The Relativity of Simultaneity

[arfa brane]

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.

Are you saying here, that a 'source' of light can determine how far it has moved after one second, by seeing how far a spherical wavefront of light that was emitted, has traveled in the same second? An observer at the source can see this wavefront expanding spherically around them, and use it as a reference?

 

[Motor Daddy]

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?

I've already described how to do it properly on the train. I even told you how to start with a stick of unknown length. Look at post 452 very carefully. You don't seem to understand what the train observer did there. He measured a stick of unknown length on the train, by measuring the TIME it takes for light to travel from one end to the other, in opposite directions. Those times reflect the actual velocity of the train, and using the equation I used in that post, you arrive at the correct length of the stick, according to the definition of the standard meter. From that you can calculate the velocity of the train.

I repeat, the light travel times already reflect the velocity of the train, because light travels independently of frames.

 

[Motor Daddy]

Are you saying here, that a 'source' of light can determine how far it has moved after one second, by seeing how far a spherical wavefront of light that was emitted, has traveled in the same second? An observer at the source can see this wavefront expanding spherically around them, and use it as a reference?

The point is that you can see what an absolute velocity is in that example.

When you have two sources separated by a distance, and the sources emit light simultaneously, where the lights spheres meet in the middle is the midpoint. It doesn't matter what the sources do after they emit light, the lights will meet at the original midpoint in space. If an object was at that midpoint when the lights were emitted, and the object is not struck by the lights simultaneously, then the object had an absolute velocity. It's not even debatable!

 

[Neddy Bate]

What do you advise him to do?

I've already described how to do it properly on the train. I even told you how to start with a stick of unknown length. Look at post 452 very carefully. You don't seem to understand what the train observer did there. He measured a stick of unknown length on the train, by measuring the TIME it takes for light to travel from one end to the other, in opposite directions. Those times reflect the actual velocity of the train, and using the equation I used in that post, you arrive at the correct length of the stick, according to the definition of the standard meter. From that you can calculate the velocity of the train.

I repeat, the light travel times already reflect the velocity of the train, because light travels independently of frames.

He already told you, in post 457, that you are not allowed to use your wire-pulling synchronization method, because no one knows how the motion of the train will affect it.

Can you re-work your post 452 without the wire-pulling synchronization method?

 

[Motor Daddy]

He already told you, in post 457, that you are not allowed to use your wire-pulling synchronization method, because no one knows how the motion of the train will affect it.

Can you re-work your post 452 without the wire-pulling synchronization method?

Use whatever method you need to to get the clocks in absolute sync as accurately as you can. Using light is not going to work because light travels independently of frames.

Suppose I tied the ends of the wires to scales and hooked the scales on each end of the train. I made each wire equally taught to start, so that the scales each read 10 lbs of force. I then cranked the handle. Are you saying that one scale would increase in force at a greater rate than the other? It doesn't have to be wire, it could be gears, or mechanical devices to sync the clocks, using equal force to "pull the triggers" on the clocks, that are calibrated prior to "start" at exactly the same amount of force.

 

[Neddy Bate]

Use whatever method you need to to get the clocks in absolute sync as accurately as you can. Using light is not going to work because light travels independently of frames.

Suppose I tied the ends of the wires to scales and hooked the scales on each end of the train. I made each wire equally taught to start, so that the scales each read 10 lbs of force. I then cranked the handle. Are you saying that one scale would increase in force at a greater rate than the other? It doesn't have to be wire, it could be gears, or mechanical devices to sync the clocks, using equal force to "pull the triggers" on the clocks, that are calibrated prior to "start" at exactly the same amount of force.

Well, you might notice that Einstein uses light to synch his clocks. So obviously you two are not working with the same model.

None of the sync methods you mentioned are allowed. Pete already showed you that moving clocks along the train makes them tick faster if you move them toward the rear, and slower if you move them toward the front. The same kind of thing will happen with all of the sync methods that you mentioned. In one direction, the method will run slow, and in the other direction it will run fast.

 

[Motor Daddy]

Well, you might notice that Einstein uses light to synch his clocks. So obviously you two are not working with the same model.

None of the sync methods you mentioned are allowed. Pete already showed you that moving clocks along the train makes them tick faster if you move them toward the rear, and slower if you move them toward the front. The same kind of thing will happen with all of the sync methods that you mentioned. In one direction, the method will run slow, and in the other direction it will run fast.

You're full of it. That's Einstein's crap, not mine.

I can use whatever method I deem appropriate to accurately sync two clocks. Einstein doesn't set the rules in my world, I do. Who the heck is he to tell me what I can and can't do? I will pull the triggers on each clock with exactly the same amount of force, and they will start in sync.

He doesn't want anyone to sync clocks, as that would prove his theory wrong. Using sync'd clocks makes his house of cards crumble!

And who the heck is he to tell me it's impossible to measure an absolute velocity? I did it! Take that, Einstein! Eat your words!

 

[Pete]

I've already described how to do it properly on the train. I even told you how to start with a stick of unknown length. Look at post 452 very carefully. You don't seem to understand what the train observer did there. He measured a stick of unknown length on the train, by measuring the TIME it takes for light to travel from one end to the other, in opposite directions.

You might be right, but you haven't proved it. You haven't responded to post 457:

It doesn't matter how long it takes to start each clock, the point is that they start simultaneously.

It certainly matters.
In this mathematical world, motion affects clocks, which includes all time-related processes such as tension waves through materials.

You have a wave moving through a wire. How does that motion affect the process of signal propagation?

I don't know, and neither do you.

I'll use any method necessary in order to measure as accurately as I can.

Please do. That means you must be able to accurately predict the result of your method in this mathematical world.

You are adding an assumption to the mathematical world of this exercise regarding the way that tension waves propagate through materials.

The mathematical world is defined as follows:
Assumptions:

• The embankment is at rest
• Light travels at c with respect to the embankment
• Clocks on the embankment are synchronized with each other
• The train observer knows that light travels at c with respect to something at rest
• The train observer doesn't know that the embankment is at rest
• The train observer doesn't know that the embankment clocks are synchronized
• The train observer has precise clocks, but he doesn't know if they're synchronized
• Moving clocks run slowly by the Lorentz factor
• Moving rulers are shorter in the direction of motion by the Lorentz factor

You want to add another assumption.
MD's extra assumption

• The time for a longitudinal wave to propagate through a given length of moving material is equal in each direction.

This assumption looks entirely reasonable, but I'm not sure if it's compatible with the time dilation aspect of this world.

But...
I defined the original mathematical world to both be mathematically compatible to Einstein's world and to retain absolute simultaneity. Your assumption breaks that compatibility, so I suggest a different assumption:

Pete's extra assumption

• The speed of longitudinal wave propagation through a material moving at speed v follows the same rules as the speed of timed mechanical motion along a moving surface.

For example, a robot that takes 1 step per tick of its clock will take more time to forward through the train than to move rearward. Under my assumption, the same applies to longitudinal wave propagation.
I suggest that this assumption is also reasonable.


So now we have two different mathematical worlds to consider.

One (your adaption) is not compatible with Einstein's world, and (as you correctly point out) allows all observers to identify their absolute state of motion and true synchronization.

The second (my adaptation), leaves the train observer and embankment observer unable to confirm their state of motion.


So far, this has been a productive exploration. Where will we go from here, MD?

I'd like to continue to explore the practicality of the train-standard. What about you?

 

[Neddy Bate]

I can use whatever method I deem appropriate to accurately sync two clocks. Einstein doesn't set the rules in my world, I do.

Yes, but you and Pete agreed to work in a mathematical world with certain rules. You're supposed to put your own world on hold. Pete is demonstrating that it is very difficult, perhaps even impossible, for the train to measure its own velocity using only light, sticks, and clocks. Sure you could do it with absolutely synchronized clocks, but it won't work if the clocks really aren't as perfectly synched as you think they are.

 

[Pete]

You're full of it. That's Einstein's crap, not mine.

I can use whatever method I deem appropriate to accurately sync two clocks. Einstein doesn't set the rules in my world, I do. Who the heck is he to tell me what I can and can't do? I will pull the triggers on each clock with exactly the same amount of force, and they will start in sync.

Yes, we all agree that in your mathematical world that will work.

But in this exercise, we're exploring my mathematical world. In my mathematical world, the signal (the tension wave) through the wires will take longer to reach the forward clock than the rearward clock, and the clocks will not be synchronized.

 

[James R]

Motor Daddy:

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.

Yes. And if Einstein's speed-of-light postulate is correct, then a source at the centre of the train will be at the centre of the sphere at all times in the train frame, since the speed of light in that frame is 299792458 m/s in both directions, and in the train frame the source never moves at all.

In the rest of this reply, my answers assume that Einstein's second posulate (about the constancy of the speed of light in all frames) is correct, and that your postulate that the speed of light varies between frames is incorrect. The only way to know whose postulate is actually correct is to look at real-world experiments, of course.

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.

In the train's frame, lights travelling from the centre to the ends impacts the ends at the same time. The light travels equal distances, as measured by the train rulers, at the same speed (in accordance with Einstein's postulate). Therefore, it takes the same time.

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!

You still seem to be struggling with the difference between the two frames. Do you understand that the walls of the train, for example, are always at rest in the train frame, and always moving in the embankment frame? We discussed what a reference frame is at length. Do you accept this statement, or not? If you do not, then the only possible conclusion is that you don't truly understand what is meant by "the reference frame of the train".

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.

In the frame of the train, the embankment must always be in motion. That follows from the basic definition of what a reference frame is. Do you need me to walk you through the definition again?

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.

Show me your real-world evidence that proves this.

I must have asked you to do this about a thousand times by now. But what have you provided in terms of real-world experimental evidence? Nothing. Nada. Zip. Nil.

If you want to make claims about the real world, you'll need to start supplying some real-world evidence at some point. Do you ever intend to actually do that?

The embankment in this example can't be in motion, it is simply impossible.

An empty, unsupported claim from you.

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?

To measure a stick he sends a light pulse along the stick and times how long it takes. The length of the stick is the travel time of the light multiplied by 299792458 m/s. Simple.

Of course, when you do it, you can't use 299792458 m/s unless you're in the embankment frame. Otherwise, you'll get the wrong answer because the speed of light in any other frame is different according to you.

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 motion. No experiment you can do will ever prove that the embankment is absolutely at rest. Equal travel times for light using the embankment clocks force you to conclude that the embankment is at rest in the embankment frame. But equal travel times for light using the train clocks force you to conclude that the train is at rest in the train frame, too. So is the train or the embankment really at rest? The question has no meaningful answer. All we can say for sure is that they have a relative velocity to one another.

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.

I've covered this at least three times now. See the top of this post for the latest.

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?

No. Nothing can move faster than light. You can pick any frame in which the train travels slower than the speed of light, though.

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!!

Not at all absurd. Yes, you can pick any velocity for the train that you like. The only thing that matters is that the relative velocity of the train and the tracks is always the same.

Examples:

1. Embankment at rest, Train at 50 km/hr.
2. Embankment at 50 km/hr, train at 100 km/hr.
3. Embankment at -25 km/hr, train at +25 km/hr.
4. Embankment at -50 km/hr, train at rest.
5. Embankment at 2219 km/hr. train at 2269 km/hr.

Options 1 to 5 are just different choices of reference frame. 1 happens to be the rest frame of the embankment. 4 happens to be the rest frame of the train. 2,3 and 5 are frames in which both the embankment and the train move.

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.

Which lights impacted the embankment observer simultaneously? Are you talking about one experiment or two here? I can't respond to this because it's unclear.

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.

Light travels independently of objects and your Motor Daddy "space". Therefore, in the stick's frame the times are always the same.

I use the standard definition of the meter.

No you don't. The standard definition makes no mention of an absolute rest frame.

You, however, like to pretend that there is a different standard meter for each different frame.

There is a different "standard metre" in each frame! Or, rather, the definition of the metre is the same in every frame, but when we compare metres between frames we find they are not the same length.

A metre in a particular frame is always the distance light travels in 1/299792458 seconds, as measured by the clocks in that frame. Since clocks in different frame tick at different rates, the "standard" metre in a frame has a different length than the "standard" metre in any other frame.

"Wait!", I hear you cry, "Clocks tick at the same rate in all frames!"

I say to you: prove it! Hint: You'll need some real-world evidence.

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.

What, exactly, is wrong with the statement I made? You can't just shout "wrong" and then talk about something else. Tell me exactly what is wrong about what I wrote in the quoted text here.

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!!!

Sure it is.

 

[Motor Daddy]

Motor Daddy:



Yes. And if Einstein's speed-of-light postulate is correct, then a source at the centre of the train will be at the centre of the sphere at all times in the train frame, since the speed of light in that frame is 299792458 m/s in both directions, and in the train frame the source never moves at all.

That simply can't be, James, because if you say the light from the center of the train impacts the ends of the train in the same amount of time, then you are also saying that lights emitted from the ends of the train simultaneously will reach the midpoint of the train simultaneously. But it is clearly stated in Einstein's chapter 9 that the lights impacted the train observer at different times.

You seem to fail to realize that the lightening strikes occurred simultaneously at A and B, and they DID NOT impact the train observer simultaneously. How do you reconcile the fact that the lights were emitted simultaneously at the ends of the train, and they reached the train observer at different times??

The rest of your reply bases its assumptions on Einstein's incorrect 2nd postulate.

I'll say it again, James, the situation is not reversible. The train observer can't justify the train being at rest and the embankment being in motion, because each observer was at the midpoint between A and B when the lightening struck A and B simultaneously. The embankment observer was impacted by the lights simultaneously and the train observer was impacted by the lights at different times. In order to reverse the situation, the train observer would have to be able to say that it was himself that was impacted by the lights simultaneously, and that the embankment observer had the lights hit him at different times. That must occur to be able to make the statement that the train was at rest and the embankment was in motion. The lights impacting the embankment observer simultaneously proves the embankment was at an absolute zero velocity. The lights impacting the train observer at different times proves the train was in motion. That is not a reversible situation!!!!

 

[Motor Daddy]

Yes, we all agree that in your mathematical world that will work.

But in this exercise, we're exploring my mathematical world. In my mathematical world, the signal (the tension wave) through the wires will take longer to reach the forward clock than the rearward clock, and the clocks will not be synchronized.

Let me get this straight. I hook a force meter to the wall at each end of the train and tie a rope to each of them and extend each rope to the center, where there is a crank that rotates a shaft. I attach one rope to the top of the shaft and one rope to the bottom of the shaft and slightly crank until the ropes are taught. I adjust as necessary so that the meters have the same force on them. I then crank the handle. Are you saying the force will build at different rates on each meter if the train has an absolute velocity greater than zero?

 

[Pete]

I'm saying that when you change the force on a rope, that change in force isn't immediately felt at the other end. It takes time for that change to get from one of the rope to the other.

And we know that in this world of time dilation, time depends on motion.

 

[Motor Daddy]

I'm saying that when you change the force on a rope, that change in force isn't immediately felt at the other end. It takes time for that change to get from one of the rope to the other.

And we know that in this world of time dilation, time depends on motion.

So you say if I crank for .1 second, at the .1 second mark it will read a greater force on one meter than the other meter?

 

[Pete]

So you say if I crank for .1 second, at the .1 second mark it will read a greater force on one meter than the other meter?

It might.
I don't know what it will do in this mathematical world.

Like I said, we'll have to make an assumption.

 

[Motor Daddy]

It might.
I don't know what it will do in this mathematical world.

Like I said, we'll have to make an assumption.

So you have doubts about the equation f=ma?

Do you also have doubts about torque being force times distance?

How about work? Do you have doubts about work, and HP, and watts?

Do you really doubt HP=torque*RPM/5252???

Do you doubt 1 HP=550 ft-lb of work per second???

 

[Pete]

Do you understand the concept of the propagation of a wave through a material?

Feel free to provide a rigorous derivation of a wave propagation equation under the given assumptions of this mathematical world, MD.

Or, you can accept that you're adding another assumption that might be true.

 

[Motor Daddy]

Do you understand the concept of the propagation of a wave through a material?

Feel free to provide a rigorous derivation of a wave propagation equation under the given assumptions of this mathematical world, MD.

Or, you can accept that you're adding another assumption that might be true.

You are doubting f=ma. Prove your assertion!

 

[Pete]

Prove yours
I make no assertion.