Does the *First Postulate* Prohibit different time dilations?

[Ibix]

The principle of relativity says that the laws of physics are the same in any inertial frame. That means that a clock moving at half light speed in some frame must operate the same regardless of why it's traveling at half light speed - i.e., whether it accelerated or I did.

Have a rolex and a light clock on the platform, synchronised in that frame. Rig a bomb so that they explode if they are out of sync. Observed from this frame, then, they do not explode.

Now observe them from the train frame. If there is a different time dilation formula for the two clocks they now tick at different rates. They explode.

The proposal is inconsistent with the principle of relativity since different frames analysing the same system see different outcomes.

I think this is the full version of the argument A.T. has made several times.

 

[Herman Trivilino]

I am trying to critically examine Greene's argument and reasoning that IF different clocks gave different time dilation THEN the First Postulate would be violated. Is it well-settled that it would?

Yes. See Post #24. It's the direct response to the question you asked. Until you can understand that, or explain what it is about it that you don't understand, you'll never be satisfied with any of the responses you're getting here.

 

[Dale]

I would appreciate a "professional scientific reference".

Sure. Here is a college lecture where the argument is used:
https://www.coursera.org/learn/einstein-relativity/lecture/qRmOC/time-dilation

Here is a textbook where it uses the argument even before deriving time dilation in order to justify the use of a light clock in the first place
*link deleted, possible copyright violation*

And of course the Greene book which is not a professional source, but clearly makes the argument.

Now, please do not continue without posting references supporting your argument.

Edit: also
https://newt.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm
http://faculty.tnstate.edu/louyang/teach/Phys2020/ppt/Walker3_Lecture_Ch29.ppt

 

[Physics_Teacher]

Sure. Here is a college lecture where the argument is used:
https://www.coursera.org/learn/einstein-relativity/lecture/qRmOC/time-dilation

Here is a textbook where it uses the argument even before deriving time dilation in order to justify the use of a light clock in the first place
http://web.pdx.edu/~pmoeck/books/Tipler_Llewellyn.pdf

And of course the Greene book which is not a professional source, but clearly makes the argument.

Dale, appreciate the effort you made. Will look at these carefully and post here whether all is now clear or will specify I have further doubt regarding the arguments they make. As per our correspondence, I want to keep within the rules of the forum.

 

[Physics_Teacher]

Sure. Here is a college lecture where the argument is used:
https://www.coursera.org/learn/einstein-relativity/lecture/qRmOC/time-dilation

Here is a textbook where it uses the argument even before deriving time dilation in order to justify the use of a light clock in the first place
http://web.pdx.edu/~pmoeck/books/Tipler_Llewellyn.pdf

And of course the Greene book which is not a professional source, but clearly makes the argument.

Now, please do not continue without posting references supporting your argument.

Edit: also
https://newt.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm
http://faculty.tnstate.edu/louyang/teach/Phys2020/ppt/Walker3_Lecture_Ch29.ppt

I have looked over the links. I did not find anywhere an argument that IF clocks have different time dilation THEN one would be able to Detect Absolute Motion. Absolute Motion (to me at least, see my post #11) is needed to violate the First Postulate.
(There never was a doubt that "motion" could be detected if clocks have have different time dilation)
I will leave it at that, given the rules imposed against my making further argument that the First Postulate is not violated in this situation.

I was never attempting an argument against time dilation being same for all clocks - was only examining the claim that First Postulate would be violated it were not.

 

[Herman Trivilino]

(There never was a doubt that "motion" could be detected if clocks have have different time dilation)

If it's possible to detect motion then it's possible to detect the absence of motion. For example, if you can detect that the train is moving then you can, by definition, determine when it's not moving. Otherwise your detection of it moving is meaningless and not physical. Having an ability to detect motion and its absence is what is meant by the detection of absolute motion.

 

[Dale]

I did not find anywhere an argument that IF clocks have different time dilation THEN one would be able to Detect Absolute Motion.

Are you looking for exactly that phrasing? Sorry, that is silly. Whether they express it as "if ... then ..." or otherwise, or if they call it "the first postulate" or the "principle of relativity" is simply a matter of style. Please read and understand the substance of the argument and don't require other authors to make exactly the same stylistic choices you would make.

Can you yet present an author who agrees with the substance of your argument?

 

[Physics_Teacher]

Are you looking for exactly that phrasing? Sorry, that is silly. Whether they express it as "if ... then ..." or otherwise, or if they call it "the first postulate" or the "principle of relativity" is simply a matter of style. Please read and understand the substance of the argument and don't require other authors to make exactly the same stylistic choices you would make.

I was never worrying about phrasing such as "if ... then ..." or otherwise, or if they call it "the first postulate" or the "principle of relativity." Quoting what I said: "I did not find anywhere an argument that IF clocks have different time dilation THEN one would be able to Detect Absolute Motion."

Can you yet present an author who agrees with the substance of your argument?

The first postulate is from Galilean relativity. All physics authors over the centuries have talked of First Postulate and preferred frames strictly in terms of experiments that can Detect Absolute Motion; the exceptions are a handful recent authors today, such as Brian Greene, who say knowing just that a train is in "motion" (not specifying Absolute Motion) would violate First Postulate. I believe Einstein would never have agreed with such reduction of the First Postulate, and the second postulate is needed to establish (Lorentz transformations derivation) that all clocks must have same time dilation.

 

[Ibix]

I believe Einstein would never have agreed with such reduction of the First Postulate, and the second postulate is needed to establish (Lorentz transformations derivation) that all clocks must have same time dilation.

No, for reasons already stated.

 

[Dale]

knowing just that a train is in "motion" (not specifying Absolute Motion)

Again, this is a stylistic choice. Saying that something is "in motion" without a specified reference frame or reference object is the same as "Absolute Motion". Why should you demand that he use your words?

 

[Justintruth]

The classical laws of mechanics define an inertial frame of reference as one where Newtons law of inertia holds.

The classical transformation laws show that any frame of reference moving relative to an inertial frame of reference with constant velocity will also be an inertial frame of reference.

The classical laws of electromagnetism (Maxwell's equations) predict that electromagnetic waves (light) moves at c relative to any inertial frame of reference.

So we have a contradiction because if I take the velocity of a light pulse relative to some inertial frame of reference, and apply the classical transformation equations to transform the speed of light to another inertial frame moving relative to the first, I get a speed of the light wave relative to the second that is different than c as measured relative to the first.

But Maxwell's equations predict that the speed of the light will be c relative to both frames. That is the contradiction.

This can easily be solve by asserting that Maxwell's equations apply only in one frame and that in all others they do not apply. We call the frame in which they apply "privileged".

Einstein showed that if, instead of assuming that the classical laws of electromagnetism are wrong, and there are privileged frames, you assume they are right, at least as far as they predict that light will travel at c relative to any frame moving at constant velocity relative to some frame of reference where it travels at c, then you get transformation equations that contradict the classical transformation laws, and you get the rest of the theory.

You cannot take the principle of relativity to imply that light moves relative to any frame at c. For example you can have a world in which there are two photons, one at rest in one frame, and the other at rest relative to some other inertial frame. The first photon moves in the second frame and the second photon moves relative to the first. That is a consistent theory in which the principle of relativity holds because the laws are the same in both frames, but the principle of the constancy of the speed of light does not hold, because for either single photon the velocity relative to each of the two frames is different. But in fact the first principle does not even imply constant velocity of light, or even the existence of light.

I think that Greene meant that if you use classical theory then you cannot base a clock on the motion of light (say one second is *defined* to be the time light takes to cover 186,000 miles) because if you measure two such clocks, they will disagree depending on the different light velocities in a given frame. By classical *definition* two clocks must agree.

The principle of relativity does not imply any set of physical laws.

Orodruin wrote: "I created this thread to *rigorously* examine the claim, such as in Brian Greene's book, that principle of relativity prohibits different clock mechanisms from having different time dilation. I emphasize "rigorously."" [Mentor's note: Orodruin didn't write that, the original poster did]

Rigorously the principle of relativity does not prohibit different clock mechanisms from having different time dilation. The definition of a "clock" in classical mechanics does. It does by definition. Time is absolute by assumption and clocks by definition measure it so if one clock has any dilation of any kind relative to another then one of them is wrong. Not so in Einstein's theory. If you have a theory that allows time dilation of one class of clocks over another and this theory holds in each frame then you are consistent with the principle of relativity. If for example you take two different frequencies of photons and define time by them and assume either classical or relativistic Doppler effect then you have a consistent theory in which the laws are the same in each frame but clocks disagree with each other. There is dilation of one set relative to the first and contraction otherwise. Then you just make the laws of physics depend on which type of clock you have and you have a consistent theory. It fails because of it's complexity but it is logically rigorous.

I don't think Green meant that the principle of relativity prohibits different clock mechanisms from having different time dilation. It does not. It is silent on the definition of time and on clocks. However, if you use the classical definition of time and clocks then you cannot have time dilation of one clock relative to another when measured in the same units. If you add the Newtonian transformations and ask where can Maxwell's laws hold you get the answer "only in one class of frames (stationary relative to each other, inertial, etc)" and you can call these frames "privileged".

 

[Dale]

If you have a theory that allows time dilation of one class of clocks over another and this theory holds in each frame then you are consistent with the principle of relativity.

I will ask the same thing of you that I asked of the OP. Do you have a reference that supports this claim (that this set of premises is self consistent)? I do not think this is a self consistent premise.

 

[Herman Trivilino]

Time is absolute by assumption and clocks by definition measure it

Metrologists don't assume clocks measure time, they demonstrate it. The amount of time measured by clocks will differ, but the smaller the amount they differ by the better the demonstration of their validity. Currently the best clocks differ by a second in several billion years. This amount that they differ by doesn't change when they don't move relative to each other, but it does change when they do.

 

[Herman Trivilino]

Metrologists don't assume clocks measure time, they demonstrate it. The amount of time measured by clocks will differ, but the smaller the amount they differ by the better the demonstration of their validity. Currently the best clocks differ by a second in several billion years. This amount that they differ by doesn't change when they don't move relative to each other, but it does change when they do.

So if you have two clocks on a moving train, they stay in sync with each other (within that one second per a few billions of years) because they are not moving relative to each other. When we compare them to a stationary clock on the platform they therefore show the same amount of time dilation. That is the point made by Greene that was mentioned in the original post.

There is nothing more to it and I don't understand why it's such a big deal to some people to learn that absolute motion can't be detected. This has been known and well-understood for more than a century. If our understanding of it were incorrect many of our modern technologies wouldn't work, the most outstanding example being the global positioning system (GPS).

 

[Nugatory]

You cannot take the principle of relativity to imply that light moves relative to any frame at c.

Which is to say that Einstein's second postulate is necessary. We've had a number of threads on this question over the years. However...

For example you can have a world in which there are two photons, one at rest in one frame, and the other at rest relative to some other inertial frame. The first photon moves in the second frame and the second photon moves relative to the first. That is a consistent theory in which the principle of relativity holds because the laws are the same in both frames,

How are the laws the same in both frames? Maxwell's laws of electrodynamics cannot hold in both frames, because they they have no solution in which a flash of light in vacuum is moving at any speed except $c$. To maintain consistency with the principle of relativity you would have to propose some other laws of electromagnetism, ones that are consistent with a frame-dependent speed of light.

 

[Herman Trivilino]

How are the laws the same in both frames? Maxwell's laws of electrodynamics cannot hold in both frames, because they they have no solution in which a flash of light in vacuum is moving at any speed except $c$. To maintain consistency with the principle of relativity you would have to propose some other laws of electromagnetism, ones that are consistent with a frame-dependent speed of light.

To qualify as laws they'd have to explain Nature's behavior. Makes me wonder why anyone would bother proposing explanations of Nature's behavior that are inconsistent with the way Nature behaves. Seems torturous, or at the very least uncomfortable.

 

[Justintruth]

I will ask the same thing of you that I asked of the OP. Do you have a reference that supports this claim (that this set of premises is self consistent)? I do not think this is a self consistent premise.

Which is to say that Einstein's second postulate is necessary. We've had a number of threads on this question over the years. However...
How are the laws the same in both frames? Maxwell's laws of electrodynamics cannot hold in both frames, because they they have no solution in which a flash of light in vacuum is moving at any speed except $c$. To maintain consistency with the principle of relativity you would have to propose some other laws of electromagnetism, ones that are consistent with a frame-dependent speed of light.

From Einstein's paper "The Foundation of the General Theory of Relativity" 1916

http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_GRelativity_1916.pdf

"If a system of co-ordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws also hold good in relation to any other system of co-oordinates K’ moving in uniform translation relatively to K. This postulate we call the “special principle of relativity”"

The principle of relativity, as stated above by Einstein, is silent on optics. You cannot derive from the principle of relativity anything about optics, electricity and magnetism, or clocks other than if you have a theory of them valid in one frame then it must be valid in other frames.

Orodruin wrote: "I created this thread to *rigorously* examine the claim, such as in Brian Greene's book, that principle of relativity prohibits different clock mechanisms from having different time dilation. I emphasize "rigorously."" [Mentor's note: Orodruin didn't write that, the original poster did]

The principle of relativity as quoted above does not prohibit different clock mechanisms from having different time dilation:

Consider two clock mechanisms C1 and C2 and assume that relative to a system of co-ordinates K there is some law that says that the time dilation of clocks of type C1 is some function f() and the the time dilation of clocks of type C2 is some function g() such that f() is not equal to g(). Suppose further that both f'() and g'() are the functions that govern the dilation in some frame K'. Further suppose f()=f'() and g()=g'(). Then these laws are consistent with the special principle of relativity and they predict that time dilation be different for different clock mechanisms. As a concrete example let f()=2*g() and let delta t'=v * delta t.

In theoretical work it is important to trace logically to the assumptions involved. Orodruin wanted a "rigorous" examination of a certain claim that the principle of relativity prohibits different clock mechanisms from having different time dilation. As long as you propose a theory that says that if different clock mechanisms do have different time dilation in one frame, and that same situation is present relative to all frames moving with constant velocity relative to the first, then the principle of relativity holds.

So the principle of relativity as stated by Einstein does not prohibit different clock mechanisms from having different time dilation.

A more interesting question is whether the meaning of time itself prohibits it. Certainly if all mechanisms had different dilation then the notion of time itself would not be very useful. One might say of such a world, that clocks don't exist. However, setting optics aside, if all mechanisms operated according to Newtonian mechanics except one then the concept of time would be useful and a theory could be constructed that was consistent with the principle of relativity.

That this world is counterfactual is not a problem as it is only being cited to illustrate the absence of logical dependence of conclusions about clocks (or optics, or electromagnetism) on the principle of relativity as stated by Einstein. Counterfactual arguments are routinely used to illustrate lack of logical dependence.

As a historical note, the principle of relativity in Einstein's 1903 paper was restricted to electricity and magnetism. So in a sense he generalized the principle in 1917 not only by making laws invariant relative to more general coordinate transformations, but technically he also expanded the principle to apply to physical laws in general.

 

[Justintruth]

To qualify as laws they'd have to explain Nature's behavior. Makes me wonder why anyone would bother proposing explanations of Nature's behavior that are inconsistent with the way Nature behaves. Seems torturous, or at the very least uncomfortable.

The reason that it is neither "torturous nor uncomfortable" is that it is only being used to show an absence of logical dependence. It is not being proposed as a candidate for experimental confirmation.

If I were to say, "All women wear dresses. This person is wearing a dress. Therefore this person is a woman". You might be inclined to say "What if your father wore a dress?" without even blushing over the fact that he never did. It illustrates the flaw in the derivation.

 

[Ibix]

Consider two clock mechanisms C1 and C2 and assume that relative to a system of co-ordinates K there is some law that says that the time dilation of clocks of type C1 is some function f() and the the time dilation of clocks of type C2 is some function g() such that f() is not equal to g(). Suppose further that both f'() and g'() are the functions that govern the dilation in some frame K'. Further suppose f()=f'() and g()=g'(). Then these laws are consistent with the special principle of relativity and they predict that time dilation be different for different clock mechanisms. As a concrete example let f()=2*g()

What, exactly, does that mean? The time dilation factor at rest must be 1 or else the clock is time dilated at rest. In this scheme, assuming that $f$ and $g$ are playing the role of a generalisation of Lorentz's $\gamma$, one or other clock is time dilated at rest. Unless you mean that $f$ and $g$ are the decrease in clock rate? That is, assuming $f$ in vanilla special relativity would be $1/\gamma-1$. But in that case this scheme is inconsistent with the principle of relativity since it's trivial to set up a scheme where the clocks continue to work in their rest frame but fail in any moving frame.

 

[Dale]

You cannot derive from the principle of relativity anything about optics, electricity and magnetism, or clocks

This is not true.

The principle of relativity as quoted above does not prohibit different clock mechanisms from having different time dilation:

This is precisely the point that you were asked to support with a reference. I do not think this is true, and I have not seen any reference supporting this claim.

the time dilation of clocks of type C1 is some function f() and the the time dilation of clocks of type C2 is some function g() such that f() is not equal to g(). Suppose further that both f'() and g'() are the functions that govern the dilation in some frame K'. Further suppose f()=f'() and g()=g'().

I doubt that all of these "suppose"s are self consistent.

That this world is counterfactual is not a problem ... Counterfactual arguments are routinely used to illustrate lack of logical dependence.

Agreed. But even a counterfactual argument must be self consistent. Despite the routine use of counterfactual arguments in the literature, this specific argument does not appear, leading me to believe it is not merely counterfactual but is not even self consistent.

 

[Herman Trivilino]

If I were to say, "All women wear dresses. This person is wearing a dress. Therefore this person is a woman". You might be inclined to say "What if your father wore a dress?" without even blushing over the fact that he never did. It illustrates the flaw in the derivation.

Consider an identical chain of logic applied to the situation involving light beams rather than clothing:

All light beams in a vacuum move at speed $c$. This beam is moving at speed $c$ in a vacuum. Therefore this beam is a light beam.

If I were indeed proposing this as a valid argument your point about clothing would demonstrate the fallacy of my point. But I'm not so it doesn't.

Something has you believing that there is a way to refute the Principle of Relativity, but it was pointed out that the way you've proposed it would require a change in the current laws (laws that describe Nature's behavior) to another set of laws that describe a behavior that doesn't match Nature's behavior.

So just because what you propose is logically valid doesn't mean it matches Nature's behavior. The current accepted proposals are also logical, but they have the added advantage of matching Nature's behavior.

 

[Dale]

So just because what you propose is logically valid doesn't mean it matches Nature's behavior.

I personally doubt that it is even logically valid.

 

[Dale]

The reason that I am so skeptical of the self consistency of the proposition is because of the attached derivation (and other similar derivations referenced in the introduction)
https://arxiv.org/abs/physics/0302045

Only two transformations between inertial frames are consistent with the principle of relativity. Specifically, the Galilean transform and the Lorentz transform. In both cases the time dilation is the same for all clock mechanisms.

So I think that the principle of relativity is inconsistent with clocks of different types having different time dilation (as does Greene and several other physicists). A researcher claiming the opposite would need to show a flaw in these derivations, and I have not seen such a paper, nor apparently has anyone else.

 

[Herman Trivilino]

I personally doubt that it is even logically valid.

I agree that the original argument presented by the OP and defended by Justintruth is not logically valid. I was referring to the tangent he took following Nugatory's post.

Anyway, I just don't understand why creationists find it necessary to attack the Principle of Relativity. I at least think I understand their other stances, but not this one. And I suppose it would be off topic to pursue it here.