The burn mark problem

[Jack_]

Don't be so fucking lazy, Jack.
If you pay attention to what peple say and put in the effort required to understand, you'll learn a lot and get a lot smarter.

On the other hand, if you're happy with how smart you are and much you know know now, feel free to keep your head in that bucket.

LOL, you have no idea what I can do.

I read the response and from my logic, AN says very little.
Just because it is some deep thought to you that is you and not me.

Did you ever consider I read right through his noise where he did not achieve the objective.

Do you remember what is what?

Specifically, outlines and describe the components of LT and expalin them.

Since AN is unable to do it, perhaps you can then.

Let me know when you figure out the term +-(v/c)d switches between the two light emission points in the frame.

See, I am already there.

 

[Jack_]

Again with the clocks?

Shit on a fucking shingle, Jack, how can you be so thick? I've seen Tellytubbies episodes with more to say.

Time, Jack. Not clocks. Time doesn't need clocks.

Time, distance, and motion form a triad. Any two imply the third.

d = vt
v = d/t
t = d/v


Jack,
Are you claiming that there is no such thing as time?
Do you think that you can form a meaningful mathematical model of reality without time?
If so, then SR is the least of your worries. You should instead work on proving that Newtonian mechanics is inconsistent.

I gave you time in this experiment. You seem so caught up on it.
Did you need help understanding it? It is just as devastating to SR.


Assume the standard configuration using O and O'
Each agree in their own frames they will start a clock at co-location and stop the experiment when the time reaches an agreed upon d/c where d is some chosen agreed value between the two.
When the experiment ends, they mark a measuring rod in their own frames only describing the positions and distances.

Here is what O marks.
BM-------(v/c)d-------O>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>d

Here is what O' marks.
O'>>>>(v/c)d>>>>O>>>>>>>>>>>>>>>>>>>>>>>>>d

They get back together after the experiment with their rods in the same frame and compare them.
BM--------(v/c)d--------O>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>d..Measurin g rod of O
O'>>>>>(v/cd>>>>>O>>>>>>>>>>>>>>>>>>>>>>>>>d................ ..............Measuring rod of O'

By matching up O and O', they find two different light paths.

All is consistent with SR with the following conditions met in each frame.
1) Light is measured c in each frame
2) The light emission point in the frame is located at the observer in the frame.
3) O and O' are separated by their relative motion caused by v. While light moved d, the frames diverged by (v/c)d
4) Light travels d in ct.= c(d/c)

Hence, SR is the theory of two different light paths.

 

[AlphaNumeric]

You say very little.

So its my fault you can't explain yourself properly and I had to ask you to clarify your poorly worded request? You wanted me in this thread from the off. Just because I say things you don't want to hear doesn't mean I'm going to go away now you've tired of me.

x' = ( x - vt )λ

x' = xλ - vtλ

What is xλ and what is vtλ. Pleae be specific on their meaning and why they are in the equation.

Then expain the subtraction.

x-vt is a shifting of the origin of your coordinates due to the fact the new frame is moving relative to the old one and thus their origins have a time dependent relative displacement. λ is the dilation factor which is needed in order to leave $$ds^{2} = -dt^{2} + dx\cdot dx$$ invariant, since translations of the type x-> x-vt are not symmetries of the metric alone. In order to leave ds invariant the time components also transform, since dx'/dt is non-zero, and thus results in the space-time interval under going a rescaling which is in turn countered by the Lorentz factor which you're labelling λ.

Not that any of this has anything to do with the fact you've not justified your claims, you're throwing terminology around in a way which suggests you are unfamiliar with it and that you are failing to grasp what is little more than a class exercise.

You complain I say very little to you but when I ask you direct things you seem to ignore them.

 

[Pete]

What? The starting line is a member of each frame. Remember? We had two frames co-locate at the starting line.

Now, are you claiming you know specifically where this line is in space?

The starting line is a line painted on the ground. We know specifically where it is on the surface of the Earth.

Do you agree that it makes sense at the end of race to say that the race started where the starting line is now?

Or do you claim you know specifically where this line was in space at the start of the race?

 

[Jack_]

The starting line is a line painted on the ground. We know specifically where it is on the surface of the Earth.

Do you agree that it makes sense at the end of race to say that the race started where the starting line is now?

Or do you claim you know specifically where this line was in space at the start of the race?

Yes, sure, if you are going to choose a preferred frame, I guess that works. But, then we are no longer doing SR.

 

[Jack_]

So its my fault you can't explain yourself properly and I had to ask you to clarify your poorly worded request? You wanted me in this thread from the off. Just because I say things you don't want to hear doesn't mean I'm going to go away now you've tired of me.

x-vt is a shifting of the origin of your coordinates due to the fact the new frame is moving relative to the old one and thus their origins have a time dependent relative displacement. λ is the dilation factor which is needed in order to leave $$ds^{2} = -dt^{2} + dx\cdot dx$$ invariant, since translations of the type x-> x-vt are not symmetries of the metric alone. In order to leave ds invariant the time components also transform, since dx'/dt is non-zero, and thus results in the space-time interval under going a rescaling which is in turn countered by the Lorentz factor which you're labelling λ.

Not that any of this has anything to do with the fact you've not justified your claims, you're throwing terminology around in a way which suggests you are unfamiliar with it and that you are failing to grasp what is little more than a class exercise.

You complain I say very little to you but when I ask you direct things you seem to ignore them.

x-vt is a shifting of the origin of your coordinates due to the fact the new frame is moving relative to the old one and thus their origins have a time dependent relative displacement.

No, insufficient.

time dependent relative displacement

what is this specifically and why.
also why is it equal to the exact value of the difference in the light emission points.

Also, explain whe the frames consider their light emission points to be correct.

Again, you have said very little.

Do you need help?

 

[Jack_]

The starting line is a line painted on the ground. We know specifically where it is on the surface of the Earth.

Do you agree that it makes sense at the end of race to say that the race started where the starting line is now?

Or do you claim you know specifically where this line was in space at the start of the race?

Or do you claim you know specifically where this line was in space at the start of the race?

Yes, I know how to find this.

 

[James R]

LOL, you have no idea what I can do.

I've developed a very good idea of what you can do - and more significantly what you can't do - just from reading this thread.

You have a large ego, but lack the knowledge to back it up.

 

[Pete]

Or do you claim you know specifically where this line was in space at the start of the race?

Yes, I know how to find this.

So after the race is run, you think that it is wrong to say that the starting line still marks the starting point of the race?

When someone runs a 100m race, it is sensible to say that they ran 100m, right?

 

[Pete]

I am OK with your calculation.

It is consistent with the fact that the light beam in O' starts at O' and ends up a distance d/? from the BM which has been my point all along.

Hooray! You see that SR is consistent!

You agree that according to O', the light flash has travelled a distance d/λ from the BM by the time the burn mark reaches O'.
And you also agree (from the calculations shown above) that this is what is predicted by SR, according to what we know about O.

However, when O' moves to the BM, the O from has the light beam d + (v/c)d down the x-axis.

Note the disagreement.

You seem to be in the midst of editing that first sentence, but your meaning is clear enough.
Yes, in rest frame O at time t=d/c, the light flash is a distance d+(v/c)d from the burn mark.

You imply there is a disagreement, but I say that your calculations are wrong, that you incorrectly just apply length contraction and don't follow the rules of special relativity. Let's see what happens when we do it properly.

Consider the light flash in O at the time that O' meets the burn mark.
At this time:
t=d/c
The light flash is at:
x=d

SR says that this event occurs in O' at:
$$x' = \gamma(x + vt)$$
$$t' = \gamma(t + \frac{vx}{c^2})$$

$$x' = \gamma(d + vd/c)$$
$$t' = \gamma(d/c + \frac{vd}{c^2})$$
$$t' = x'/c$$

Note the agreement: O' also claims that the light reaches λ(d + vd/c) at t'=λ(d + vd/c)/c

(Note that these transformations can be performed much more elegantly using the tools described by Alphanumeric. However, using them comfortably requires a deeper understanding of geometrical maths methods than I possess.)

So, you see that your calculation of x'=λ(d + vd/c) is correct, but you fail to consider according to SR, the light reaches this value of x' at a later time in O', well after O' reaches the burn mark.

 

[Pete]

Again, you have said very little.

Again you have problems understanding concepts that are not that difficult.

You clearly want help, because you're too lazy to put in the small modicum of effort required.

 

[Pete]

Yes, sure, if you are going to choose a preferred frame, I guess that works. But, then we are no longer doing SR.

Sure we are. This is Galileo's idea from 400 years ago, carried over into SR unchanged.

Galileo's whole point was that these sort of terms (like "where" and "stationary") are relative, and make sense as long as you state or imply a reference frame.

Since the implied frame of reference is the race track, it makes perfect sense to say that the race started at the starting line.

You could also state another frame of reference (such as the Sun), and say that the race started hundreds of kilometers away in whatever direction if you wanted.

Or if the race was on board a ship, you could also sensibly consider the ship's motion relative to the sea.

Note that this isn't about special relativity - it's even simpler.

 

[Pete]

Hence, SR is the theory of two different light paths.

Yes, Jack.
The starting location of the light flash depends on your chosen frame of reference.
This is nothing new. The idea dates back at least to Copernicus and Galileo.

So what's your point?

 

[AlphaNumeric]

Again, you have said very little.

Because you are vague in what you ask and the origin of the individual components is largely irrelevant. It's a change of basis which is constrained by the space-time metric. It's like asking where sin and cos come from in a rotation of a 2d plane, they are the most general expressions which leave the space-time metric invariant when combined in a way determined by ds.

Further more you have completely failed, in both this thread and the one in the maths forum, to respond to any direct questions I have asked you. You don't respond to my explaination that SR is as consistent as Euclidean geometry. You don't respond when I ask you to justify your claims. You don't respond when I point out your misuse of terminology.

You throw about things like 'decidable'. Are you familiar with such concepts on a working level? This is another way of saying "Do you have mathematics knowledge equivalent to a mathematics graduate". If so where did you get it. If not why are you throwing such terms around. I've tried to engage you in a discussion on such things as the geometry of groups, which is relevant to the examination of Lorentz transformations, but you haven't responded to any of that. If you are as educated in all this as you'd like us to believe why are you ignoring anyone who tries to take the conversation down a path which requires a working maths knowledge?

Do you need help?

Yeah, why don't you explain what the point of your questions are and then I'll know how to phrase my responses. You being vague doesn't mean you can then turn around and say "Oh look you couldn't respond in such a way as to meet my undefined vague criteria" and claim some kind of victory.

Pete is willing to discuss the specifics of Lorentz transforms on the coordinates. To be perfectly honest, as I've said before, I find doing that extremely tedious. Getting bogged doown in a particular case doesn't lead to anything interesting in my opinion. It's much better to talk about the Lorentz structure of a system as a whole. For instance, special relativity is used all the time in quantum field theory (which is something which would test the kind of experiments you keep pitching and it's enormously accurate) but when you're formulating the question "Is this quantum field theory Lorentz invariant" you don't put in the 4x4 matrix general expression for a Lorentz transformation, you use the fact the Lagrangian is a Lorentz scalar, ie all space-time indices are contracted. Then you know that no matter what convoluted experiments with accelerating particles here and there and at different times it is impossible to construct a system which violates Lorentz symmetry.

This kind of fundamental building Lorentz symmetry into a theory is one of the first things you cover when doing quantum field theory. Around the time time in GR you find out how to show that GR has an underlying local SR symmetry. Can you tell me how this is done? Its one word, I just want to see if you know it.

Pete is obviously willing to talk about the specifics of a component by component Lorentz transformation. I'm happy to talk to you about the issue of Lie groups and their relation to the kind of geometry used in physics. You previously get narked I'd dared to 'lecture' you on mathematics, as if you are already a well read person in it. I haven't seen you display any kind of knowledge I wouldn't expect a 1st year physics undergrad to know. Of course I haven't seen all your posts so if you have an example of you cracking out some serious mathematics I'd appreciate a link to it. I, unlike you, don't mind if I happen to be wrong. Though you (and other hacks) might not think it, I acknowledge I am wrong a lot.

 

[Jack_]

I've developed a very good idea of what you can do - and more significantly what you can't do - just from reading this thread.

You have a large ego, but lack the knowledge to back it up.

Well thanks James R.

 

[Jack_]

So after the race is run, you think that it is wrong to say that the starting line still marks the starting point of the race?

When someone runs a 100m race, it is sensible to say that they ran 100m, right?

You are correct if we pick the earth as a stationary frame.
So, that is the starting point in the earth frame.

I thought we were talking about 2 frames.

 

[Jack_]

Hooray! You see that SR is consistent!

Existential quantification does not imply universal quantification .

You agree that according to O', the light flash has travelled a distance d/λ from the BM by the time the burn mark reaches O'.
And you also agree (from the calculations shown above) that this is what is predicted by SR, according to what we know about O.

I do not agree with this above. O has noithing to do with O' being stationary and concluding d/λ. That would be frame mixing.

You seem to be in the midst of editing that first sentence, but your meaning is clear enough.
Yes, in rest frame O at time t=d/c, the light flash is a distance d+(v/c)d from the burn mark.


You imply there is a disagreement, but I say that your calculations are wrong, that you incorrectly just apply length contraction and don't follow the rules of special relativity. Let's see what happens when we do it properly.

I know what LT calculates.

But, let's focus on the BM problem because that is what this is about.

How, I changed the problem slight to clear up your confusion by having each frame run the experiment internally for a time t=d/c and mark on a rod
1) Their position
2) The other frame's position
3) The position of the leading edge of the light beam.

We then bring the two back together in the same frame and compare the rods.
I am afraid I have circumvented LT all together and if LT is consistent, it should make sense.

Well it does not.

So, you see that your calculation of x'=λ(d + vd/c) is correct, but you fail to consider according to SR, the light reaches this value of x' at a later time in O', well after O' reaches the burn mark.

It is the case that t' will be much later under LT for this.
But, LT does not match the burn mark problem

I think the smoke is now clearing.

Now that you know what LT says, think the problem through and see what you come up with without LT. Any intelligent person can do this.

hat is why I did it again for you only in the context of the stationary frames.

You mentioned several times something about learning.

Let me know when you have done the problem without using LT and using only pure logic.

The answers are different and that is the point of this thread.

 

[Jack_]

Again you have problems understanding concepts that are not that difficult.

You clearly want help, because you're too lazy to put in the small modicum of effort required.

You have absolutely no idea what I am thinking.

Are you claiming to be a mind reader?

 

[Jack_]

So you've given up the idea that time is not relevant to your experiment, then. Good.

Yes, Jack.
The starting location of the light flash depends on your chosen frame of reference.
This is nothing new. The idea dates back at least to Copernicus and Galileo.

So what's your point?

Let me make sure I understand you.

Are you now agreeing with the fact that SR is the theory of multiple light emission points?

 

[Jack_]

Because you are vague in what you ask and the origin of the individual components is largely irrelevant. It's a change of basis which is constrained by the space-time metric. It's like asking where sin and cos come from in a rotation of a 2d plane, they are the most general expressions which leave the space-time metric invariant when combined in a way determined by ds.

Further more you have completely failed, in both this thread and the one in the maths forum, to respond to any direct questions I have asked you. You don't respond to my explaination that SR is as consistent as Euclidean geometry. You don't respond when I ask you to justify your claims. You don't respond when I point out your misuse of terminology.

I posted a very clear and concise proposal for you on your concept of a consistent space from applying LT in the other thread.

You will find you will not be able to answer it and hence I gave you an extremely direct answer on your opinion you will not find elsewhere.

So, answer over there as I do not want to repost it here.

You throw about things like 'decidable'. Are you familiar with such concepts on a working level? This is another way of saying "Do you have mathematics knowledge equivalent to a mathematics graduate". If so where did you get it. If not why are you throwing such terms around. I've tried to engage you in a discussion on such things as the geometry of groups, which is relevant to the examination of Lorentz transformations, but you haven't responded to any of that. If you are as educated in all this as you'd like us to believe why are you ignoring anyone who tries to take the conversation down a path which requires a working maths knowledge?

Like I said, I gave you a very specific example in the other thread without simply tossing around words. Like I said, I will provide the answer to the question and prove it mathematically. If you are all this in SR you will be able to provide an answer and prove it also.

Once you give up, let me know and I will step up and solve the problem.

Yeah, why don't you explain what the point of your questions are and then I'll know how to phrase my responses. You being vague doesn't mean you can then turn around and say "Oh look you couldn't respond in such a way as to meet my undefined vague criteria" and claim some kind of victory.

Victory to me is putting someone into a contradiction. I think you are describing your own version of victory.

This is why I asked you specifically asked to explain LT. You see, you are the one that claimed to know all about it.

We will see what happens from there.

Pete is willing to discuss the specifics of Lorentz transforms on the coordinates.

Pete is doing homework problems, not explaining the reasoning behind the LT equations and further not thinking through the BM problem without LT.