "Loedel lines", either. The various texts and research papers on relativity that I have read have not used those terms, and they did not come up in my formal studies of relativity.

Okay. The main thing is that we both work to make sure we understand each other. If we think we're talking about the same thing when really we're talking about two different things, that makes the conversation a waste of time for both of us.

It's fine. I'll assume that when you write Y, it's the same as $\gamma$. That is:

$Y=\gamma=\frac{1}{\sqrt{1-(v/c)^2}}=\frac{c}{\sqrt{c^2-v^2}}=\frac{c}{\sqrt{(c+v)(c-v)}}= \dots$

 

ralfcis:

The Earth frame is the same as Bob's frame, isn't it?

Bob is stationary at all times relative to the Earth, in your scenario in which Alice travels out from Earth and back again while Bob stays on Earth.

What is this "background frame" you mention? Who or what is stationary in the "background frame"?

Can you please show me how you calculate 3/5c from -1/3c and +1/3c?

What is the frame of the "Loedel diagram". Can you show me a "Loedel diagram"? What is a "Loedel diagram"?

That's all fine. I'm happy to refer to the Earth/Bob frame as "stationary" and the Alice frame as "moving". We both agree that, in Alice's frame, Alice considers herself "stationary" and Bob to be "moving".

We also both seem to agree that there are no preferred frames - no frame is "absolutely" at rest. I don't know what the "background frame" is that you mentioned above, though.

No. It's not stuck on that.

All I'm saying is there's nothing in the universe we can point to and say "that's absolutely at rest". You agree with that, don't you?

It seems to me that in your Alice and Bob example, we only need Alice and Bob. Why do we need two more "participants"?

But your red "Alice" line in that diagram is in motion in the 'x' coordinates of your diagram, so this diagram doesn't show Alice as "stationary".

Yes, because most diagrams like this are drawn with the x coordinate increasing to the right, whereas yours increases to the left. Yours is a kind of mirror-image diagram, compared to what we usually see.

We agree that, from Alice's perspective, she stays still and Earth flies away from her.

All of space is "blank" in this scenario, except for Alice and Bob (or Earth, if you prefer). It's not clear what your "background coordinates" are attached to. Who or what is stationary in your "background" coordinates? Is there anything?

Space isn't a substance. You can't measure the speed of "space".

A vacuum is a region of space that contains nothing. You can't move "nothing", so I guess it's okay to say you can't move a vacuum.

It's sort of the same thing as saying you can't move the hole in a doughnut. The hole isn't a thing you can move. The doughnut is a thing you can move.

I agree about space. Light, on the other hand, can be thought of as little particles: photons. Those are things that can move from one place to another.

Relative to the blank space? The blank space is not a thing. You just said that, didn't you?

I don't know what you mean by that. Clocks in different frames tick at different rates, but given coordinates of a spacetime event in any one frame, all other frames can always calculate what the equivalent coordinates of the event would be according to their own clocks.

Could you please supply the equations or transformations you use to convert to a "Loedel" diagram or frame, or whatever it is?

Really?

What are the alternative postulates you're using for your "Epstein depiction"?

As far as I can tell, Epstein diagrams are fully consistent with the "assumptions of relativity".

In what way was it "doctored"?

Are you saying that Minkowski diagrams are incorrect, or tell lies, or something?

 

ralfcis:

This is the first time I've come across Epstein diagrams.

I've done a little reading up on them. As far as I can tell, they are just another way of illustrating spacetime events, using a system of polar coordinates rather than Cartesian ones. They are fully consistent with special relativity.

I do not believe that Epstein supports/supported the "non-constancy of c as a velocity". Epstein diagrams seem to assume that c is the same in all frames, consistent with SR.

I think you might be unnecessarily tying yourself in knots trying to understand Epstein diagrams, especially when you seem so confused about the basics of the Alice/Bob example.

I suggest that, in our ongoing conversation, we leave discussion of Epstein until late - at least until after you have responded to my posts #58 and/or #71/72.

When are you going to get to those, by the way? Do I have to wait months? A year?

Above, you claimed you were responding to my post #27, but then you went off onto this tangent about "reverse Minkowski" diagrams and then Epstein, so that you didn't really respond to my post at all.

Do you think you can possibly stay focussed long enough to try responding directly to the points I put to you in posts #71 and 72, say? Could you please try that now?

Minkowski didn't fudge his diagram. What are you talking about? Minkowski diagrams are straightforward. They just plot space on one coordinate axis (one dimension only, obviously), and time on the other axis (or ct, which is just a "scaled" time coordinate).

As far as I can tell, so far from my reading on this, that's not all it does.

But we can discuss this later.

You should realise that Epstein's book, in which he introduces his diagrams, is an idiosyncratic, non-mainstream view of relativity. It's not "wrong", but it requires careful reading. Here's an extract from one review:

The myth is introduced with the idea of “enabling the inquiring mind to feel at home in a mysterious universe” (page 77). It is a unique and appealing idea, and it works. We are asked to believe that everything always travels at the speed of light. When an object is “at rest”, it is actually traveling at the speed of light through time; as speed through space increases, speed through time decreases. By imagining the arrow that describes the velocity as rotating in a space-time diagram, the results of the first 4 chapters can indeed be easily visualized. The myth has some problems, however.

Dr. Epstein never clearly points out that his space-time diagram is not the standard space-time diagram. Maybe this doesn’t matter to a reader who has no professional interest in the subject, but if any readers go on to study relativity seriously, they will be very confused. The myth seems to blur the distinction between proper time and coordinate time, in particular the fact that proper time is different for each different reference frame seems to get lost when Epstein talks about the twin paradox, especially in figure 5-11. His description of the resolution of the paradox occurs in a figure caption and is very weak. His attempt to explain the reasons behind the myth fails dismally.​

 

My advice would be to forget about general relativity completely at first, and just concentrate on special relativity.

The mathematics of special relativity only requires algebra, for the most part. To understand general relativity, on the other hand, you need to be very familiar with calculus, for starters. It also helps to have a good understanding of linear algebra. Many physics majors who encounter general relativity for the first time at Masters or PhD level usually find that they have to learn all about tensor calculus from scratch, as well as lots of technical stuff about metrics, affine connections and other esoteric mathematical topics.

If I were you, I'd get a decent book that just covers special relativity, first.

Here's a really good one you can download for free. At least one of the writers is a giant in the field of relativity:

http://www.eftaylor.com/spacetimephysics/

 

Well, maybe I'm just not understanding your answers. It doesn't look to me like you've answered most of my questions.

I'd appreciate it if you could respond point-by-point to posts #71 and 72, saying which parts you agree with and which parts you disagree with. That would be very helpful in narrowing down the territory in which we might potentially disagree.

For the most part, it seems like your numerical results reproduce the results of special relativity. That's not surprising, since for the most part you seem to be using the equations of special relativity to calculate things.

What I'm trying to figure out is where you think SR has problems, or is wrong. You talk of things like Minkowski "fudging" his diagrams, for example, but you don't point to anything specific that would show any "fudging". And then, occasionally, you make claims that relativity is "stuck" on something or can't deal with some problem you think you've cracked, but when questioned on specifics you just start talking about something different.

I've already done that. Where your analysis has generated different answers to the ones SR would provide, I have shown you how SR would calculate its answers, so you can compare.

You are very welcome to point out any errors you have found in SR's methods, or in my use of SR in analysing your scenarios. I invite you to do that.

You complain about the thread ballooning, but you keep introducing new material and new ideas all the time, without ever dealing with objections to one of your ideas or calculations or graphs before moving on to present a different one, or three.

Look: it's easy. I'm making it easy for you. Forget that we're up to post #109. Just respond to posts #71 and 72. Just two posts out of 100. And we'll see how we go after that.

If, on the other hand, you're unwilling or unable to engage with my objections at this time, for whatever reason, then I'll stop wasting my time for now. I'll leave you to think about what I have written, and if you ever come up with some answers to questions and objections I have put to you, we can talk about it after you finally respond.