Relative Velocity Experiment - A Matter of Discussion

[Dale]

it isn't entirely clear what he means by "stationary" and "the stationary system".

"Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the “stationary system.”"

It is just a label for an arbitrary inertial frame.

https://www.fourmilab.ch/etexts/einstein/specrel/www/

 

[CKH]

Thanks Dale. In my carelessness I missed this. So now I believe in all cases he is referring to inertial frames.

In the clock synchronization with points A and B, I guess he means A and B are points at rest in the same IRF?

So now I can state a definition more accurately: Time in an inertial frame may be defined by any chosen clock at rest in that frame. That clock must be read at it's position.

Other clocks in the same frame can be synchronized with that clock using the specified procedure.

Is this what is meant by Proper Time?

Does that sound about right?

 

[ghwellsjr]

I thank you very much for your patience. Despite several attempts on my side, it is clear that we still are not debating the same issue. I hope this new input will do better.

Maybe so but it appears that you are demanding that I produce for you an explanation that claims a physical interpretation of the Coordinates.

This is a misunderstanding again. I made clear that coordinates are not physical quantities. Contrary to your statement, I claim that it is not possible to derive a complete model of the physical behaviour of each clock from SR formulas.

If you define the speed of each clock according to an IRF and you state the amount of Coordinate Time the clock moves at that speed, then SR can determine the amount of Proper Time that the clock accumulates. If the clock then accelerates to a new speed, you can repeat the process as many times as you want for a complete model of the physical behavior of each clock. This is based on the so-called Time Dilation formula.

Or, if you define the speed of each clock according to an IRF and you state the amount of Proper Time the clock moves at that speed, then SR can determine the amount of Coordinate Time that the clock accumulates. If the clock then accelerates to a new speed, you can repeat the process as many times as you want for a complete model of the physical behavior of each clock. This also is based on the so-called Time Dilation formula.

If this isn't the sort of thing you are after then you will have to tell me how I missed the boat once more.

… the "build up" of Proper Time each time it visits the inertial clock indicates the difference in the Proper Times between the two clocks. Isn't that simple?… so that when they reunite, the difference in their Proper Times is the same when analyzed in the first frame.

This is not the point. I've made explicit than I don't challenge this. The gap in elapsed time between both clocks, as predicted by SR upon completion of the first revolution, relates to the whole time interval covering two consecutive “visits”. But please concentrate on the interval between the first two “visits”, I mean before the first revolution of the non-inertial clock has completed. SR cannot demonstrate what fraction of this gap has been acquired during the first half (or any other fraction...) of the first revolution. SR does not cater for a continuous model for the physical behaviour of the clocks, it only provides discrete values for the delay corresponding to the successive discrete events named “visit”.

I don't see why you are saying this. In the rest frame of the inertial clock, the clock moving in a circle accumulates Proper Time in a linear manner. During the first half of the revolution it accumulates one half of its total time for the loop. In other frames, Relativity of Simultaneity plays a part such that the half-way point in Coordinate Time which is proportional to the half-way point in the Proper Time of the inertial clock is no longer the half-way point in the Proper Time of the accelerating clock. In this case, the term "half-way point" is ill-defined.

The only situation in which SR cannot precisely determine the progress of Proper Time for the clocks in a scenario is when the scenario is ill-defined having nebulous setups for the scenario or imprecise terms. It happens all the time here on PF but it is the fault of the poster rather than SR, don't you agree?

In my input #23 I intentionally started my presentation of the usual “twins scenario” before the first collocation event of both clocks: two identical clocks A and B moving toward each other at a constant closing speed v. At this stage, SR cannot state whether one of them ticks slower than the other.

A constant closing speed does not identify an IRF. Pick an IRF and the speeds of both clocks are identified and so are their Time Dilations. As I said, ill-defined scenarios come up all the time in PF. Remember, Time Dilation is a coordinate effect and you need to state the scenario in terms of a coordinate system in order to determine both the speed of each clock and the Time Dilation of each clock.

Then both clocks cross over close to each other and this is the first collocation event. Timers are reset on both clocks. From that point onward both clocks continue their journey and now move away from each other. SR still cannot state anything about a possible difference in their physical behaviour. Further on, the motion of clock B gets reversed so that both clocks move again toward each other at a constant closing speed v. SR still cannot state anything about a potential difference in their physical behaviour. But IFF clock B joins clock A, then SR can state a posteriori that a delay affects clock B as compared to clock A, this delay being globally acquired over the global time interval between the first and the second collocation. SR does not and cannot state how this delay has built-up between both collocations.

This is simply not true. Clock B will accumulate exactly half its total Proper Time between the two colocations at the point its motion gets reversed. All frames will agree on this fact. They will not agree that this happens at the halfway point in the Coordinate Time between the two colocations.

Conversely, when physicists assume that this delay has built-up steadily all along the time interval, they give precedence to the rest frame of clock A over any other IRF: they interpret the coordinate values of the periods corresponding to the rest frame of clock A as a physical model for the behaviour of both clocks. Such an interpretation goes beyond what can be rationally derived from the SR theory. There is no objective reason to give precedence to any specific IRF.

But all IRF's will show a steady build-up of the delay during the first part of B's trip away from A and another steady build-up of an equal delay during the last part of B's trip back toward A. The two build-ups can have different rates based on the different Time Dilations in the different IRF's caused by the different speeds, but this is what SR is all about.

The same reasoning applies equally for the time interval between two consecutive collocations or “visits” in the periodic scenario proposed by Einstein. SR does not state which fraction of the global time gap is acquired during a given fraction of the revolution. It only calculates a discrete (i.e. non-continuous) adjustment of the time delay for each revolution taken as a whole.

I already addressed this issue. It's because of Relativity of Simultaneity. What is a particular fraction of time for the inertial clock is not the same fraction of time for the accelerated clock.

SR theory affirms the physical time displayed on each and every clock no matter what its motion.

I'm not convinced: SR only provides discrete values corresponding to collocation events. Any continuous extension connecting these “dots” consists in an interpretation which goes beyond SR. Every such interpretation breeches the equivalence of IRFs.

I hope I have been able to show you that each of these three sentences is incorrect.

I hope we are now addressing the same issue.

Me too.

Thanks.

You're very welcome.

When are you going to start on Doppler?

 

[ghwellsjr]

You already asked this but I guess my answer didn't make sense to you. Let me try again.

You are talking about the Coordinate Time of an Inertial Reference Frame (IRF) which does not have to be associated with any actual clock or clocks. However, sometimes people, including Einstein, use the Proper Time of two or more clocks at rest at different locations in an IRF to illustrate the Coordinate Time at different Coordinate Locations. But after you understand what Coordinate Time is all about, you need to disassociate it from any real clocks, otherwise the Lorentz Transformation will be a meaningless exercise and you will be forced to believe that only certain IRF's are preferred (those that have real clocks at rest in them).

Note: Maybe we should take this to another thread like "Einstein's definition of time". I don't want to derail the poster's thread.

Words don't make much sense if you don't know the definitions a person is using. That is, in my experience, the biggest problem in communication.

I don't know how you define Coordinate Time and Proper Time.

I don't define those terms, I look them up. Please look them up in wikipedia or somewhere else. You will see that I am merely restating the standard definitions.

You cannot measure or "tell" time without clocks so the idea "you need to disassociate it [Coordinate Time] from any 'real' clocks" is confusing, since you haven't defined any of the terms.

You don't need real clocks in many situations. For example, I can say that an object starts at the origin of an IRF (where all the coordinates are zero) and moves at 50% c in the x direction. Then I can say without any clock that when the X-Coordinate Distance equals a particular value, the Coordinate Time is a particular value.

So, in any IRF, you can have any number of real clocks at rest or moving inertially at any speed in any direction or accelerating in any arbitrary manner.

Unless there is a real clock shortage.

Do you mean "In an IRF, you are able to have any number of 'real' clocks moving freely". That is obvious unless there is something special about a "real" clock or to "have a real clock" in an IRF.

Yes, that's what I mean. I'm sorry if I have to state something obvious but I was responding to your statement:

According to SR (by definition) a clock only measures time in the rest frame of the clock.

Also you seem to be implying that "real" clocks exist only in an IRF. Do you see how complicated it is to understand your statement?

I guess it's because I'm trying to be precise. When we're talking about Time Dilation, we are talking about real clocks in an IRF because Time Dilation is a Coordinate Effect of a real clock. You need both the clock and the IRF, by which I mean a Coordinate System.

Can you define "real" clock? What kinds of clocks aren't real?

A real clock of the type that we are considering for Time Dilation effects is one that uses independent physics to determine its timing such as an atomic clock, a quartz crystal watch, a windup clock. It does not include a clock that is plugged into the wall and synchronized to power line frequency or a cell phone clock that gets its time from the cell phone towers, or a GPS clock that gets its time from the GPS satellites or computer clock that gets its time from the internet. It also doesn't include a pendulum clock.

Clocks that aren't real are the ones that we sometimes imagine are at the coordinates of an IRF.

---

I just read the first page of the 1905 publication by Einstein. He talks about clocks. He asserts that you can read a clock (correctly) if you are close to it.

He then introduces his synchronization method for two clocks at points A and B. Oddly, he in no way restricts the relative motions of points A and point B when he defines synchronization. I'm not sure what he intends here, but the synchronization procedure seems strange unless A and B are in IRFs or perhaps even in the same IRF.

How do you interpret it?

He's talking about two points at rest in the system of Cartesian co-ordinates that he described at the beginning of the section.

Then he say this:

It is essential to have time defined by means of stationary clocks in the[?] stationary system, and the time now defined being appropriate to the stationary system we call it “the time of the stationary system".

Now it's not clear what he means by a "stationary system". Maybe he is saying that the time in the frame of the clock is measured by that clock . He already said that to read a clock you have to be close to it, but now it sounds like he's adding that this clock defines time at it's position, but only within it's reference frame (which may have arbitrary motion).

This seems to be exactly what I stated as the definition to time, except I failed to mention that you must be at the position of the clock to read it.

Or maybe by "stationary system" he means an IRF in which the clock is at rest?

Any ideas about what he means?

He's in the process of defining what an IRF is so it wouldn't be exactly correct to say he means an IRF in which the clock is at rest (although eventually it will come to that). Instead, I would revert back to his original paragraphs where he talks about the system of Cartesian co-ordinates (which includes just the three spatial coordinates).

No, at least it doesn't sound like one of the two postulates that Einstein presented.

My mistake, I meant definition of time, not an assumption (postulate) about time.

That's not a very clear definition. Could you please elaborate?

Neither is Einstein's definition. It requires some reading between the lines because in the expression "time is defined by means of a stationary clock in the stationary system" it isn't entirely clear what he means by "stationary" and "the stationary system".

The difference in my definition is the use of the term "frame". "A clock measures time in the clock's frame" instead of "stationary". I'm assuming that's what he means, but I could be entirely mistaken.

Thoughts?

I would rather say that he's going to use the first clock to define the Coordinate Time at the location of that clock. Then he's going to add a second clock some distance away that will set the Coordinate Time at its location once it get synchronized to the first cloak. At this point we image an infinite number of additional clocks are every possible location. Then we abstract away all the clocks and trust that the Coordinate Time has been adequately defined just like the Coordinate Distances are defined without the use of a network of rigid real meter sticks.

 

[ghwellsjr]

Thanks Dale. In my carelessness I missed this. So now I believe in all cases he is referring to inertial frames.

In the clock synchronization with points A and B, I guess he means A and B are points at rest in the same IRF?

So now I can state a definition more accurately: Time in an inertial frame may be defined by any chosen clock at rest in that frame. That clock must be read at it's position.

Other clocks in the same frame can be synchronized with that clock using the specified procedure.

Is this what is meant by Proper Time?

Does that sound about right?

That sounds more like what is meant by Coordinate Time. But all clocks, even the ones that illustrate Coordinate Time keep track of their own Proper Time.

 

[Dale]

So now I can state a definition more accurately: Time in an inertial frame may be defined by any chosen clock at rest in that frame. That clock must be read at it's position.

Other clocks in the same frame can be synchronized with that clock using the specified procedure.

Yes, I believe that is a reasonable definition of coordinate time in an inertial frame.

Is this what is meant by Proper Time?

I am not sure when the concept of proper time was first introduced. It was certainly some time after the 1905 manuscript. So that manuscript doesn't make any distinction between coordinate time and proper time.

Proper time is defined as $\int d\tau$ where $d\tau$ is the timelike line element. For an inertial frame $d\tau^2=dt^2-(dx^2+dy^2+dz^2)/c^2$. For a clock at rest in an inertial frame $dx=dy=dz=0$ so $d\tau=dt$.

 

[CKH]

OK, I obviously have a lot to learn about the terminology that has been established to discuss relativity.

Regarding "real" clocks. I took that for granted in that a clock must a self-sufficient time keeper, otherwise it is useless to define time. A "plugged in" clock is just a puppet of some other real clock whose location and motion are not defined by the puppet.

By the way, in part, it is all this terminology that makes things "not simple" for novices. I would not assume that what is "simple" for Einstein is simple for everyone.

 

[Dale]

By the way, in part, it is all this terminology that makes things "not simple" for novices.

I agree. I think that most of the effort in learning any field of study is spent in learning the terminology that is used. If unfamiliar terminology is used, please feel free to ask. That is one very good way to use PF as a resource.

 

[ghwellsjr]

By the way, in part, it is all this terminology that makes things "not simple" for novices. I would not assume that what is "simple" for Einstein is simple for everyone.

I think Einstein was comparing his theory to other prevailing theories of the time, most notably, one of the early incarnations of LET. In fact, it is because Einstein's theory is simpler than those other theories that motivated most of the scientists to abandon them and adopt Einstein's theory exclusively.

In addition, if you want to see the difference between a simple theory like SR and a complex one, try Einstein's General Relativity.

 

[quo]

No, the separation rate of the two flashes (according to you) is 2c. But that's not the velocity of anything.

This is a velocity, or a speed, of a distance change: v = dr/dt;

Further: There's no problem at all with having two things separate at a rate greater than c (as observed by a third frame), but their relative velocity will always be less than c.

This is at hot guess - presupposition.

It's possible to detect v > c, what is well known in the GR for example.

In the SR it's impossible to measure one-way light-speed, due to assumed a special method of clocks synchronisation (the method depends on the light speed itself, which we are intend just to measure, thus it is still unknown at this stage. It's contradictory to the axioms of SR), therefore the c is always two-way speed only in this theory.

 

[Nugatory]

This is a velocity, or a speed, of a distance change: v = dr/dt;

It is indeed the time derivative of a distance, but it's not a velocity. A velocity is the time derivative of the position of something, and there exists no coordinate system in which the time derivative of the position of the light flash is $2c$ (or for that matter, anything except $c$ in the flat spacetime that SR deals with).

It's possible to detect v > c, what is well known in the GR for example.

Yes, but there we go out of way to use the term "coordinate velocity" to make it clear that this isn't a real speed; the worldline of a particle moving with such a velocity is still timelike everywhere.

 

[ghwellsjr]

In the SR it's impossible to measure one-way light-speed, due to assumed a special method of clocks synchronisation (the method depends on the light speed itself, which we are intend just to measure, thus it is still unknown at this stage. It's contradictory to the axioms of SR), therefore the c is always two-way speed only in this theory.

What do you mean by the one-way light-speed is contradictory to the axioms of SR? Einstein's second postulate (I assume that's what you mean by axiom) is that the unmeasurable one-way light-speed in any Inertial Reference Frame is equal to the two-way speed of light which is measured at c.

 

[Nugatory]

By the way, in part, it is all this terminology that makes things "not simple" for novices. I would not assume that what is "simple" for Einstein is simple for everyone.

I doubt that it was simple for Einstein before he had figured it out - the concepts are actually not all that hard, the hard part is recognizing and letting go of assumptions ("at the same time", "really at rest", ...) that are deeply ingrained and get in the way.

You're right that terminology doesn't help any, but we're kinda stuck with that problem. These are new concepts, there is no existing terminology to describe them, so we have to come up with new terminology... And that is pretty much necessarily going to be as unfamiliar as the concepts themselves.

 

[quo]

What do you mean by the one-way light-speed is contradictory to the axioms of SR? Einstein's second postulate (I assume that's what you mean by axiom) is that the unmeasurable one-way light-speed in any Inertial Reference Frame is equal to the two-way speed of light which is measured at c.

In fact the c = const in the relativity theory is a math trick only.
This is quite invisible in the equations, because there is always the compound: cdt, never the dt alone directly.
Therefore if the c changes, in any way, the SR interpretes this as the dt instead of the light speed changes (the relative simultaneity, ect.), and this gives the same equations, thus the results also.

I stay in place and there is the lightspeed, say from the sun, c relative to me.
Now I start to move with a speed v > 0, and the light reaches me still with the same speed c?

This is the most I know ridiculous impossibility, only idiot can believe in this. :)

 

[phinds]

I stay in place and there is the lightspeed, say from the sun, c relative to me.
Now I start to move with a speed v > 0, and the light reaches me still with the same speed c?

This is the most I know ridiculous impossibility, only idiot can believe in this. :)

Then all serious physicists and knowledgeable students of physics are idiots, according to you.

 

[Nugatory]

This is the most I know ridiculous impossibility, only idiot can believe in this. :)

You'd think so, wouldn't you? But experiment after experiment has shown that this really is the way the world works.

It might be a little bit less surprising if you know that the speed of light can be calculated from Maxwell's laws of electricity and and magnetism (google for "Maxwell's equations"). Now imagine me on Earth sending a light signal to someone on Mars. We're both sitting comfortably at rest at our desks in our homes on our respective planets, so it will be very hard to make a case that one of us is "really moving" and the other isn't - yet Mars is moving at many kilometers per second relative to earth. The signal leaves me traveling at speed $c$ relative to me, just as I expect from the laws of E&M. The only way it won't be traveling at speed $c$ when it reaches him is if the laws of E&M are different on Mars and on Earth - yet he is at moving at many kilometers per second relative to me.

So you get to take your choice: Either the laws of E&M change according to your motion; or everyone gets the same laws of E&M and therefore the same speed of light no matter how they're moving. Experiments have come down decisively on the side of "same speed of light".

As a historical note... this was THE great unsolved problem of physics between 1861 when Maxwell's equations were discovered, and 1905 when Einstein discovered relativity.

 

[ghwellsjr]

What do you mean by the one-way light-speed is contradictory to the axioms of SR? Einstein's second postulate (I assume that's what you mean by axiom) is that the unmeasurable one-way light-speed in any Inertial Reference Frame is equal to the two-way speed of light which is measured at c.

...I stay in place and there is the lightspeed, say from the sun, c relative to me.
Now I start to move with a speed v > 0, and the light reaches me still with the same speed c?

This is the most I know ridiculous impossibility, only idiot can believe in this. :)

I agree that what you said is ridiculous but that's not what Special Relativity says. Please re-read the quote of mine again and you should see how what you said is not what SR says.

If you still don't see the difference, please elaborate.

 

[CKH]

I stay in place and there is the lightspeed, say from the sun, c relative to me.
Now I start to move with a speed v > 0, and the light reaches me still with the same speed c?

This is the most I know ridiculous impossibility, only idiot can believe in this. :)

Well, it is experimentally true, so we are stuck with it. Einstein's explanation is that space and time depend on the movement of an observer in such a way that the measurement of c always gives the same value.

LET (Lorentz Ether Theory which is mathematically equivalent to SR) explains it a somewhat different way. LET analyzes propagation of waves (which comprise both light and matter) in a fixed medium called the ether. LET concludes that moving clocks actually run slower and moving meter sticks are shorter. This results in a measured constant speed for c by moving observers.

So the seemingly impossible happens because moving observers don't make that same measurements as an observer at rest with the source of light.

 

[nitsuj]

In fact the c = const in the relativity theory is a math trick only.
This is quite invisible in the equations, because there is always the compound: cdt, never the dt alone directly.
Therefore if the c changes, in any way, the SR interpretes this as the dt instead of the light speed changes (the relative simultaneity, ect.), and this gives the same equations, thus the results also.

I stay in place and there is the lightspeed, say from the sun, c relative to me.
Now I start to move with a speed v > 0, and the light reaches me still with the same speed c?

This is the most I know ridiculous impossibility, only idiot can believe in this. :)

lol...just when you thought you understood geometry, you realize in reality velocity is a crucial component. Physically more important than the shapes of things at a distance is the order of local "happenings".