The Relativity of Simultaneity

[James R]

Motor Daddy:

For completeness, I will respond to your post about Einstein's thought experiment.

Let's look at Einstein's train thought experiment in Chapter 9. The Relativity of Simultaneity. Einstein, Albert. 1920. Relativity: The Special and General Theory.

Einstein conveniently forgot to put numbers to the thought experiment, so let's do it for him, shall we?

He didn't forget.

Real physicists work with algebra, calculus and other mathematical tools, not just arithmetic. They do that because doing it that way means that you solve more than one problem at a time. Moreover, you can look at your solutions and see which factors were important and which cancelled out during the analysis. Finally, you avoid all the messy streams of numbers, like the ones you've been posting. More on that in moment.

The observer on the train measures the time it takes light to go from the rear of the train car to the front of the train car, which is 11.9915 meters in length in the train frame. Light takes .00000004 seconds to travel the length of the train. That means the absolute velocity of the train is 4,958 m/s.

Why choose a train that is 11.9915 metres long? Why not make it 12 metres, or 10 metres? 11.9915 is just an arbitrary mess.

Or did you choose that number because you took the speed of light to be exactly 299792458 metres per second, and you wanted the travel time to be exactly 0.00000004 seconds?

The number 299792458 is not important in analysing this situation, you know. You can use 300000000 and the general conclusions will be the same. If time dilation and length contraction do not exist, then approximating the speed of light by 300,000,000 m/s won't affect that conclusion. For ease of calculation, you may as well use nice round numbers.

If you did use c=300,000,000 m/s, then in 0.00000004 seconds light would travel exactly 12 metres.

Your first error also appears here: measuring the travel time of light on the train tells you nothing about the speed of the train relative to the embankment.

The observer on the tracks measures the time it takes light to travel the distance between two clocks on the track, which is 1 meter. It takes light .0000000033356409519815204957557671447492 seconds to travel the distance, which means the track has an absolute zero velocity.

Again, measuring the light travel time on the track tells you nothing about the absolute speed of the track.

It is 10 meters from A to B on the train in the train frame, and 10 meters from A to B on the embankment in the embankment frame.

That's wrong, because in actual fact the embankment sees the train as length contracted, and vice versa. So, at least one of your figures must be wrong.

Both observers are at the midpoint between A and B in their respective frames.

Lightening strikes A and B as the two points on the train coincide with the two points on the embankment.

Coincide in space, or in time, or both? Spatially separated events that are simultaneous in one frame cannot be simultaneous in any other frame.

Light takes .000000016678204759907602478778835723746 seconds for each light from A and B to strike the embankment observer.

Ok. Then you're implying that the events at A and B occurred simultaneously in the embankment frame. That means they were not simultaneous in the train frame.

It takes .00000001667792893852027063502108370407 seconds for light to travel from B on the train to the train observer at the midpoint. It takes .000000016678480590418212900804736688488 seconds for light to travel from A on the train to the midpoint observer on the train.

Are those times measured in the embankment frame or the train frame? If they are supposed to be in the train frame, then they can't be different and you're wrong. I assume, therefore, that you're measuring the times in the embankment frame.

So, the train observer had the light from B impact him .00000000000055165189794226578365298441767877 seconds before the light from A impacted him.

Makes sense, since the train observer is moving towards the location of the strike at B and away from A.

Since the light from B impacted the train observer .00000001667792893852027063502108370407 seconds after 12:00:00 and it took light .00000001667792893852027063502108370407 seconds to travel from B to his midpoint position, the train observer concludes the strike occurred at B at exactly 12:00:00. Since the light from A impacted the train observer .000000016678480590418212900804736688488 seconds after 12:00:00 and it took light .000000016678480590418212900804736688488 seconds to travel from A to his midpoint position, the train observer concludes the strike occurred at A at exactly 12:00:00.

But you've measured the times in the embankment frame, then simply assuming that the times measured in the train's frame are the same. That's just wrong, and it's an assumption you have not established is valid at all.

So both observers acknowledge that the strikes occurred at exactly 12:00:00 at A and B.

No. Your mistake is that you've only used the embankment clocks here, and ignored the possibility that the train clocks say something different.

Absolute simultaneity!!!

Absolute, mistake-ridden rubbish.

 

[James R]

Motor Daddy:

You may wish to look at a detailed derivation of special relativistic time dilation and length contraction that I wrote back in 2004. Since you don't understand the basics at this stage, this may be a quick way of getting up to speed just a little. You only need to read one post.

[thread=95873]Special Relativitistic time dilation and length contraction derived[/thread]

 

[Neddy Bate]

Let's look at Einstein's train thought experiment in Chapter 9. The Relativity of Simultaneity. Einstein, Albert. 1920. Relativity: The Special and General Theory.

It simply boils down to the fact that the train observer and the embankment observer both agree that the strikes occurred at A and B simultaneously.

The embankment observer says that the strikes were simultaneous, because they reached her simultaneously, from equal distances away.


The train based observer says that the strikes were not simultaneous, because they did not reach her simultaneously, from equal distances away.


That is all.

 

[Pete]

The embankment observer says that the strikes were simultaneous, because they reached her simultaneously, from equal distances away.


The train based observer says that the strikes were not simultaneous, because they did not reach her simultaneously, from equal distances away.


That is all.

Hi Neddy,
That also relies on light approaching the train observer at equal rates from each end of the train, which isn't one of the premises in the particular approach I'm taking in this exercise.

 

[Motor Daddy]

James. I am arguing Einstein is wrong, why would I use his methods, or postulates? You seem to think that I have to use his methods and work under his postulates to prove him wrong. That's absurd.

 

[Motor Daddy]

The train observer doesn't yet know if his clocks are dilated or by how much, but we do.

No we don't know that. Where did you prove that? That stems from using Einstein's methods, not mine.

We've established that in the mathematical world we're working in, moving clocks run slowly.
So we conclude the train clocks are dilated, elapsing one tick every 1.0000000001367545 seconds.

We have NOT established that. Show me where we established that, other than you starting with that assumption, which I disagreed with at the beginning.

 

[Pete]

Remember the agreement:

Here's a deal for you:
We're considering two mathematical worlds: Newton's world and Einstein's world.
You think that Newton's world is a better match for the real world than Einstein's.
I think that Einstein's world is a better match.

If you agree that only actual measurements of the real world (ie experiments) can decide who is right, then I'll show you the numbers in Einstein's world, one small step at a time, so you can point out any problems.

Deal?

How about this. We have a deal, but first you prove to me a relativity of simultaneity exists before you start using it in your method of calculations. Show me your numbers of Chapter 9 and prove to me that a relativity of simultaneity actually exists as Einstein claims it does. Prove it! Show me the numbers!

Do you want to see the numbers in Einstein's mathematical world, or not?

 

[Motor Daddy]

Remember the agreement:




Do you want to see the numbers in Einstein's mathematical world, or not?

We are going step by step, hashing out our differences as they appear. You can't just start with the premise that clocks magically run slower or faster, and that rulers expand and contract, just like I can't say the train observer knows both strikes occurred simultaneously because we've established that as a fact on the embankment.

You've shown nothing to back up your assertion that clocks run differently on the train, or that rulers are contracted on the train. The train is a separate issue, of which the observer on the train knows only what he knows in his own little world.

 

[Motor Daddy]

If you agree that only actual measurements of the real world (ie experiments) can decide who is right, then I'll show you the numbers in Einstein's world, one small step at a time, so you can point out any problems.

Where are your actual measurements on the train that says the clocks run slower, and the rulers are contracted, just knowing what you know on the train? That's the deal, remember?

 

[Pete]

We are going step by step, hashing out our differences as they appear. You can't just start with the premise that clocks magically run slower or faster, and that rulers expand and contract, just like I can't say the train observer knows both strikes occurred simultaneously because we've established that as a fact on the embankment.

:shrug:
That's the agreement we made.
I said I'd show you the numbers in the world of length contraction and time dilation.
You said we had a deal.

 

[Motor Daddy]

:shrug:
That's the agreement we made.
I said I'd show you the numbers in the world of length contraction and time dilation.
You said we had a deal.

I quote the deal again:

If you agree that only actual measurements of the real world (ie experiments) can decide who is right, then I'll show you the numbers in Einstein's world, one small step at a time, so you can point out any problems.

 

[Pete]

You've quoted [post=2749117]post 129[/post] of this thread.
That post very clearly states that I would be working show tin the mathematical world of time dilation and length contraction.

And as you quoted, I said I'd show you the numbers in Einstein's mathematical world.
In return, you would agree that only actual measurements of the real world (ie experiments) can decide who is right.

We're not doing actual measurements in the real world here, MD.
I'm not actually looking at a train going past an embankment at 4958m/s.
I'm just typing on a keyboard and putting words on a screen.
We're working out the numbers in Einstein's mathematical world.

You asked for the numbers, over and over again. Now you're getting them.

The topic of this thread was brought up in another ([post=2749116]Light at Light speed[/post]), and I'm bringing it back here to avoid a major sidetrack in that thread.

Here's a deal for you:
We're considering two mathematical worlds: Newton's world and Einstein's world.
You think that Newton's world is a better match for the real world than Einstein's.
I think that Einstein's world is a better match.

If you agree that only actual measurements of the real world (ie experiments) can decide who is right, then I'll show you the numbers in Einstein's world, one small step at a time, so you can point out any problems.

Deal?

How about this. We have a deal, but first you prove to me a relativity of simultaneity exists before you start using it in your method of calculations. Show me your numbers of Chapter 9 and prove to me that a relativity of simultaneity actually exists as Einstein claims it does. Prove it! Show me the numbers!

I'll start from the assumptions that:

• the embankment is at rest
• light travels at c with respect to the embankment

then show that in the mathematical world of time dilation and length contraction:

• The train observer can't tell how fast he's going. His best measurements tell him he's at rest.
• He can't synchronize his clocks with the embankment clocks. His best synchronization methods make his clocks out of sync with the embankment clocks
• The clocks he synchronized as well as he possibly could tell him that the lightning strike at the front of the train happened before the lightning strike at the back of the train.

I'll go one step at a time, and wait for your questions and corrections before proceeding.

In return, I expect that if I am able to do this to your satisfaction, then you will agree:

• that Einstein's world is a logically consistent world, and
• that if actual measurements in the real world match Einstein's world better than your own conceptual model, then your own conceptual model is wrong at relativistic speeds.

Agreed?

 

[Motor Daddy]

We are using clocks, rulers, and light to measure with. We've shown that using the speed of light, and light travel time, that the embankment was at a zero velocity and that the train has a 4,958 m/s velocity.

So far we've established that the lights hit the train observer at different times. We've also established that the train observer doesn't know the velocity of the train, or even if the train is at a zero velocity. The only thing he knows for sure is that the lights hit him at different times, and that he is at the midpoint of the train.

Carry on with your measurements, like you agreed. If you can establish time dilation and length contraction in the train frame, by all means, go for it.

I know how to measure from within the train, do you?

 

[origin]

James. I am arguing Einstein is wrong, why would I use his methods, or postulates?

Here is the problem - you are doing more than saying Einstein is wrong, you are saying that real measurements of the speed of light are wrong.

Special Relativity was Einstiens theory that expalined the consequences of the actual measurements of the speed of light. Particularly the aspect that regardless of the reference frame the speed of light is always measured as c.

You disagree with this real world result (whether you realize it or not). You think that the speed of light is a constant similar to the speed of sound.
As an example; if you are on a train that is going .5 the speed of sound then any sound waves eminating from the train will move out in the direction of travel at .5 the speed of sound relative to the train, and will move out opposite to the direction of travel at 1.5 the speed of sound relative to the train.

Measurements and experiments have shown (for over 100 years) that this is not the case for light. Regardless of the motion of the light source or the observer the speed will always be measured as c. On a train that is moving at .5c a head light will have the beam move at c relative to the train AND relative to an observer on the bank.

Before any discussion of simultaneity can be considered you must explain why you are disregarding measurements of the speed of light. Or at least supply some evidence that your idea that the speed of light is somehow affected by the motion of the source.

I have asked you for evidence of your conjecture several times and you have ignored these requests. Since this concept is central to your analysis I would think that you would want to address it.

How about it?

 

[Pete]

This is my mathematical world, MD.
In this mathematical world, moving clocks run slowly and moving rulers are contracted.

You agree that the train clocks are moving. Therefore they run slowly, whether the train observer knows it or not.

Agreed?

I know how to measure from within the train, do you?

What do you suggest, MD?

 

[Motor Daddy]

Here is the problem - you are doing more than saying Einstein is wrong, you are saying that real measurements of the speed of light are wrong.

Special Relativity was Einstiens theory that expalined the consequences of the actual measurements of the speed of light. Particularly the aspect that regardless of the reference frame the speed of light is always measured as c.

You disagree with this real world result (whether you realize it or not). You think that the speed of light is a constant similar to the speed of sound.
As an example; if you are on a train that is going .5 the speed of sound then any sound waves eminating from the train will move out in the direction of travel at .5 the speed of sound relative to the train, and will move out opposite to the direction of travel at 1.5 the speed of sound relative to the train.

Measurements and experiments have shown (for over 100 years) that this is not the case for light. Regardless of the motion of the light source or the observer the speed will always be measured as c. On a train that is moving at .5c a head light will have the beam move at c relative to the train AND relative to an observer on the bank.

Before any discussion of simultaneity can be considered you must explain why you are disregarding measurements of the speed of light. Or at least supply some evidence that your idea that the speed of light is somehow affected by the motion of the source.

I have asked you for evidence of your conjecture several times and you have ignored these requests. Since this concept is central to your analysis I would think that you would want to address it.

How about it?

I've done so many times on this board. The meter is defined by light travel time. They are inseparable. If you say light traveled for 1 second, it is irrefutable that it traveled 299,792,458 meters, because a meter is defined by light travel time. You can not separate the distance and time. Do you understand that? If not, learn it, it is CRUCIAL!

It is also irrefutable that if you are 299,792,458 meters away from a light source when the light is emitted, if light doesn't impact you in 1 second, you moved, and from that you can calculate your velocity during that one second, because light always travels 299,792,458 m/s in a vacuum!

 

[Motor Daddy]

This is my mathematical world, MD.
In this mathematical world, moving clocks run slowly and moving rulers are contracted.

You agree that the train clocks are moving. Therefore they run slowly, whether the train observer knows it or not.

Agreed?


What do you suggest, MD?

Pete, are you suggesting that you are incapable of establishing time dilation and length contraction in the train frame? Are you now wanting to implement something that you haven't shown with actual measurements? We are dealing with actual measurements of distance and time using light. No magic tricks or illusions are accepted in this example.

Show me your measurements on the train using light, clocks, and rulers, and any other apparatus you need to sync the clocks.

 

[Pete]

One step at a time, MD.
We'll get to measurements on the train when we've agreed on the current step.

In this mathematical world, the moving clocks on the train tick slowly.

At t=0.000, the train observer's clock at M' reads t'=0.000, .

At t=16.67792893852027 ns , the slow M' reads 16.67792893623949 nanoticks (would it help if I say 'ticks' instead of 'seconds'?)

At t=16.67848059041821 ns , the slow M' reads 16.67848058813736 nanoticks.

Agreed?

 

[Motor Daddy]

One step at a time, MD.
We'll get to measurements on the train when we've agreed on the current step.

In this mathematical world, the moving clocks on the train tick slowly.

At t=0.000, the train observer's clock at M' reads t'=0.000, .

At t=16.67792893852027 ns , the slow M' reads 16.67792893623949 nanoticks (would it help if I say 'ticks' instead of 'seconds'?)

At t=16.67848059041821 ns , the slow M' reads 16.67848058813736 nanoticks.

Agreed?

I don't understand.

The train observer has clocks on the train that tick as one. Where does the difference come in play?

You say "At t=16.67848059041821 ns , the slow M' reads 16.67848058813736 nanoticks."

So are you saying that one clock on the train clicks t=16.67848059041821 ns, and the other clock on the train clicks 16.67848058813736 nanoticks???

So, one clock on the train clicks slower than the other clock on the train?? :shrug:

 

[Pete]

I don't understand.

The train observer has clocks on the train that tick as one. Where does the difference come in play?

No, so far only one train clock has been described.

You say "At t=16.67848059041821 ns , the slow M' reads 16.67848058813736 nanoticks."

So are you saying that one clock on the train clicks t=16.67848059041821 ns, and the other clock on the train clicks 16.67848058813736 nanoticks???

I'm saying that after 16.67848059041821 seconds (you can measure this using embankment clocks if you like, because we know that they're sync'd and not dilated), the M' train clock reads 16.67848058813736 nanoticks.