On Einstein's explanation of the invariance of c

Motor Daddy:

I'm not sure how you propose to define a "duration of time" other than as the time interval between two readings on a clock. If clocks tick at different rates in different reference frames, then they will record different durations between events. And that is what is, in fact, observed experimentally.

You are correct that light travels a specific distance in a given time, but that's not "absolute". The statement is true in any given reference frame provided the distance and the time are both measured in the same frame. That is the most that can be said. It is, however, a very significant statement; it's one of only TWO fundamental postulates of special relativity. It's postulation is justified retrospectively by experiment, of course. Experiment is always the final arbiter. You can imagine all kinds of things, but if your imaginings don't match what is actually observed then you need to go back to the drawing board.

Not at all. One of those lights might have started earlier than the other one, for example.

The speed of light is the same in all reference frames. Light is a special case in that regard, since the same cannot be said of anything that travels slower than light in any reference frame.

You can't measure distance using light without also using a clock. Or, equivalently, you can't measure a time interval using light without also using a ruler of some kind. In other words, you can use the constancy of the speed of light either as a ruler, in which case you need a clock, or you can use the light as a clock, in which case you need a ruler. You can't use light to measure both time and distance simultaneously.

That's a function of recent history (past 50 years or so). Initially, the speed of light was measured. Those measurements got more and more accurate over time, until finally the accuracy of the speed of light measurement was more accurate than the then-current definition of the metre. So, the definition of the metre was changed to depend on the speed of light, rather than the reverse. Note, however, that a clock is still required to determine how long a metre is using light. In other words, we need a prior definition of the second to define the metre.

Yup. So you need to know how long a second is first, independently of the speed of light. Agree?

Yes.

Perhaps you'll find this surprising, but the answer to this question is, counter-intuitively, "No."

You haven't defined "closing speed" at all here. It could have two possible meanings (at least). For example, it could mean the speed of the light that somebody moving with the meter stick measures, in which case the closing speed is always exactly 299792458 m/s. Alternatively, perhaps you mean the difference between the speed of light and the speed of the stick, as measured by you from some other reference frame (such as on the ground) - in which case the closing speed can never be greater than 2 times 2997924588 m/s.

By the way, do you believe in the speed of light as an absolute speed limit? If you do, why do you believe that? (This is a very relevant question, though that probably isn't obvious to you.) If not, can you give an example of an object that travels faster than the speed of light?

Here's one scenario in which the closing speed could be 2 m/s:

Your stick is clocked at a speed of 299792456 m/s travelling relative to the ground, say. The same observer on the ground sees the light catching up to the stick (travelling in the same direction) at 299792458 m/s.

How long does it take the light to go from one end of the stick to the other in that case?

The answer depends on what you mean by "metre stick", which you did not specify. Is it a stick that is 1 metre long when it is measured at rest? Or is it a stick that is 1 metre long when you measure it flying past you as you stand on the ground? In the former case, the light will pass it in a very short time indeed, because the length of your "metre" stick will have contracted to close to zero length (I can give you the exact length if you like) in the ground frame. In the second case, the light will take half a second to go from one end to the other. However, in that case your "metre" stick has a much much longer rest length than 1 metre.

Yes, provided the distance and time are both measured in the same reference frame (which is the only sensible thing to do). But when you measure, say, the distance between two objects in different reference frames you will get different answers. If you choose to do that using light, then your light will still travel the same distance in the same time, but both the distance and time taken for the light to go from one object to the other will change, keeping the speed of light the same.

If you want to discuss relativity, it's useful to use the language that physicists use. Here are a couple of definitions for you:

"Event" = a particular point in space and time. An event can be specified using four coordinates, all measured in the same reference frame. For example, (x,y,z,t), where x,y,z are the spatial position of the event and t is the time at which it occurs.

"Simultaneous" - 2 events are simultaneous in a particular reference frame if and only if their time coordinates are the same.

As you can see, "Light traversing space" cannot be an "event", since it encompasses multiple points in space and time. And "simultaneous" in the context of "light traversing space" is not a term that uses the language of physics in the standard way.

Some examples of events in spacetime:

1. Light is emitted from a source at a particular place and time.
2. Light hits a detector at a particular place and time.
3. Light is half way between two detectors at a particular place and time.
4. A train is at a certain point on a track at a particular place and time.

Examples of things that are NOT events in spacetime:

1. Light travels from point A to point B.
2. A clock moves from point A to point B.
3. A clock remains stationary for 10 minutes.
4. A metre stick sits on the ground at the instant a clock reads 1:00 pm. (Can you see why this one isn't an event? This is important.)

The problem you have is that all objects, like a train or two clocks on opposite ends of a pole, have length. And that length changes in different reference frames. Therefore, even though the speed of light does not change in different frames (which is would if it didn't obey Einstein's relativity - agree?) the time it takes the light to traverse an object will change with the length of the object.

Actually, it strikes me as interesting that you seem to believe that light has the same speed in all reference frames. Do you believe that? If so, why do you believe that? It obviously is NOT true of balls, cars, planes, people, etc. So why light?

We're using your method here, not Einstein's. Remember I asked you to give me the method.

To find the distance between two clocks using light travel time, Einstein would use exactly the same method you want to use!

In other words, he'd start with two synchronised clocks, fire a light pulse from one to the other, measure the elapsed time and calculate the distance using x = ct.

The difference between you and Einstein is that Einstein says that the time interval you measure when you do this will depend on which reference frame you do it in. The speed of light doesn't change.

What I find strange is that you apparently agree with Einstein that the speed of light is the same in all reference frames, which is totally counterintuitive and at odds with every other experience of object speeds in your life, and yet at the same time you dispute the logical consequences of this observation that you say you believe in.

This is a straw man you keep putting up. It should be clear by now that I'm very happy to determine the distance between two clocks using exactly the method you say we should use. Where we differ is that you imagine that you can have a constant speed of light in all reference frames and somehow maintain an absolute space and time. That notion is not just experimentally inconsistent - it's logically inconsistent.

Woah! Ok, now.

Now it sounds like you're saying that the measured speed of light should vary between reference frames. Is that what you're saying?

Think about your car-passing-a-bus example. If you're inside the bus, you don't think the length of the bus is different from the length somebody on the roadside would measure, do you?

For simplicity, let's say the bus is 10 metres long, the bus is travelling at 10 metres per second along the road and the car is travelling at 11 metres per second along the road.

Now, somebody sitting on the bus says the bus is stationary relative to them as they sit in their seat. Right? That is, they are travelling at 10 metres per second along the road, and the bus is travelling at 10 metres per second along the road, so their relative speed is 10 - 10 = 0 metres per second - there is no relative motion between the bus and the person in it. Agree?

Now, a person on the roadside says the car takes 10 seconds to pass the bus (i.e. 10 seconds is the time from when the front of the car is level with the back of the bus to the time when the front of the car is level with the front of the bus). Do you agree? (How did you work it out?)

So, what is the speed of the car as measured by the guy in the bus? Well, that guy says the car must travel 10 metres (length of the bus) in 10 seconds, so according to the guy in the bus the car's speed must be 1 metre per second. Agree?

So, what have we discovered? The speed of the car is 11 metres per second according to a person on the roadside. But the car's speed is 1 metre per second according to the guy on the bus. Agree? The roadside and the bus are two difference reference frames.

Of course, you'll have no argument about this basic explanation of what a reference frame is, I'm sure. Right? You already know all this stuff.

Ok, so the speed of the car is reference-frame dependent. We agree on that, right?

Now, replace the car with a beam of light passing the bus. Suppose the roadside observer measures the speed of light as 299792458 m/s. Then the guy on the bus says the speed of light is 299792448 m/s (i.e. 10 m/s less). Do you agree?

Now, here's a potential point of conflict: Einstein says the guy on the bus measures the same speed for the light as the roadside observer, that is 299792458 m/s. There's no difference in speed according to Einstein.

Now, I'm not clear whose point of view you adopt on this question. So let me ask you:

1. Is the car's speed different depending on whether you measure it on the bus or on the roadside?
2. Is the speed of light different depending on whether you measure it on the bus or on the roadside?

If you want to avoid Einstein's relativity, then your answers to both of these questions must be "Yes". So, just to clarify, what are your answers?

Note that Einstein's answer to question 1 is "Yes" and to 2 is "No". Galileo and Newton would answer "Yes" and "Yes".

What's Motor Daddy's answer?

 

Motor Daddy:

Ok. If I answer those questions of yours, do you undertake to respond in full to all the questions I asked you in post #701?

Because, having spent some time on that post, I'd hate to think you were unwilling to engage in good faith.

 

Ok, Motor Daddy.

As a gesture of my good faith, I will answer your questions. I trust you will reciprocate by answering mine. Because not to do so would be intellectually dishonest of you, wouldn't it? And you're a man of integrity, I can tell.

Here's one way:

The "100 m/s" measurement is performed using apparatus located beside the track, of course - not on the train. So, I'm only able to measure 100 m/s "outside the box", as it were. Speaking technically, the 100 m/s figure is measured in the reference frame of the ground. The speed of the train in it's own rest frame is, of course, zero.

To measure the speed of the train in the ground reference frame, I line up hundreds of clocks along the railway line, spaced at, say, 1 metre intervals. To get the spacing correct, I manufacture lots of identical metre sticks, then lay them out end-to-end along the track. Then, at every metre mark I place a clock. I designate a particular clock to be called "x=0" distance. At the same instant that I set that clock to "t=0", I send a light pulse out from that clock along the train track. When the clock at x=1 metre receives the pulse, I set that clock to "t=1/299792458 seconds". When the clock at x=2 metres receives the pulse, I set that clock to "t= 2/299792458 seconds" etc. At the end of this process, all clocks are synchronised in the ground reference frame.

Now, as the train is travelling along the line, I send two light signals out from the clock at x=0, towards the train. The light signals are spaced consecutively, say at a 1 second interval (the exact interval is not important). When the first light pulse reaches the back of the train, I note the location of the back of the train by counting my metre sticks from x=0 to the back of the train, and also note the time recorded on the clock nearest the back of the train when the pulse hits.

When the second pulse hits the back of the train, I repeat the recording procedure.

Now I calculate the speed of the train relative to the track as follows: I take the two position readings and subtract the first one from the second, to get a displacement. I take the two time readings and subtract the first from the second to get a time interval. Then I divide the displacement by the time interval and that gives me the speed of the train relative to the ground.

Alternatively, once the clocks are synchronised, I can throw away the metre sticks and just use the timing information. If the time between the pulses being sent is z seconds, then the speed of the train is:

\(v = c\frac{t_2 - t_1 - z}{t_2 - t_1}\)

where \(t_1,t_2\) are the times recorded on the clocks for arrival of the light pulses at the back of the train.

[quite]Do you know the distance between clocks? How did you determine the distance between the clocks using only light travel times? Again, show your work.[/quote]

I have given a procedure for measuring the distances above.

Now, you might suggest that I could measure distances without the rulers as follows: Take my bunch of clocks. Synchronise them all in the one location. Then carry all the clocks out along the track and place them at any desired location. Designate one clock as x=0 and send a light pulse out from it at t=0. Then, when that pulse passes a clock somewhere along the line, record the position of that clock as 299792458 m/s times whatever time the clock reads.

The problem with this method is that it involves moving the clocks after they have been synchronised. And we can't simply assume that moving clocks will stay synchronised. That, after all, is something we want to test. We can't assume it in advance.

So, clearly the metre-sticks + clocks + light synchronisation procedure is superior to the light-signals + pre-synchronised clocks procedure.

To measure the speed of the ground relative to the train, I would set up my many metre sticks and clocks on the train, then send light signals along the train until they were level with a particular point on the ground.

Following this procedure, I would deduce that the speed of the ground relative to the train was equal in magnitude to the speed of the train relative to the ground. (can you see why?)

But it's not clear to me that you're asking for a relative speed here. It sounds a lot like you're asking what the absolute speed of the ground is. There is, of course, no such absolute speed to be measured. I have to set my clocks and rulers up somewhere, and they can only ever measure the speed of the ground relative to the platform they are on.

There's no way to measure an "absolute" speed of anything. If you think there is, then it is incumbent upon you to provide instructions.

Yes, that's what you think you've done. But all you've really done is provide a procedure similar to mine (though inferior, for the reasons I've given above) for measuring a relative speed - of the train relative to the ground, for example. Moreover, when you claimed to calculate the absolute speed of the train from on the train itself, you merely assumed, without any evidence at all, that the transit time of light between two clocks fixed to the train would be different in the two directions as measured on the train.

So, what your arguments reduce to are a bunch of unsupported assumptions, sloppy reasoning and inaccurate and/or ambiguous expression on your part. Hardly an encouraging effort in debunking relativity.

I seriously doubt you can know those distances using only light times and Einstein's methods. In fact, I know you can not measure those distance using light, as Einstein did not understand light travels independent of objects.

 

Motor Daddy:

As you can see from my previous post, my measurements assume a fixed speed of light. There's no measuring of the speed of light involved. So saying that I "insist on measuring the speed of light" in "almost every experiment" is a straw man.

But you say you agree that the speed of light is the same in all reference frames. That is postulate #1 of Einstein's special relativity. So we have established that you agree with one of the two postulates.

The other postulate is that the laws of physics take the same form in all inertial frames. I assume you understand what that postulate means. If not, I can explain it to you.

Do you agree with the second postulate? If not, which laws of physics change between different reference frames, and how do they need to be changed?

If, on the other hand, you agree with both postulates, then we're done. You then have no option but to affirm length contraction, time dilation, relativity of simultaneity, a speed-of-light speed limit, \(E=mc^2\) and the rest. Because they all follow directly from the postulates. Unless you can prove a contradiction, that is.

Why, do you think, has no material object ever been observed to travel faster than the speed of light? Just coincidence? It's not important, but I'm interested in your thoughts on this.

Consider, for example, particle accelerators. Physicists keep building bigger and bigger accelerators, yet they never manage to accelerate those protons to faster than the speed of light. What's going wrong?

Yes, but an object that is one metre long in one reference frame is not 1 metre long in a different frame.

I could find the length of a stick using the exact method I gave for determining the speed of the train in my previous post. Part of that procedure involved measuring two distances that two light pulses travelled. If I can do that, I can measure the length of any stick, regardless of its velocity.

I can do as well as you can. All I need to do is work in the frame of the bus. Your problem is that you think you get the same answer as that in every frame. I know better.

It's not a conclusion. It's a premise used to illustrate a point. If you're talking about reference frames, you must introduce a relative velocity at some point in the discussion. That's what "relativity" is about, whether you prefer the Einstein kind or the Newtonian/Galilean kind.

Ok. Take the standard example where lightning is observed to strike two points on a moving train. Light from each strike travels along the train towards an observer on the train who stands exactly half way between the strike points. If the light from the strikes reaches the observer on the train simultaneously, and the train is travelling along the track at 3c/5, where c is the speed of light, did the lightning strikes hit the train simultaneously (a) from the train observer's point of view, and (b) from a ground-observer's point of view?

I assume your answers are "yes" and "yes", because you say simultaneity is absolute (i.e. events that are simultaneous in one frame are simultaneous in every frame).

Using the fact that the speed of light is the same in both frames, show me your mathematical proof of your answers in BOTH frames. be careful not to mix quantities from different frames.

Let's ignore Einstein for now. The method I have given in the previous post for determining the train's speed doesn't use a "round trip" for light. It's one-way. Let's discuss that.

But the situation you have described here does not have the car's speed as the same in all reference frames. If the car's apparent speed varies depending on whether you're on the road or on the bus, then the car's speed is different for the road and the bus. It is not the same in the two reference frames.

Einstein knows the constant speed of light c (same in all reference frames). Then, he only has to measure the time it takes light to travel in whichever reference frame he wants to use, and he can calculate the distance travelled in that frame. Or vice versa (if he measures the distance he can calculate the time taken). And having made a measurement in one frame, he can also calculate the corresponding results that would be measured in any other frame.

Right. So that would be like your strange car that always has the same speed, no matter whether you measure it from the bus or from the road - a car that would behave completely contrary to your everyday experience. And you agree with Einstein on this point.

From this statement, I'm still not clear on your answers to the two questions numbered "1" and "2". Please be explicit. Give "yes" or "no" answers to those two questions.

 

Motor Daddy:

No. There's no track velocity in any of my equations or calculations. I gave a method for calculating the speed of the train relative to the track. That's the best I can do. In fact, that's the best anybody can do, since there is no absolute speed.

If you think you can calculate the absolute speed of the train, then you need to tell me how to do it. Give me your step-by-step method.

Sure I do. I gave you a precise, step-by-step method of measuring it.

Yes I do. I just looked at how many metre sticks it covered. Or, alternatively, I just measured the time it took to travel then multiplied by c.

If by "actual" you mean "absolute" then you're right, because there's no such thing.

You have no way of calculating any "actual velocity" either. Nobody does.

But I gave you an explicit method for determining the train's velocity using light signals. To claim I haven't done so is churlish. It is not any kind of absolute velocity, but that's no fault since no such thing exists.

"But wait!" I hear you cry, "The velocity of light is absolute!"

No it isn't. Since light has the same velocity in all reference frames, then no particular reference frame is more "correct" or "preferred" than any other. The velocity of light is the same in all reference frames, but is in no way "absolute". If light had an absolute velocity, then we'd expect it to vary as we changed reference frames, the same as the velocity of everything else varies as we change reference frames. Also, light would have a "rest frame" in which its velocity could be observed to be zero, just like the guy on the bus observes the bus to have zero velocity relative to him, no matter how fast the bus is moving along the road.

I assume I manufactured my metre sticks in the rest frame of the tracks, perhaps using light signals in conjunction with clocks synchronised in that frame.

Of course, there's no such thing as "the velocity" of the tracks, if you're talking about an "absolute" velocity.

Also, you shouldn't get hung up on metres. The only requirement for my measurement process is to have a number of sticks of the same length. They don't have to be a metre long. I could measure all distances in units of "stick-lengths", and express the speed of light as, say, "stick-lengths per second". That wouldn't change the results of relativity one jot.

There is no "wrong", because there is no "absolute". Sure, rest-frame metre sticks have different lengths to moving-frame metre sticks, but if you bring two metre sticks to relative rest in ANY reference frame then they'll both observably have the same length.

Not at all. That's the beauty of relativity. The laws of physics stay the same in all inertial reference frames. As long as I make all measurements consistently in the same reference frame, all my calculations will be correct. Moreover, I can translate those measures to any other reference frame on request.

I made no assumption about the track velocity. On the contrary, I explicitly showed you that the velocity of the train relative to the track would be equal in magnitude to the velocity of the track relative to the train (for example).

There's a lovely symmetry there which you are attempting to completely toss out by pretending there is some magical "special" frame with absolutely zero velocity, even though you can give no procedure for identifying such a frame.

[quite]Again, all your measurements are based on a zero velocity track. Can you prove the track is at a zero velocity?[/quote]

I am free to assume, without any physical consequence whatsoever, that any ONE particular object is at zero velocity in any problem. I can then calculate/measure all distances, times, speeds relative to that reference and then can translate those value to any other frame of reference you care to specify. It's a marvellously useful technique in physics.

I send out a light pulse and time it for 1/299792458 seconds. I mark off where it started and where it was after the given time. The distance so marked is a metre in the rest frame of the clocks used to measure the time.

 

Motor Daddy:

I notice that you missed most of the questions I asked you in post #707. I'll wait for you to catch up before posting again after this post.

Where?

Done in the post prior to this one. A meter, as you know, is defined to be the distance travelled by light in 1/299792458 seconds. Notice that no reference frame is mentioned in the definition, which means you can make the measurement in ANY reference frame. In particular, you don't need to make it in some imaginary "absolute" frame.

So we agree. Great!

But you don't know the "absolute" velocity of any frame any more than Einstein does.

If you think you do, please name a reference frame you know the absolute velocity of, and tell me what the absolute velocity is of that frame.

Alternatively, I assume you have identified an "absolute zero velocity" frame. Which frame is that?

---

I'll wait now until you catch up with my previous questions to you.