The Relativity of Simultaneity

[Dywyddyr]

Unlike Einstein's methods, my numbers are not based on suspicion, assumption of convenience, pretend, superstition, religion, nor were they implanted in me by aliens.

Or actual hard experimental evidence.

Gee, I wonder if they're based on ignorance (I note you carefully didn't include that in your list).

 

[Motor Daddy]

This would be extremely tough. Last I checked, the embankment moved with the Earth and the Earth rotated at 330m/s while in revolution around the Sun with 30km/s while the Sun moved wrt the distant stars at 337km/s. Tough!

That's something you'll have to address with Einstein, it's his example. I'm just sticking with the example and telling you like it is. It is impossible for the embankment to NOT be at a zero velocity.

 

[Motor Daddy]

Or actual hard experimental evidence.

Gee, I wonder if they're based on ignorance (I note you carefully didn't include that in your list).

Suspicion, assumption of convenience, and pretend are Pete's words describing the process of determining a frame's velocity.


Maybe you can help Pete? Tell me how you determine a frame to be at rest? Start by telling me what you mean by the term "at rest." At rest compared to what? What facts or definitions do you base your pretend zero velocity of a frame? Prove the velocity of the frame, whether it is zero or greater than zero. Prove it!

 

[arfa brane]

Motor Daddy, would you agree that a frame of reference has three coordinates in space and one in time? That's a real dunbass question, because of course any point has t,x,y,z coordinates; I think you know this, you're just acting like a dumbass.

Then the velocity of two frames of reference is just about whether the distance between them changes, in time? It doesn't make any real sense to talk about velocity if you have only one frame of reference?

 

[Tach]

That's something you'll have to address with Einstein, it's his example.

No, it isn't. It is your very own madness.

I'm just sticking with the example and telling you like it is. It is impossible for the embankment to NOT be at a zero velocity.

lol, few ideas but fixed

 

[James R]

Motor Daddy:

You haven't replied to post #389.

Also:

Maybe you can help Pete? Tell me how you determine a frame to be at rest? Start by telling me what you mean by the term "at rest."

Pete's method is fine. Send a light pulse in both directions between two points. If they have the same travel time, then the two points are at rest in the frame of the clocks that are being used to make the time measurements.

Prove the velocity of the frame, whether it is zero or greater than zero. Prove it!

You can't prove it with some kind of theoretical argument. You need to actually go out into the real world and make real measurements.

 

[Pete]

You miss my last post, MD, or are you ignoring it?

Remember that we're conducting this exercise in a purely mathematical world.
If you want to talk about the real world, we'll need to do some real experiments, and I don't have any atomic clocks and a few kilometres of precision engineered wire handy.

The observers in this exercise might have to suspect, assume, or pretend certain things, but we do not. You and I must be able to rigorously predict every measurement made in this mathematical world from the assumptions we agreed on.

So unless you can rigorously predict the behaviour of a wave moving through a wire from the agreed assumptions, you're just guessing. If you want a constant velocity signal, you'll have to either prove that your chosen signal behaves as you suspect, or construct something from the agreed assumptions.

Like this, for example:
The embankment observer sends two robots from the midpoint of the stick to each end. Each robot carries a clock, and passes one metre ruler every second as measured on their clocks.
As each robot reaches the end of the stick, they start the clocks there simultaneously.

 

[Motor Daddy]

Then answer my questions and stop beating around the bush. You assume the length of a stick in the train.

There is a pile of different length sticks in the train. The train observer picks one. Tell me how he determines the length of the stick in meters, using light to measure the length.

You avoid the question like the plague, because you can't do it, so your mathematical world falls apart.

In order to know the stick's length he must first measure the one way times. You ASSUME the train is always at a zero velocity. You ASSUME light takes the same time to travel the length of the stick each way.

Show me. I'll let you assume the two clocks are perfectly in sync. You do believe that two clocks could be in perfect sync, don't you?

We can't proceed with this exercise until you honestly answer my questions and measure the length of the stick using light. You don't even know how to measure using light. It's laughable, Pete.

 

[Pete]

Then answer my questions and stop beating around the bush. You assume the length of a stick in the train.

There is a pile of different length sticks in the train. The train observer picks one. Tell me how he determines the length of the stick in meters, using light to measure the length.

You avoid the question like the plague, because you can't do it, so your mathematical world falls apart.

He can't measure it using embankment-standard metres, unless he knows how fast the train is moving relative to the embankment.
He can measure it using train-standard metres, as previously described.

In order to know the stick's length he must first know the velocity of the train.

Correct.

You ASSUME the train is always at a zero velocity. You ASSUME light takes the same time to travel the length of the stick each way.

I am not the train observer. My assumptions are clearly stated. In this exercise, the embankment is defined to be at rest.

The train observer assumes the train is at zero velocity, because he can't prove that he's moving.
The embankment observer does the same.

Show me. I'll let you assume the two clocks are perfectly in sync. You do believe that two clocks could be in perfect sync, don't you?

We can't proceed with this exercise until you honestly answer my questions and measure the length of the stick using light. You don't even know how to measure using light. It's laughable, Pete.

I've answered that already, MD. More than once.

You don't seem to understand, Pete.

For instance, there is a stick on the train. How does he determine what the length of the stick is, using the speed of light and the unit of measure "meter?"

He uses his clocks to time how long light takes to travel from one end to the other, of course.

If he is given synchronized clocks, then he can determine his velocity, and adjust for time dilation to get accurate measurements in the embankment standard.

If not, then he can only get measurements in the train standard.

How is the embankment observer going? Can he prove that the embankment is at rest?

 

[Motor Daddy]

Motor Daddy, would you agree that a frame of reference has three coordinates in space and one in time? That's a real dunbass question, because of course any point has t,x,y,z coordinates; I think you know this, you're just acting like a dumbass.

Then the velocity of two frames of reference is just about whether the distance between them changes, in time? It doesn't make any real sense to talk about velocity if you have only one frame of reference?

It makes perfect sense. If a light source in space emits light, one second later the light sphere will have a radius of ~299,792,458 meters. If the source moved during that one second, the source will not be at the center of the sphere. The distance from the center of the sphere to the point the source is at one second is the distance the source traveled in one second.

It has nothing to do with another object.

Sure, you can measure relative velocity between two objects. That's not what I'm talking about, and that is not an absolute velocity.

You can say a train traveled down the tracks 50 meters per second, relative to the tracks. You can also say that the tracks had an absolute velocity of 25 m/s in one direction, and the train had a 25 m/s absolute velocity in the other direction. The later being a measure of the distance each traveled in space, relative to being measured by light.

 

[Motor Daddy]

He can't measure it using embankment-standard metres, unless he knows how fast the train is moving relative to the embankment.
He can measure it using train-standard metres, as previously described.

There is not two standard meters, Pete, there is one, and that is the distance light travels in a vacuum in 1/299,792,458 of a second. Tell me exactly how the train observer measures the length of a random stick, using light.

 

[Pete]

There is not two standard meters, Pete, there is one, and that is the distance light travels in a vacuum in 1/299,792,458 of a second. Tell me exactly how the train observer measures the length of a random stick, using light.

The embankment standard is not available to the train observer.
He has no choice except to define his own standard.
What else would you suggest he do?

What don't you understand about using his clocks to time how long light takes to travel from one end of the stick to the other?

 

[Motor Daddy]

The embankment standard is not available to the train observer.
He has no choice except to define his own standard.
What else would you suggest he do?

What don't you understand about using his clocks to time how long light takes to travel from one end of the stick to the other?

Again, there is not an "embankment standard meter" and a "train standard meter." There is one standard, which is defined by light travel time.

How does the train observer measure the length of a random stick, using light? I will not proceed until you answer the question. You skirted the issue earlier when you tried to use a formula with a "v" in it, of which you didn't know the value of v.

Specifically tell me how the train observer measures the length of the stick on the train.

 

[Pete]

Do you not understand the train-standard metre? It's not difficult.

I assume you want the train observer's measurement to be in embankment-standard metres.

We've established that the train observer can't make any measurement in embankment standard metres without knowing his velocity.

If he has synchronized clocks at each end of the train, he can measure his velocity by timing a light flash forward and rearward:

Forward time = 2 ticks
Rearward time = 0.5 ticks
$$\frac{v}{c} = \frac{2/0.5 - 1}{2/0.5 + 1}$$
v = 0.6 c

If he knows his velocity, he can measure the length of a stick:
Put a timer at one end of the stick and a mirror at the other.
Send a flash from the timer to the mirror and back again.
t' = elapsed time in kiloticks
t = elapsed time in seconds = gamma.t'
L = length of stick = c.t/2

Edit:
Made a mistake, and forgot to allow for the different forward and rearward propagation times along the stick.
The last line should be:
L = length of stick = t(c+v)(c-v)/2 = c.t' / 2.gamma

 

[Pete]

Goodnight.
Have you discovered that in this mathematical world, the embankment observer can't prove he is at rest?

 

[Motor Daddy]

Do you not understand the train-standard metre? It's not difficult.

I assume you want the train observer's measurement to be in embankment-standard metres.

No, you assume wrong. I want the length of the stick in meters, as defined by the one and only standard definition of a meter.

We've established that the train observer can't make any measurement in embankment standard metres without knowing his velocity.

Why do you insist that there is an embankment standard meter and a train standard meter? Show me in the definition of a meter where it says "train" or "embankment."

If he has synchronized clocks at each end of the train, he can measure his velocity by timing a light flash forward and rearward:

Forward time = 2 ticks
Rearward time = 0.5 ticks
$$\frac{v}{c} = \frac{2/0.5 - 1}{2/0.5 + 1}$$
v = 0.6 c

If he knows his velocity, he can measure the length of a stick:
Put a timer at one end of the stick and a mirror at the other.
Send a flash from the timer to the mirror and back again.
t' = elapsed time in ticks
t = elapsed time in seconds = 1000.gamma.t'
L = length of stick = c.t/2

But in your mathematical world, the train observer always assumes his train to be "at rest," correct?

 

[Motor Daddy]

Goodnight.
Have you discovered that in this mathematical world, the embankment observer can't prove he is at rest?

Wrong again.

1. We've already established that the embankment has an absolute zero velocity in reality. You agreed that in this situation, it would be impossible for the embankment to have any other velocity other than zero, because A and B on the train aligned simultaneously with A and B on the embankment, and when they were aligned the lightening strikes occurred, simultaneously. The embankment observer was equal distance from A and B, and the lights impacted him simultaneously. The ONLY velocity the embankment could have had was a zero velocity. The same can't be said for the train observer because the light impacted him at different times. So it is impossible for the train observer to correctly conclude that it was the embankment that was in motion, and the train was not in motion ("at rest"). That means the train was in motion, period!


2. The embankment observer can perform the same procedure as the train observer measuring a random length stick, and will find the one-way times to be identical in each direction. The only way that is possible is if the embankment was at a zero velocity.

3. Tell me how, in your mathematical world, the train observer can assume to be at rest, and at the same time say the train had a velocity, in order to accurately measure the length of the stick?

4. My measurements of the stick on the train and the stick on the embankment are dead nuts accurate, because they were both measured using light, and light travels independently of frames, so the light travel times already reflect the frame's absolute velocity, or lack thereof.

 

[Motor Daddy]

Motor Daddy:

You haven't replied to post #389.

Motor Daddy:
We're comparing the train's clocks with the embankment's clocks here. An observer on the train does not think the train's clocks are dilated in any way. The train observer says the embankment clocks are dilated, because in the train's frame the embankment moves and the train is at rest. And the reverse applies to the embankment observer, who says his own clocks are fine and the train clocks are dilated.

The train observer can't conclude correctly that the train was at rest and the embankment was in motion, because the lights impacted him at different times. The train observer must conclude that since A and B on the train were aligned with A and B on the embankment when the lightening strikes occurred at A and B, that the train was in motion. It's not up for debate, the train must have been in motion and the embankment must have been at an absolute zero velocity. The train observer is dead wrong to assume the train is at rest. It's not an opinion, it's a fact!

The train isn't at rest with respect to the tracks. It is travelling at 0.5c along the tracks. Or, equivalently, the train is at rest and the tracks are travelling backwards at 0.5c relative to the train.

Wrong, it is not possible for the embankment to have been in motion.

No. The train is always at rest in its own frame. How many times do I need to say that? Every object is at rest in its own frame. If you understand what a reference frame is, as you say you do, then this one is a no-brainer.

No, what you mean is that it is assumed by Einstein that everyone can assume their frame to be at rest and the other frame to be in motion. That is simply false. Things don't work that way in the real world. The embankment in this example can't be in motion, it is simply impossible. That means the train observer is wrong to assume his train to be "at rest." Furthermore, if you say the train observer can assume correctly to be at rest, tell me how he determines the length of a random stick. He can't assume to be at rest and also assume to have a velocity. Take your pick, James, which one is it?

The train travels at 0.5c relative to the tracks. That's the only thing that matters.

No, that's not the only thing that matters. That is simply relative motion. That says nothing about the absolute motion of each the train and the tracks. The relative motion could be 50 m/s, while the absolute motion of the train could be 25 m/s in one direction, and the tracks have an absolute motion of 25 m/s in the opposite direction, in the same duration of time.

There is no absolute zero velocity. Only relative zero velocity. And the train is not at zero velocity relative to the tracks. It's at 0.5c.

No, you're wrong again. If a source in space emits light and one second later the source is at the center of the light sphere, then the source had an absolute zero velocity, and likewise, if the source is not at the center of the light sphere then it had an absolute velocity greater than zero, relative to the point in space that is the center of the light sphere, which is the point in space where the source originally emitted the light.

Yes, you can work in any frame you like, including on in which the train travels at 274,000 m/s with respect to that particular frame. But the question you asked concerned how far ahead of the train the light was in the embankment frame or the train frame, so I worked in the two frames you asked about. Obviously.

So I am correct to assume the train to have a 250,000 m/s velocity, and you are correct to assume the same train to have a 789,000,000,000,000,000,000 m/s velocity? Basically, you can randomly pick any velocity you desire and say that is the velocity of the train, and be correct, without performing any measurements. That's absurd, James, and you know it!!

Yes. Just pick any frame that is not stationary relative to the train and the tracks. For example, use a frame travelling in the direction of the train at 0.1c. In that frame, the tracks are travelling backwards at 0.1c, and the train is travelling forwards at less than 0.5c.

Wrong, that would be stupid to assume such such a thing. To always be able to assume any velocity you desire is absolutely absurd! The embankment in this exercise can not possibly have a velocity greater than zero because the lights impacted the embankment observer simultaneously, and they impacted the train observer at different times. That is not a reversible situation, James.

No they aren't. There's no reference to any absolute zero frame in the definition of the metre and the second. A brief internet search will quickly confirm that for you.

If a meter stick is in motion the times can't possibly be the same in each direction. it's simply impossible, because light travels independently of objects.

You must use the definitions that actual physicists use. You can't just make up your own and pretend they are real.

I use the standard definition of the meter. You, however, like to pretend that there is a different standard meter for each different frame. Like Pete, who continuously refers to an embankment standard meter and a train standard meter. There is ONE standard meter, not two or more!!!

Not true. The Lorentz transformations give a precise translation between spacetime coordinates in any two frames. They allow us to convert lengths and times between frames. But when you've done the conversions, you find that lengths and times are relative (i.e. frame-dependent - different in each frame). There's no problem with that. Relativity is completely self-consistent. Unless you can show that it isn't, that is.

Wrong, in this example, it is impossible for the embankment to have been in motion. It was the train that was in motion. The train observer is flat out wrong to assume he was at rest and the embankment was in motion. He is just flat out wrong! The situation is NOT REVERSIBLE!!!

 

[Pete]

No, you assume wrong. I want the length of the stick in meters, as defined by the one and only standard definition of a meter.

Why do you insist that there is an embankment standard meter and a train standard meter? Show me in the definition of a meter where it says "train" or "embankment."

The train observer can't use the standard metre as traditionally interpreted on the embankment. He has no choice except to interpret it in a way that he can actually use.
I call this adaptation the "train standard metre", and I use the term "embankment standard metre" for the traditional interpretation.

But in your mathematical world, the train observer always assumes his train to be "at rest," correct?

No, he does not. He would in fact prefer to know what the train's velocity actually is.
Since he can't determine that velocity, he is forced to make an assumption that is consistent with his measurements, and the most natural assumption to make is that the velocity is zero.
He could use any other assumed train velocity, but it wouldn't be as convenient for most requirements.

Wrong again.

1. We've already established that the embankment has an absolute zero velocity in reality. You agreed that in this situation, it would be impossible for the embankment to have any other velocity other than zero, because A and B on the train aligned simultaneously with A and B on the embankment, and when they were aligned the lightening strikes occurred, simultaneously.

Yes we have established that.
But the embankment observer has not.

The same can't be said for the train observer because the light impacted him at different times. So it is impossible for the train observer to correctly conclude that it was the embankment that was in motion, and the train was not in motion ("at rest"). That means the train was in motion, period!

In this exercise, the train is definitely in motion, and the embankment is definitely at rest. There is no dispute about that.

The dispute is whether the embankment observer can prove it.

The embankment observer can perform the same procedure as the train observer measuring a random length stick, and will find the one-way times to be identical in each direction. The only way that is possible is if the embankment was at a zero velocity.

The train observer also gets identical one-way times if he has to synchronize his own clocks. ([post=2753794]post 393[/post]).

4. My measurements of the stick on the train and the stick on the embankment are dead nuts accurate, because they were both measured using light, and light travels independently of frames, so the light travel times already reflect the frame's absolute velocity, or lack thereof.

You are not the embankment observer, MD. Only the train and embankment observers make measurements. You and I calculate the results of those measurements in this mathematical world.

I agree that the embankment observer's measurements are accurate.
But he can't find a way to prove it.

 

[Pete]

MD, there's a very relevant question that has been asked a few times and not answered.

The train observer really wants to know the train's velocity, and use the standard metre and second rather than defining an ad hoc 'train standard'.

What do you advise him to do?

The only suggestion I can give him is to keep records using the train-standard until he has access to the embankment again, so he can then convert all his train-standard measurements into proper measurements.