On Einstein's explanation of the invariance of c

BenTheMan:

Motor Daddy and I aren't quite sick of it yet. You don't need to participate. Please don't close it.


Motor Daddy:

Wrong. "At rest" means "Not moving". "At rest" means zero velocity. Also, you can be at rest and still be accelerating. That's exactly what happens (momentarily) every time you put your foot on the accelerator to start your car moving from the traffic lights.

You're merely repeating an unproven assertion.

Yes, objects can traverse "space". Part of what you are saying there is that objects can move - something I obviously don't deny. The other part of what you're saying is that there is a mysterious stationary substance called "space" that is absolutely at rest, which is wrong.

You can't measure the motion of an object in your "space". The most you ever actually manage in your thought experiments is to stand outside the thing you're measuring and measure light travel times in that external frame of reference. I know that's not what you think you're doing, but that's what you're doing. When your method works, that is.

I understand perfectly what you are saying. It is based on the false imagining that the light travel times measured inside the ship can be different in the two directions. That's error number one. Error number two is your belief that if you measure the times using clocks in another reference frame for the same light, you'll measure the same times.

A spaceship always has zero velocity in its own rest frame, by definition. And no experiment can contradict that. If you see a spaceship moving, then you're watching it fly past. You're not sitting in it.

By the way, if you're sitting in it and you look out the window at the stars and planets passing by, then you say the stars and planets are moving, not the spaceship. That's what reference frames are all about. People sitting on those planets say the spaceship is moving and the planets are stationary. Change of reference frame - see?

Your idea that some things are "really" stationary and others are "really" moving with respect to "space" is false. There's no standard of absolute rest. It just doesn't exist.

I set the problem; you're telling me how I constructed it? :bugeye:

No, (a) because you assume that the one-way light travel times measured in the ship will be diffferent, and (b) because you assume that anyone in any frame will measure the same one-way travel times. Both of those assumptions are wrong.

No. Light just travels the same distance in the same time in any reference frame. And if you think this statement and your statement are saying the same thing, then you don't know what a reference frame is.

No. I want to say that an object has zero velocity if you're sitting on it and measuring its speed in its own reference frame.

But you can't tell me that. You always in fact are implicitly introducing another external reference frame. You call it "space" and you think it's special, but it's just one more frame and has no special status.

You can't measure distance or time in the absence of a reference frame. A reference frame is what enables these measurements - otherwise quoted times and distances are meaningless.

Yes.

So, repeat after me: "I agree with Einstein that the speed of light is the same in all frames."

Go on, let me see you write that. Can you bring yourself to do it?

I understand that if an object has speed relative to a particular reference frame, then what you say here is perfectly true. In that case I agree with you completely. Where we disagree is in your imagining an absolute standard for speed which you call "space". Space is a nothing. It is not a substance.

I agree, but it's not a velocity "in space". It's a velocity relative to some reference frame which is implied and not absolute.

NO! That's where you're absolutely and utterly wrong.

The speed of light is the same IN ALL REFERENCE FRAMES. Therefore, I can make the measurement in ANY reference frame I like and find the correct answer.

I have no argument with that at all. As long as both times are measured in the same reference frame, the relative speed v calculated for the object will be correct for that frame, as will the distance d.

There's nothing absolute about this calculational method, except for the incorrect assumption that the c refers to the speed of light relative to an absolute "space", and the assumption that v is the speed of the object relative to that "space".

And, of course, there's your incorrect assumption that if we make the measurement in the frame of the ship then T and t will be different.

Correct. Time dilation and length contraction are never an issue if you stick to one reference frame. They only ever come into play when you want to translate from one frame to another.

No. The best you can do with light travel times is to find the relative velocity of the ship - relative to some specified frame of reference, that is.

 

Motor Daddy:

I'm going to reply to you in two posts. In this one, I'm going back to basics for a minute, just to make sure we're on the same page regarding reference frames, definitions of velocity and so on. In the next post I'll respond to your previous post.

Here's what a reference frame is, approximately. We'll work in one spatial dimension for simplicity. Imagine you have constructed 100 identical straight sticks of equal length. The exact method of construction and the exact length is not important, as long as the lengths are the same when you lay one stick on top of another.

Now, to constuct a reference frame, you lay out your 100 sticks end-to-end along a straight line. You now have a distance scale. If you want the distance from the end of the row of sticks to some other point on the line, you just count how many sticks there are between the end and the point you're interested in.

Now, as well as a distance scale, we need some clocks. At every intersection of two sticks along the line, we place a clock. All of the clocks along the line are adjusted so that they read the same time always. Again, we won't worry about the exact method used to synchronise them for now; we just assume they are synchronised.

So, a reference frame is this set of sticks and clocks.

Now, suppose we number the intersections between any two sticks. We start at the end of the row (let's say) and call that position zero. The next intersection is position 1, the one after that position 2 etc. We now have a definition of position relative to our reference frame.

Imagine a ball located at some particular intersection, say number 57. Then we say the position of the ball is at x=57 (sticks).

Next we define velocity. If an object moves from one position to another along our line of sticks, then while it is moving it has a velocity equal to the number of intersections crossed divided by the time taken (as measured on the clocks). For example, if the ball moves from location x=57 to x=58 in 2 seconds, then it has a velocity of 1 stick per 2 seconds or 0.5 sticks per second.

Finally, we have acceleration, although that is not important to our discussion. Acceleration is the rate of change of velocity. For example, if the ball changes speed from 3 sticks per second to 5 sticks per second in a time of 1 second, then its acceleration is 2 sticks per second per second, or 2 sticks per second squared.

Now, let's be clear about what is meant by the term "at rest". An object, such as the ball, is at rest in our reference frame if its position is not changing with time. In other words, if it stays at x=57 then it is at rest with respect to this reference frame. It's velocity in this case is the change in position over time, and since its position is not changing, the velocity is zero when it is at rest. "At rest" says nothing about acceleration. "At rest" simply tells you velocity is zero.

Now, consider a different type of motion. Imagine the ball is "stationary" (whatever that means), and we move our whole assembly of sticks and clocks past the ball. Can you see that, in the reference frame we have constructed, the ball now has a velocity? The reason is that the stick intersections (57,56, 55, 54...) are moving past the ball, and so its position in the reference frame is changing over time. Therefore, in the reference frame of the sticks/clocks, the ball has a velocity, because of the way we defined velocity.

We could achieve the same velocity for the ball in a different way, of course. We could hold the stick and clocks "stationary" and move the ball along the sticks, instead of holding the ball stationary and moving the reference frame. In either case, the speed of the ball would be the same in the reference frame.

Now, suppose we put our whole assemblage of sticks and clocks in an aeroplane which is flying above the Earth. And suppose we place our ball at x=57 and leave it there.

Now, relative to our reference frame of sticks and clocks, the ball is at rest. Recall that we defined "at rest" to mean that an object does not change position, and position is defined by the intersections of the sticks. So, our ball is at rest in this reference frame. Note that the motion of the plane is completely irrelevant to whether the ball is at rest in the reference frame. As long as the ball stays at x=57 it is at rest, by definition.

Ok, so now we have a definition of "reference frame", "position", "velocity" (and "acceleration", though we needn't worry about that right now).

So, let's now consider TWO reference frames, by which I mean two identical sets of sticks and clocks laid out parallel to each other. Obviously, we can slide one entire set of sticks along the other set of sticks, so that each set of sticks has a velocity relative to the other set. For definiteness, let's assume on set of sticks is laid out on the Earth (attached to it) and the other set of sticks is laid out in our aeroplane, which is flying parallel to the Earth's surface, in the direction that both sets of sticks are laid out.

Now consider the ball on the plane. Suppose it just sits in the aisle at location x=57 relative to the sticks on the plane. Then, the ball is at rest relative to the plane's reference frame. But the ball obviously has some velocity relative to the ground's set of sticks, its position on those sticks is changing as the plane flies past.

So, is the velocity of the ball "really" zero, as indicated by the plane's reference frame, or is it "really" 800 km/hr (say), as indicated by the Earth's reference frame? Answer: it is BOTH.

Or, to put it another way, it makes no sense to say "The ball's velocity is zero" unless you specify which reference frame you're using. You ought to say "The ball's velocity is zero in the reference frame of the plane", or equivalently "The ball's velocity is zero relative to the plane." Obviously, at the same time the ball's velocity is NOT zero relative to the ground.

More points to appreciate: EVERY reference frame - every set of sticks and clocks - is attached somewhere. The position of any given object may be different in different reference frame, as may its velocity and acceleration. Also, it makes no sense to define "position", "velocity" or "acceleration" in the absence of a reference frame.

When it comes to light, we can consider a light photon as just another ball moving along our lines of sticks. If light covers a certain number of sticks in a certain amount of time (as measured by the clocks at the intersections) then light has a certain speed determined by the reference frame. Up to this point I have talked about lengths in terms of stick lengths. Obviously, if we can somehow ensure that each stick has length 1 metre, then we can get velocities in metres per second.

Ok, that's enough background.

What I need from you, Motor Daddy, is some indication of whether you agree with the above description of what a reference frame is, as well as definitions of position and velocity. Because if we can't agree on these basics then we can't possibly begin to discuss relativity.

So, please let me know if you think any of the above definitions or explanations I have given here are unworkable.

 

Motor Daddy:

In this post I'll reply to your previous post.

This is Physics 101. "At rest" means "zero velocity in a particular reference frame". Look it up if you don't believe me. The same definition is used in every physics textbook and on every reputable physics site on the internet.

Referring to my previous post, you will see that "at rest" means only "not moving with respect to some reference frame". So when you ask me "compared to what", I say "compared to the reference frame I'm using". Think of sticks and clocks if you want a concrete picture.

You say "in your universe the ship never moves". Clearly that is not true. Read the previous post. The ship will never move relative to a bunch of sticks that are nailed to its floor, but it can certainly move relative to a bunch of sticks nailed to the Earth. How do we tell whether it is moving or not? Step 1: specify which reference frame we want to use. Step 2: See if the ship's position changes over time by looking at its position along the line of sticks. Easy.

Wrong. 60 mph means you're moving across sixty mile-long sticks every hour. Since you have a velocity, you're not at rest. BUT, where are these sticks attached to? They are attached to the road. So, to say it properly "You're travelling at 60 mph relative to the road."

Suppose you have another line of sticks inside the car, nailed to car's floor. The car's position never changes relative to them, so in that reference frame the car is at rest.

Suppose a plane is flying above the road. Then, the car is moving relative to the sticks that are nailed to the floor of the plane, but not at 60 mph, because obviously the car moves along the plane's sticks at a different rate than it moves along the road's sticks.

Also, notice that the ROAD is moving at 60 mph relative to the car. As measured on the car's set of sticks, a fixed point on the road moves along those sticks. So, in the car's frame the road is not "at rest". Nor is the road "at rest" in the plane's frame.

I agree. Here you're using sticks nailed to the road, which is fine.

What are your "space" sticks nailed to?

I understand that you have a set of sticks nailed somewhere and light travels along those sticks. Therefore it has a velocity. Your problem is that you don't know where your sticks are nailed.

Let's go back to your original thought experiment with one-way travel times in the spaceship. First, consider a set of sticks nailed to the floor of the spaceship. What I am telling you is that light travels along that set of sticks at the same rate in both directions, always. This is completely against what you might expect, but also completely compatible with your claim in this thread that the speed of light is always the same in every frame. Right?

Now, perhaps at this point you want to change your mind and say that the speed of light is NOT always the same after all, with respect to the sticks nailed to the floor of the spaceship. If so, please let me know, because that would be a very significant change to your argument.

Next, consider a set of sticks nailed to the Earth. The spaceship has a velocity relative to that frame, and so does the light going in both directions along the spaceship. For that frame, those sticks, I agree with you that light takes a different time in the two directions, for exactly the reasons you say it does. What I have been trying to point out to you up to this point is that you are still using a set of sticks to make this argument. Whether those sticks are nailed to ground, or strung up between Earth and the Sun or whatever, they must be there (notionally).

What you say is true when you're using the sticks located outside the spaceship, strung up between Earth and the Sun, that the spaceship flies along.

What you say is false when you're using the sticks located inside the spaceship, nailed to the floor. You say you agree that light travels at the same speed in all reference frames. Therefore it must cover the same number of sticks in the same amount of time inside the ship. Right?

The reason the times are different outside the ship is that the points of emission and reception of the light are moving relative to those sticks outside. But they are at rest relative to the sticks inside. See?

Correct. The ship can never have motion with respect to sticks nailed to its floor. Agree?

The only way the times can be different inside the ship (relative to the sticks on the floor) is if the speed of the light is different in the two directions inside the ship. Do you agree? i.e. the light has to cover more sticks in one direction in a certain time than in the other direction. Because inside the emitter and detector both sit at fixed points on the sticks nailed to the floor of the ship. The number of sticks between the emitter and detector doesn't change, so the only way the time taken for the light can change is if the speed of the light is different depending on the direction.

But you say the speed of light is the same in both directions. Can you now see the contradiction?

So, do you still maintain that the speed of light is the same in both directions relative to the sticks inside the ship, or do you want to modify your argument that the speed of light is only the same in both directions relative to sticks that are nailed down to "space"?

Something has to give in your argument.

What I am telling you is that a set of sticks nailed to the Earth is just as good as one nailed up between the Sun the and the Earth. In the frame of the sticks nailed to the Earth, the sun really does move. In the frame of the sticks nailed up between Earth and the Sun, the Sun doesn't move. And there's no way you can say what is real and what isn't, because you always need to use a set of sticks somewhere to measure positions, velocities and so on.

So, in my terms, the object is sitting at a fixed particular position on some set of sticks that are nailed to "space".

Where is this "space". How can I nail my sticks to it? And how can I be sure my sticks aren't moving with respect to "space"?

A frame (set of sticks) is always at rest with respect to itself, obviously. The sticks that make up a frame never move relative to each other. Other objects may or may not be at rest relative to a given frame.

So, does it have a constant velocity inside the spaceship? Yes or no? i.e. relative to the sticks nailed to the floor of the ship?

Or does it only have a constant absolute velocity, by which you mean velocity relative to sticks nailed to "space"?

Actually, the metre is defined to be the distance that light travels in 1/299792458 seconds relative to ANY frame. The definition is based on Einstein's postulate that the speed of light is the same in every frame.

The reason the definition doesn't mention a particular frame is because any frame will do in this special case.

 

Motor Daddy:

I'm glad we agree on the basics of reference frames, and I think we now agree on what is meant by "at rest". I'll wait for your next post.

 

Motor Daddy:

Thanks for your post. I think I understand where you're coming from, but I have some issues with your approach. This post may be a little repetitive, but if I say the same thing in a few different ways then maybe you'll start to see where I'm coming from.

What you're saying is that light lays out a certain number of sticks per unit time, full stop. The sticks always have the same length in every reference frame, and time is the same in every reference frame.

But there's a conflict here. If I measure up some metre sticks using light, then nail them to the floor of the spaceship, then they should indicate the correct length of the spaceship, regardless of whether it is moving or not. It doesn't change length just because it is moving. So, if there's an emitter and detector of light at opposite ends of the ship, inside, then when light is emitted it should start laying down sticks of length equal in length to the sticks nailed to the floor of the ship, one metre every 1/299792458 seconds. If you're inside the ship and you count up the number of sticks layed by light between the emitter and the detector, then there must be an equal number to the number nailed to the floor.

If this was not the case, then the speed of light as measured using the sticks nailed to the floor would necessarily be different from the speed of light determined by the sticks layed by the light.

And yet, you claim that the speed of light is the same whether you measure it inside the spaceship or outside.

Now, as far as I can see, you have a number of options for solving this apparent problem:

(a) you can say that when the spaceship is moving, we're not allowed to use the spaceship's sticks to measure distances, because the distances we obtain will be wrong. In that case, the speed of light measured using the spaceship's sticks is definitely NOT the same as the speed measured using light's sticks, so you need to give up your claim that light has a constant speed in all reference frames. OR

(b) you can maintain a constant speed of light by adjusting the "apparent" length of the ship's metre sticks according to its velocity, so that when we count sticks in the spaceship as light travels and count the sticks laid by the light we end up with the same number. This maintains the constancy of the speed of light in both frames, but introduces a "length contraction" effect when light travels in one direction, and a "length expansion" effect when light travels in the other direction. These effects would not be "real", but apparent. When we laid out the sticks laid down by light next to the ones nailed to the ship, we'd see that their lengths did not match. Moreover, in one direction the ship's sticks would be shorter than light's sticks, and in the opposite direction the ship's sticks would be longer than light's sticks. OR

(c) You could maintain the constancy of the speed of light by playing with the times inside and outside the spaceship, pretending in effect that spaceship clocks run slower than outside clocks when light travels in one direction and faster when it travels in the other direction. OR

(d) You can adopt Einstein's approach to the problem and alter both distances and time so as to maintain the constancy of the speed of light in all frames.

These are the only options I can see to resolve your problem. Maybe you can think of something else; I'm not sure. But as far as I can see, you're forced to choose one of these.

Yes. So, suppose light is travelling from the rear to the front. According you you, it lays more sticks than are nailed to the floor of the ship. Let's say 27 metre sticks are nailed to the floor between the attachment points of the source and detector of the light. And suppose the light takes 54/299792458 seconds to go from the source to the detector.

Now, according to you, the light ought to lay down 54 sticks in total over that time. The speed of light relative to its own sticks is the distance covered (54 sticks) divided by the time taken (54/299792458 seconds), which gives 299792458 metres per second.

But in the frame of the spaceship, the light covered 27 sticks nailed to the floor in a time of 54/299792458 seconds, which gives a calculated speed of light of 149896229 metres per second for the light.

To repeat myself, I can only see four ways to deal with the discrepancy:

(a) you can say that when the spaceship is moving, we're not allowed to use the spaceship's sticks to measure distances, because the distances we obtain will be wrong. We MUST use only light's sticks. In that case, we can never make a reliable measurement using metre sticks, because we never know in advance whether an object is moving with respect to "space" or not. OR

(b) you can maintain a constant speed of light by adjusting the "apparent" length of the ship's metre sticks according to its velocity, so that when we count sticks in the spaceship as light travels and count the sticks laid by the light we end up with the same number. For example, you could say in this example that, given the speed of the ship through space, the ship's sticks have an "effective" length of only half a metre instead of one metre. This maintains the constancy of the speed of light in both frames. OR

(c) You could maintain the constancy of the speed of light by saying that the clocks on the spaceship tick only half as fast as clocks in "space" as the light travels from the rear to the front. Again this would maintain the speed of light in both frames. OR

(d) You can adopt Einstein's approach to the problem and alter both distances and time so as to maintain the constancy of the speed of light in all frames.

I can't see any other options.

But do you agree that if I measure the speed of light using the spaceship's sticks then I'll get the wrong answer?

So, am I not allowed to use the spaceship's frame for measurements? Should I always measure things using light relative to "space"? Or can you fix your system some other way so that I can accurately measure lengths using metre sticks inside the spaceship?

It's important to realise that you haven't answered the question I asked here. If we accept your premise that light always lays the same number of sticks in the same amount of time, something has to give in the spaceship frame. Either the speed of light is not the same in that frame, or else we need to adjust lengths, times or both to make sure that the speed of light stays constant in that frame. Or, we give up on using any frame but that of "space", and say we must use light for every length measurement, because we can never rely on the accuracy of metre sticks laid by anything but light.

It is no mistake. Einstein's postulate is that the speed of light is the same in all frames. That is, if you measure the speed using sticks nailed to the ground and again using sticks nailed to the spaceship you get the same answer for the speed of light. The way that happens in relativity is that metre sticks inside the spaceship actually have different lengths to metre sticks on the ground, and clocks inside the spaceship actually tick at a different rate to clocks on the ground.

I agree with you that if measurements are made in a frame in which the ship is moving (such as the ground frame), then light will lay more or less ground-length sticks in each direction. This is because light must travel at the same speed in both directions in the ground frame.

Similarly, in the spaceship (and we do not agree on this), light must lay equal numbers of sticks in each direction in order to have the same speed in both directions in the spaceship frame. That's Einstein's picture.

Yes, I understand what you're saying. I just know that your picture is inconsistent.

I'm not actually clear about what your argument is with Einstein's picture. The discussion about what is "real" and what is "illusion" needs fleshing out. What matters to a physicist is that we have a workable model that gives the right answers so we can do physics. The model should match what we measure in reality. All tests of Einstein's theory give a good match to what is measured. So, in a sense it's a philosophical question about whether space "really" contracts in different frames, or whether time "really" dilates, or whether these are "illusions". What we do know is that there's nothing illusory about the results of twin-paradox experiments, for example. Things really do seem to experience time at a different rate when in motion. Either that, or something else is going on that gives an outcome that makes it look exactly like that is happening.

Anyway, what I'm saying is that I'm not sure how you think that Einstein's theory is flawed. Again, I see at least two possible arguments:

(a) Einstein's theory is self-inconsistent (i.e. has mathematical errors).
(b) Einstein's theory is consistent but does not match real-world observations (in which case you need to point out which real-world experiments diagree with Einstein's predictions).

But surely "space" is a frame just like every other?

 

Motor Daddy:

When you say "the ship moves relative to light", you're not using the reference frame terminology that I thought we agreed on earlier. To say that the ship moves "relative to light" introduces a picture by which a bunch of sticks is stationary with respect to the light, and the ship's velocity is measured relative to those sticks.

As soon as you say "light moves at speed c", you're automatically talking about a frame other than one in which the individual photons of light maintain constant positions relative to the measuring sticks.

Apart from this point, I understand what you're saying, though.

Obviously, in general the length of the ship is NOT determined by the light travel time. The ONLY time that the length of the ship is correctly recorded by light, according to you, is when the ship has zero velocity. If the ship has any other speed, light will have to travel a longer or shorter distance from one end of the ship to the other. Moreover, the ONLY time the rulers nailed to the ship agree with the light travel time is when the ship has zero velocity, according to you. Those rulers were calibrated correctly using light, we assume, so the rulers always measure the correct length of the ship. Light gets it wrong if the ship has a velocity, because we need to factor in the velocity of the ship in order to "correct" the length of the ship when we measure it with light.

But this isn't the main problem. I'll get to the main problem shortly.

I think you misunderstand. I am not using the sticks nailed to the ship to measure the velocity of the ship; I'm using them to measure the velocity of light inside the ship. The velocity of the ship is always zero with respect to the sticks nailed to its floor; I believe we have already agreed on that.

You claim I cannot use the sticks nailed to floor of the ship to measure the speed of light. But if those sticks have been properly calibrated using light previously, before they were nailed to the floor and while they had zero velocity, then those sticks all have the same length as the sticks that light lays down. Also, the clocks in the ship all keep time just the same as clocks everywhere else in the universe, according to you.

So why can't I measure the speed of light in the reference frame of the ship? Surely I should be able to measure how far light travels in a given time using my correctly-calibrated sticks on the ship and correctly calibrated clocks on the ship, and get the correct answer for the speed of light inside the ship. Shouldn't I? And that measured speed should naturally match the unchanging, defined speed of light, always, according to you. How could I use correct sticks and clocks and yet calculate a speed of light that is wrong?

The ONLY way this could happen is if I'm (a) just not allowed, by fiat of Motor Daddy, to measure the speed of light at all, OR (b) the speed of light is ONLY 299792458 m/s in a frame that has zero velocity, so I should expect a "wrong" answer in the ship's frame when it has a velocity.

If (a), then I'm not clear why I can't measure the speed of light. Apparently I can measure the length of any object other than light, so why can't I measure light? Why does light have to be merely defined? Wouldn't measuring the speed of light be a good way to confirm that I'm using correctly-calibrated rulers and clocks?

If (b), then you have to give up on your claim that the velocity of light is the same in all reference frames, because as I have clearly shown, under your assumptions the speed of light MUST be different in the reference frame of the travelling ship compared to its speed in a ship that has zero velocity.

This is currently the number 1 thing that is making your theory self-inconsistent. And it could be easily fixed, as far as I can tell. All you have to do is to say that light ONLY has a measured speed of 299792458 m/s when measured in a frame that has zero absolute velocity. Why use Einstein's postulate when (a) you say you disagree with Einstein, and (b) it makes your theory inconsistent?

What stops me from measuring it? Nothing. But if I do, I'll calculate a different speed for the light depending on the velocity of the ship through "space". So, what you're really saying is you don't want me to go off and measure the speed of light. You'd rather pretend that it has the same speed in all frames. If I actually measured it in the ship's frame, I'd discover that light doesn't have the "correct" velocity in that frame, so your solution is to forbid me from doing the experiment that proves this aspect of your theory false.

Only at the expense of dispensing with the constancy of the speed of light in all reference frames. As I said, I don't know why you're so keen to hold onto that postulate, which after all is one Einstein introduced, and you say you disagree with him about just about everything else.

Those equations are correct provided that (1) the light travel times are different in the two directions, and provided that (2) the light travel times are measurably the same in whatever frame you measure them in (i.e. no matter whether you measure the times using clocks on the ground, on the spaceship or on a different spaceship flying parallel to the first at a different speed).

Your error is that you assume both of these provisos, completely without any actual evidence to back up your assumptions. In fact, assumption (2) turns out to be completely wrong. Assumption (1) is true in every frame except for the frame of the ship (i.e. its rest frame). In the frame of the ship the light travel times are in fact always equal.

Therefore, if you actually used your equations in a real-world experiment that measures the light travel time using clocks on the ship, then your equations would tell you that the ship always has zero velocity. And this would happen no matter how fast the ship was flying with respect to anything else you care to name.

We can go back and forth on this forever and get nowhere: "The travel times will be different." "No they won't". "Yes they will". Repeat ad nauseam. I'm just telling you, in the full expectation that you'll continue to make the assertion regardless.

Then you MUST agree that the naive calculation of the speed of light using the ship's sticks gives a different value for the speed of light than the "correct" value.

To use a reference frame, I should not need to add in "hidden" information about the ship's speed in order to calculate the "correct" result for the speed of light. Something is wrong here. Either the ship's frame is not correctly calibrated, or else it does give correct answers but the speed of light is not the same in the ship's frame as it it outside.

You often complain that Einstein needs to know the velocity of a frame before he can start doing anything, but it seems to me that in this instance it is you who needs to know the ship's speed in advance in order to "correct" the measurements to give the correct speed of light in the ship's frame.

If you like, you can assume I'm doing it as a check to make sure that the rulers I nailed to the floor and the clocks I'm carrying on the ship are correctly calibrated so that I can use them to perform correct measurements on other objects.

You're telling me that before I can do this check, I first need to determine the velocity of the ship using your methods, so I can "correct" all my subsequent measurements made using light.

Taking that point to its logical conclusion, before I can measure anything, anywhere, I must always first use your method to determine the velocity of the thing I'm standing on. So, I need to measure the velocity of the Earth before constructing any metre sticks using light to measure teh correct length in a metre stick factory, for example.

What is the velocity of the Earth, by the way? I assume you have this important piece of information to hand.

But all speeds of objects in the ship that I calculate using the ship's sticks will be wrong, won't they? To get the correct speeds I need to add or subtract the ship's velocity to or from all measured speeds. More generally, I'll need to perform a vector addition or subtraction, because the ship may be moving in a different direction than the object I'm trying to measure the speed of inside the ship.

No, and I never said I was trying to do that. Doing that will always give an answer of zero speed. I think we agree on that, don't we? And to get the true speed of the ship, I need to use light to determine it, as per your recipe. That's the first step before I can measure anything else inside the ship.

This is the current crux of our disagreement. You're saying to get the right answer for the speed of light in the ship's frame, I need not only the measurements of distance covered and time taken, but ALSO I need to know the ship's velocity in advance. Whereas Einstein says you can just make the measurements and calculate the result. Done.

Call me perverse for daring to want to measure the speed of light rather than accept a definition, but I wonder what people did with such problems prior to the redefinition of the metre in the 1960s. One wonders how physicists ever got any useful work done, since they couldn't accurately measure anything without having access to your measurement procedure. And since they still don't correct for the Earth's absolute velocity through space when they do experiments in their labs today, all the currect results of physics must be wrong, too.

Well, not really, because the ship is really moving too. The real distance moved by that table can only be determined by light. Right? Metre sticks are mostly useless, because they are invariably used in frames that are themselves moving.

I've never said I could do that, or rather I said that the result of such a measurement will always be zero. You're got a wrong idea here.

No. I haven't denied that your method works just fine if you apply it in any given reference frame. Inside the ship, it gives the correct speed - zero - because the light travel times are the same in both directions in that frame. Outside the ship the travel times will be different and you can calculate the speed of the ship relative to whatever outside frame you want to use.

You have never managed to identify the "space" frame in an unambiguous way. You can't say that is it the frame in which light travels at 299792458 m/s, because you say that light travels at that speed in every frame. But the only way you can ensure that is to introduce a correction factor based on the speed of the given frame relative to "space", and yet the speed of any frame in "space" is supposedly determined using light. Therefore, attempting to define the "space" frame using light is circular if you also want to maintain the constancy of the speed of light in all frames.

Einstein denies that the ship has a single "true" velocity relative to "space" (or "in space", if you prefer). He says that in its own frame it always has zero velocity. In the Earth frame it has some other velocity. In the frame attached to the Andromeda galaxy it has some third velocity.

Einstein asserts that the speed of light will have the same measured speed in all frames, which is why we are free to define that speed in the first place.

Importantly, Einstein's assertions are in accordance with all available experimental evidence. Your assertions are not.

So to measure the speed of light I need to measure (1) how far light travels in a frame, (2) how long it takes to do so, and (3) how fast the frame is moving and in what direction. And to work out (3) I need to measure at least 6 one-way light travel times (2 for each orthogonal direction in space).

Einstein, on the other hand, says if I want to measure the speed of light I simply measure (1) how far it travels and (2) how long it takes, and we're done.

Einstein says that to measure the speed of anything in a given frame you use the same method (1) see how far it goes, relative to the sticks in the frame, (2) see how long it takes, according to clocks in the frame, (3) divide (1) by (2) to get the answer. The same method is applied to object speeds and light speeds.

You, on the other hand, say you can't measure the speed of light in a particular frame without first knowing in advance the speed of the frame. And to know that you first have to assume a defined speed of light and make a bunch of other measurements. I'm not sure if you have different rules for measuring the speeds of other objects in a given frame. It seems to me that previously we agreed that speeds of other objects can be measured using Einstein's method in any frame. So maybe only light is special for you. That introduces an asymmetry in your theory that Einstein does not have in his.

Ok. What's the velocity of the Sun through "space"? Or the Earth, if you prefer. Or the Milky Way?

Can you tell me any of these things?

Or is it only in principle that you can tell me these things, and not in reality?

 

Motor Daddy:

Wait! Didn't you say you need TWO measurements of the light travel time to determine the velocity of the ship and its length? You can't do it with just one, can you?

If that is your position on the matter, then you have given up the notion that light travels at the same speed in every reference frame. What your real position is is that light has a constant speed in the reference frame of "space". In every other frame its measured speed is different. Sure, you can reconcile the "wrong" measurements if you happen to know the speed of the frame you measured in, but that's a correction to the basic measurements.

Einstein, on the other hand, gets the numbers right without any mucking around with correction factors.

EVERY velocity is with respect to some reference frame, so as soon as you say "light has a velocity" you've implicitly defined a reference frame of some kind. I say there is only one reference frame in which you believe that light has its defined speed: the reference frame of "space". In any other frame, the measured speed will not equal the defined speed.

In fact, you can make a set of sticks, nail it to the floor of your spaceship, make your spaceship go any speed you want, then measure the speed of light either inside or outside the ship and you'll find it has the same speed. That's in Einstein's universe, not Motor Daddy's. It's a completely counter-intuitive idea, but it's correct, as verified by countless experiments.

I note that you have now given up on your previous claim that light has the same speed in all reference frames. You have now altered that claim to read "Light has the same speed when you adjust the measured speed according to the absolute velocity of the frame you're measuring it in."

Given this amended claim, your theory is now clearly distinguished from Einstein's. I'm glad we have got to this point at least. Previously you were using Einstein's language but also arguing against the results that would be implied by that language.

At some point, if you wish to construct a truly consistent theory of physics, you'll need to somehow reconcile your speed-of-light postulate with the predictions of Maxwell's equations that light actually travels at the same speed in all frames, without any necessity for correcting the speed of the frame. Nobody else has ever managed to do that without using Einstein's spacetime, but maybe you can/have. If you've done this, I'd be very interested to see your derivations.

When you talk about light "laying sticks", those sticks are obviously "left behind" as the light travels. So, those sticks form a reference frame and the photons of light necessarily travel relative to that frame. Your contention, I assume, is that those sticks left behind by the light are absolutely at rest in "space".

That's all well and good for you to make that claim. If your theory was correct, then it would be a true claim. However, countless real-world experiments prove that the numbers do "add up" to give the same speed of light in every frame. This is actual experimental evidence that disproves your theory.

To continue to maintain that you are correct in the face of reams of actual evidence that proves you wrong is rather perverse, wouldn't you say?

Your light always travels at the same speed only in the frame of the sticks it leaves behind - the frame of "space". In every other frame, measurements should get the answer "wrong", like you say. You need to correct for the speed of every other frame when you make a measurement, in your system.

Einstein requires no correction. In Einstein's universe (i.e. the actual one) the measurements always get the speed of light correct in any frame, with nothing extra needed.

Yes, that's exactly what I'm saying. And yes, it sounds absurd. I keep saying: it's completely counter-intuitive. It goes against every instinct you have from your observations of motion in your everyday, low-speed life. But countless actual physics experiments confirm that it is true nonetheless.

No. In my analysis up to this point, I have been working with your spacetime, not Einstein's. In getting the "wrong" answer for the speed of light in the spaceship frame, I used your assumptions that rods in the spaceship have the same length as ones outside, and that clocks in the spaceship keep time with clocks outside. In the real world, in Einstein's universe, neither of your assumptions is true. Using Einstein's assumptions, when we measure the distance travelled by light and the time taken, then divide one by the other, in any frame, we get the same result for the speed of light, regardless of the "speed of the frame in space".

i.e. in the Motor Daddy universe I need to add in correction factors, whereas in Einstein's universe the answers are correct automatically.

I can't give you an answer, because I don't believe in absolute velocities through "space". You do.

I can tell you the relative velocity of the Earth, relative to myself, the Sun, the centre of the Milky Way etc.

I would have thought that it was supremely important, before you do anything else with your theory, to identify the zero-velocity "space" frame. That would be especially important because you need to know the speed of every other frame relative to that before you can do any useful physics in the Motor Daddy universe.

So what makes light special? Why don't photons of light behave just like little balls? Do you have a theoretical answer to that question?

Don't just repeat yourself and say "Light lays it's own sticks; balls do not." I'm asking you what is the physical reason why light lays its own sticks and balls do not. Do you know?

Yes, I can. Because I know from Einstein (supported by experiments) that light will have the same measured speed in every frame of reference.

All I can say to this is that it is funny that physics just seems to ... work! You've got a CD player that plays CDs. You have a microwave oven that works. You may even have a GPS receiver that works. And all of these devices were invented by physicists using Einstein's theories. They all work rather well, and yet the physics they are based on turns out to be completely wrong at its very foundations, you tell us.

I guess those physicists just hada lot of dumb luck or something.

But without correction for the velocity of the frame, your theory gets it wrong.

You previously agreed with me (and Einstein) that a ship always has zero velocity in its own frame.

Do you want to renege on that agreement now?

Interesting. Now you are saying that even though Einstein gets the wrong answers, the answers "match perfectly" with everything else we know. So maybe we can do physics with Einstein, even though his theories are 100% wrong. Is that what you're saying?

If so, then I'll be quite happy to go on using Einstein's theories, because they are so much simpler than yours. I can make valid measurements of anything in any frame that work just fine using Einstein. If I use Motor Daddy physics, I'll need to constantly introduce correction factors to correct for the "real" velocities of frames. It would be unnecessarily complicated, even if it wasn't just wrong.

He uses the sticks nailed to the floor to measure the distance in the ship's frame. He uses sticks nailed to the Earht to meaure the distance in the Earth frame. Simple!

As to "faulty sync method", you haven't mentioned that so far, so I'm not sure what you're talking about.

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By the way, I've been playing around with your method for calculating lengths using light. I've come up with the following nice formula:

\(L = \frac{2ct_1 t_2}{t_1+t_2}\)

Here, \(t_1, t_2\) are the measured light travel times in the two directions, \(c\) is the speed of light, and \(L\) is the length between the detectors.

Notice that this formula gives the length in terms of ONLY the light travel times, and the velocity of the reference frame is not needed.

This formula is correct both in the Motor Daddy universe and in Einstein's universe. The only difference is that in Einstein's universe, the measured values of \(t_1\) and \(t_2\) will vary depending on the reference frame of the clocks doing the measuring, whereas in the Motor Daddy universe those values are supposedly fixed.

In particular, if we do the experiment in the spaceship's frame, then Einstein (and experiment in the real world) tells us that \(t_1=t_2\). Therefore, in that frame (ONLY) the formula becomes:

\(L= \frac{2ct_1 t_2}{t_1+t_2} = \frac{2 c t_1^2}{2t_1} = ct_1=ct_2\)