The Relativity of Simultaneity

[Motor Daddy]

Motor Daddy:

I'd like to ask you a couple of direct questions about measurements of the speed of light on the train vs. on the embankment.

Let us assume that we have a whole bunch of identical metre rulers. One set of these we align end-to-end along the embankment. The other set we nail to the floor of the train. For simplicity, let's take the speed of light to be 300,000,000 metres per second, and assume that the train is moving at half that speed, 150,000,000 metres per second. When the train is at rest, we measure its length (using either set of rulers) to be 300,000,000 metres (it's a very long train).

Now, suppose we send a light signal from the back of the train to the front while it is moving.

I have two questions for you:

1. How many embankment rulers does the light pass between leaving the rear of the train and arriving at the front?
2. How many rulers on the train does the light pass between leaving the rear of the train and arriving at the front?
3. How much time does the light take to travel from the rear to the front of the train in the embankment frame?
4. How much time does the light take to travel from the rear to the front of the train in the train's frame?

Can you answer these questions?

I hope to show you that you do not, in fact, believe that the speed of light is the same in all reference frames, despite your repeated claims that you do. Once I have your numbers, I'll only need one more post to do that.

(Note: you may assume, if necessary, that this particular embankment is absolutely at rest.)

I never said the speed of light is measured to be c in any reference frame but a zero velocity frame. You assume I mean that, I don't. I say the speed of light is constant in space, independent of objects. I've proven that to be the case with numbers.

As a matter of fact, I've shown the speed of light CAN'T be measured to be c inside a box that has a velocity in space. There is no way you can measure light to be c inside a box that has a velocity!

 

[Pete]

How about I have the embankment observer measure the train's clocks and rulers to firmly establish that they're dilated and contracted?

 

[Motor Daddy]

1. How many embankment rulers does the light pass between leaving the rear of the train and arriving at the front?

600,000,000

2. How many rulers on the train does the light pass between leaving the rear of the train and arriving at the front?

300,000,000

3. How much time does the light take to travel from the rear to the front of the train in the embankment frame?

2 seconds

4. How much time does the light take to travel from the rear to the front of the train in the train's frame?

2 seconds


As a matter of fact:

v=(ct-l)/t

 

[Motor Daddy]

How about I have the embankment observer measure the train's clocks and rulers to firmly establish that they're dilated and contracted?

The embankment is a separate issue from the train. The train observer has no knowledge of the embankment, and the embankment observer has no knowledge of the train observer. We are determining what each of the observers measures and comparing the two answers to see if they agree.

 

[Motor Daddy]

As per our agreement, this is exercise in the mathematical world of time dilation and length contraction.

In this mathematical world, it is a fundamental fact that moving clocks run slowly and moving rulers are contracted.

This mathematical world might or might not match the real world.

Do you accept that?

No, I don't accept that, Pete. So far we've only allowed what has been measured and known to be true. Now you want to bring in something that you haven't substantiated with measurements. We are talking about measuring distance and time with light, rulers and clocks, in two separate frames. If you can show time dilation and length contraction to be true using some sort of test in the embankment frame using clocks and rulers, be my guest. Otherwise, you are throwing in something that you haven't shown to be true, and I can't accept that.

 

[Pete]

The embankment is a separate issue from the train. The train observer has no knowledge of the embankment, and the embankment observer has no knowledge of the train observer. We are determining what each of the observers measures and comparing the two answers to see if they agree.

No. I'm showing you the numbers you asked for.
This is my exercise in my mathematical world, with my rules, which you agreed to right at the start.
We agreed on a number of assumptions that I am adhering to, including time dilation and length contraction of moving clocks and rulers.

Do you understand that it this mathematical world, moving clocks are absolutely dilated and moving rulers are absolutely contracted?

You don't have to accept that this mathematical world matches the real world. You only have to consider the possibility.

 

[Motor Daddy]

No. I'm showing you the numbers you asked for.
This is my exercise in my mathematical world, with my rules.
We agreed on a number of assumptions that I am adhering to.

I never agreed to time dilation and length contraction. I am saying that if you can show it to be true in the embankment frame, or the train frame, separately, without knowledge of the other, than I can agree to it.

Do you understand that it this mathematical world, moving clocks are absolutely dilated and moving rulers are absolutely contracted?

We are using the most basic means possible, that we know to be true. A meter is defined. A second is defined. The speed of light is defined. That is what we are working with, the very definitions of light, distance, and time. I said I will allow it if you can show it to be true using the definitions of light, the meter, and the second in either frame, with no knowledge of the other. That is the premise, that the train observer has no knowledge of the outside world, right?

You don't have to accept that this mathematical world matches the real world. You only have to consider the possibility.

We are working on finding the truth, not trying to make another illusion.

 

[Pete]

I never agreed to time dilation and length contraction.

Yes, you did. It was stated very plainly in the deal I offered and subsequent clarifications.

I said I will allow it if you can show it to be true using the definitions of light, the meter, and the second in either frame, with no knowledge of the other.

In what post did you introduce that limitation?

We are working on finding the truth, not trying to make another illusion.

Yes, we are working on finding the truth. I am suggesting that the truth might be that moving clocks are dilated and moving rulers are contracted. I am inviting you to first explore the consequences, and then see if it matches what we see in the real world.

You asked for the numbers, MD. I'm giving them to you.

 

[Motor Daddy]

Why can't you prove it before you use it? That's not to much to ask. Show that it is a real.

 

[Pete]

Because this is a hypothetical, mathematical world. We're saying what if moving clocks run slowly and moving rulers are contracted, and we're exploring the consequences.

To prove it, we'd have to see if actual real world experiments match those consequences. Do you have a fast train and extremely precise clocks handy?

 

[Motor Daddy]

Because this is a hypothetical, mathematical world. We're saying what if moving clocks run slowly and moving rulers are contracted, and we're exploring the consequences.

To prove it, we'd have to see if actual real world experiments match those consequences. Do you have a fast train and extremely precise clocks handy?

...and my point is, you've already agreed to a standard definition of a second and a meter for all frames.

 

[Motor Daddy]

To be continued...

I'm going to bed now, I'm tired.

Good night.

 

[Pete]

...and my point is, you've already agreed to a standard definition of a second and a meter for all frames.

No, I did not. My assumptions are clearly listed in our agreement.

In this mathematical world, the standard second is only reliable in the stationary frame of the embankment. A perfectly constructed cesium clock on the train will run slowly, because that is the nature of this mathematical world.

The same applies to the standard metre, since the standard metre relies on the standard second, and the train observer doesn't yet know how fast he's going, so he can't make the required adjustments for his velocity.

There are physical rulers on the train that were calibrated at rest, but they are length contracted, because once again that is the nature of this mathematical world.

So all the train observer currently has to perform measurements are his short rulers and slow clocks. He knows the rules of the world, so he can figure out how slow and how short they are and make the necessary adjustments if he could first figure out how fast he's going.

That's what we'll do next.

Are you ready to proceed?

 

[Pete]

I was hoping this would be a productive discussion, MD, but you keep trying to change the agreement.
It's very frustrating.

 

[James R]

Pete:

Hi James,
Would you mind if Motor Daddy postponed answering your questions until my exercise is done? I'm deliberately avoiding talking about reference frames so far, because there are differences in the way they're understood that adds confusion.

Looks like he has already answered them. I'm almost done here, anyway.


Motor Daddy:

I never said the speed of light is measured to be c in any reference frame but a zero velocity frame. You assume I mean that, I don't.

So, let's be clear. Your claim is that postulate 2 of Einstein's special theory is false. We have:

2. (Einstein) The speed of light is the same in all inertial reference frames.
2. (Motor Daddy) The speed of light is different in every reference frame, and only has the value 299792458 m/s in a single, absolute frame. In every other frame, the speed of light will have a different measured value.

Correct?

If that's right, then you need to stop making statements like this one:

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!

In the train's frame of reference, when light travels for 1 second, it does NOT travel 299,792,458 metres as measured in the train. Note that we MUST use the train's rulers for this measurement, or else we're not really working in the train's frame at all. You can't arbitrarily mandate that we must use rulers lined up along the track to measure the speed of light inside the moving train. The train's rulers must be used in the train's frame and the track's rulers in the track's frame. Anything else involves mixing up which frame you're working in, and dismisses the whole notion of what a reference frame is.

What is irrefutable is that IF your absolute picture of space and time were correct, then light must travel at different measured speeds in different frames.

I say the speed of light is constant in space, independent of objects. I've proven that to be the case with numbers.

By "space" you mean some unidentifiable, imaginary absolute reference frame. Since you admit that we can't ensure that any measure we make is ever made in that frame, then according to your theory every real-world measurement of the speed of light in any experiment ought to give a speed different from 299,792,458 metres per second, just as measurements in the train's frame give a different speed. In other words, measurements made on any embankment anywhere should never give 299,792,458 m/s for the speed of light.

And yet, they do.

Why? Are all embankments somehow magically stationary in your "space"? How can that be?

Or, perhaps you'd like to look at it another way. Maybe you assert that before we can get a corrected measurement of the speed of light, we first have to measure the speed of the embankment we're on, using - what? - light travel times in two directions. But again, strangely, in the real world, whenever this is done the travel times turn out to be the same, which give the embankment a speed of zero as measured using your own prescribed method. And, the kicker is that when you do a real-world experiment on the moving train using your method, we ALSO find that the train's speed is zero because the measured light travel times are the same in both directions there too.

So, from real-world measurements, we are forced to conclude that the absolute speed of every object in your "space" is zero, even when objects are quite obviously moving relative to one another.

Something is seriously wrong here.

Also, go back to your last statement quoted above: "I've proven that with numbers." No you haven't. What you have done is that you have shown that IF your assumption is true, THEN the light travel times on the train will be different in the two directions (for example). That's not a proof that your underlying assumption is true, and in fact it is false.

As a matter of fact, I've shown the speed of light CAN'T be measured to be c inside a box that has a velocity in space. There is no way you can measure light to be c inside a box that has a velocity!

Since we can't identify your "space" reference frame, then every real-world measurement of the speed of light must be wrong, according to you. And yet, every time we actually make such a measurement, whether on an embankment or on a moving train, the result we get is exactly 299792458 m/s.

In other words, you're claiming that it is impossible to make a measurement that thousands of people make every day - a simple measurement of the speed of light in a particular reference frame. You can even do it by shining a laser beam on a metal ruler and measuring a couple of angles. School kids can do it, but you say it is impossible.

This is called denial of reality.

No, I don't accept that, Pete. So far we've only allowed what has been measured and known to be true. Now you want to bring in something that you haven't substantiated with measurements. We are talking about measuring distance and time with light, rulers and clocks, in two separate frames. If you can show time dilation and length contraction to be true using some sort of test in the embankment frame using clocks and rulers, be my guest. Otherwise, you are throwing in something that you haven't shown to be true, and I can't accept that.

You have no more established your position with measurements than Pete has. You haven't gone out into the real world and measured light travel times, or done any other experiment to measure the speed of light. So, you're equally throwing in stuff you haven't shown to be true, and Pete and I can't accept that.

Why should anybody accept what you say over what Einstein said, or what Pete and I say? Appeal to common sense? Appeal to Motor Daddy's authority? Both of those are logical fallacies.

Bottom line: the only way to settle the argument is to look at real-world experiments. And guess what? The data is in. Einstein wins.

---

Regarding your answers to my questions:

1. How many embankment rulers does the light pass between leaving the rear of the train and arriving at the front?

600,000,000

2. How many rulers on the train does the light pass between leaving the rear of the train and arriving at the front?

300,000,000

3. How much time does the light take to travel from the rear to the front of the train in the embankment frame?

2 seconds

4. How much time does the light take to travel from the rear to the front of the train in the train's frame?

2 seconds

Just to be clear, when we work in a reference frame, we use the clocks and metre sticks in that frame. So, putting your answers to togther we have:

Speed of light in embankment frame = distance/time = 600,000,000/2 = 300,000,000 metres per second.
Speed of light in train frame = 300,000,000/2 = 150,000,000 metres per second.

i.e. according to Motor Daddy, the speed of light measured in the train frame is half the speed of light measured in the embankment frame.

To re-state: the speed of light is not the same in all reference frames, and so Einstein's posulate 2 is wrong according to Motor Daddy.

Hopefully, after all this, you can at least articulate exactly what your position is. Your position is that Einstein's speed-of-light postulate is false. You haven't proved that in any way, of course. All you have done is to say what would happen in the real world if your position were correct. And, as far as that goes, you're right.

Now, the only step you need to take is to look at some real evidence and reach the inescapable conclusion that the real world doesn't work the way you imagine it does.

 

[Motor Daddy]

Motor Daddy:



So, let's be clear. Your claim is that postulate 2 of Einstein's special theory is false. We have:

2. (Einstein) The speed of light is the same in all inertial reference frames.
2. (Motor Daddy) The speed of light is different in every reference frame, and only has the value 299792458 m/s in a single, absolute frame. In every other frame, the speed of light will have a different measured value.

Correct?

Correct. Except light always travels at the same speed. You mean to say that light is measured to be different if measured from a frame with a velocity.

So my postulate is: The speed of light is a constant. Measurements of the speed of light will vary depending on the velocity of the frame the measurements are taken in.

What is irrefutable is that IF your absolute picture of space and time were correct, then light must travel at different measured speeds in different frames.

Light travels at a constant speed in space. The speed of light is not determined or changed by another object's speed. If you are on the train moving .5c, you will measure light to be .5c in that train. Why? Because the speed of light is a constant in space, and you are traveling in space at .5c, so you will measure the light to be .5c. Light travels at c in space, independent of objects. The speed of light is not dependent on you measuring it, it is defined! It doesn't change.

You can think of a light source in space. Light is emitted and one second later the light sphere has a 299,792,458 meter radius. If the source were to have traveled during that one second, the source would not be at the center of the light sphere, it would be closer to the outer edge of the sphere, and from that you can determine absolute velocity of the source. So if a light was emitted in space, and one second later the light was 150,000,000 meters from the source, the source had a .5c absolute velocity. An absolute velocity of .5c relative to distance and time in space.

You say that the source is always at the center of the sphere 1 second later. That is pure rubbish, James, and you know it!!!

By "space" you mean some unidentifiable, imaginary absolute reference frame. Since you admit that we can't ensure that any measure we make is ever made in that frame, then according to your theory every real-world measurement of the speed of light in any experiment ought to give a speed different from 299,792,458 metres per second, just as measurements in the train's frame give a different speed. In other words, measurements made on any embankment anywhere should never give 299,792,458 m/s for the speed of light.

If a light travel time on an embankment is the same one-way as it is the other way, the embankment has a zero velocity, so you are wrong. If the times are different a velocity can be calculated. Simple as that. Think of a light sphere, James. You can't understand that because you think the source is always at the center 1 second later. You are dead wrong!

 

[Motor Daddy]

I was hoping this would be a productive discussion, MD, but you keep trying to change the agreement.
It's very frustrating.

Proceed. I don't agree with it, and I certainly don't accept time dilation and length contraction, but I don't want to be charged with delay of game.

 

[Pete]

I'm not asking you to think it's part of the real world, I'm asking to accept it in this artificial mathematical world.

Can you accept that?

 

[Motor Daddy]

I'm not asking you to think it's part of the real world, I'm asking to accept it in this artificial mathematical world.

Can you accept that?

I can accept that it's part of the math, but not reality. Yes.

I am saying my way is the reality of light, distance, and time.

 

[Pete]

I can accept that it's part of the math

Thankyou. That's all I ask.

Recap - the story so far:

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

The scenario

Point A and point B are marked 10 metres apart on the embankment.
Point A' is moving, marked on the back of the train.
Point B' is moving, marked on the front of the train.
An observer M is standing on the embankment, halfway between point A and point B.
An observer M' is standing on the train, halfway between point A' and point B'.

The train passes the embankment at 4,958 m/s
gamma = 1 / sqrt(1-v^2/c^2) = 1.0000000001367545054905367903816

At t=0.000:

• the front of the train is passing point B
• the back of the train is passing point A
• the train observer M' is passing embankment observer M
• M' has a clock with him that reads t'=0.000
• A bolt of lightning strikes the front of the train and point B
• Another bolt of lightning strikes the back of the train and point A

At t = d/(c+v) = 16.67792893852027 ns :

• The flash from lightning bolt B reaches M' (the train observer)
• The clock at M' reads t' = t/gamma = 16.67792893623949 nanoticks

At t = d/c = 16.67820475990760 ns:

• The flash from both lightning bolts reaches M

At t = d/(c-v) = 16.67848059041821 ns:

• The flash from lightning bolt A reaches M'
• The clock at M' reads t' = t/gamma = 16.67848058813736 nanoticks

So far, I conclude that:

• the lightning bolts struck simultaneously
• the moving train is 10 actual metres long.
• rulers on the train are contracted to 1/gamma = 0.99999999986325 actual metres long
• clocks on the train are dilated, elapsing 1/gamma = 0.99999999986325 ticks every second

The only thing the train observer knows so far is:

• The train is as long as 10.000000001367545 of his rulers
• The lightning flash from the front of the train reached him when his clock read 16.67792893623949 nanoticks
• The lightning flash from the back of the train reached him when his clock read 16.67848058813736 nanoticks.

Next, the train observer will measure the velocity of the train using a single clock, a light flash, and a mirror.

He puts the mirror at the front of the train and a timer in the middle of the train.
The mirror is 5 metres from the timer.
The train observer measures this distance to be 5.00000000068377 train rulers.

When the timer starts, a light flash is sent from the M' clock to the mirror.

d/(c-v) = 16.67848059041821 ns later, the light flash reflects off the mirror.
d/(c+v) = 16.67792893852027 ns later again, the light flash returns to M'.

The timer has elapsed t/gamma = 33.35640952437684 nanoticks for the round trip.

Next, I'll present the train observer conclusions from this measurement.