Relativity and simple algebra II

If the theory is not borne out by experimental results, then we need to either modify it or throw it away and get a better theory.

Fortunately, all experimental results tend to confirm SR, so far.

 

That only shows me that you don't understand Epstein diagrams.

The radial rays on an Epstein diagram represent, essentially, the proper time axes of the objects involved. Relative speeds are represented by the angles between the rays. Where rays meet, the clocks in the different frames are mutually set to zero. Concentric circles on the diagrams represent circles of "equal proper time".

Behind the whole arrangement is what Epstein calls his central "myth" - that objects "travel through time" at a particular rate. The myth is convenient for certain calculations, but Epstein admits that it is a calculational device, rather than anything real.

On a Minkowski diagram, for instance, with axes x and ct (or x' and ct' or whatever), all light rays make an angle of 45 degrees to the x and t axes. That is not true in an Epstein diagram. Light rays emitted by a particular observer in an Epstein diagram travel at 90 degrees to the "ray" that represents that observer, because the 90 degree angle corresponds to the light moving at a relative velocity of c with respect to that observer.

As I previously advised, you probably should forget about Epstein diagrams, for now. They are not necessary, and they are obviously causing you some confusion.

 

Now you're sounding like you don't understand the scientific method.

We want to explain set of facts (or observations) F. So, we propose hypothesis H, which we think can account for facts F, and more besides. To test hypothesis H, we propose new experiments E, whose results are not known in advance. We use hypothesis H to make predictions P about what the results of E will be, if H is correct. We then conduct experiments E and compare the results R to the predictions P. If R and P all match, then we take that as evidence in support of the truth of H.

Over time, after lots of different Es have been done, hypothesis H may gain the status of a well-confirmed scientific theory T.

Nothing in this process is circular. We don't know in advance if R will match P, or not. If the results don't match the predictions of the hypothesis, then we need to modify the hypothesis and try again with new experiments, or else toss it out and go back to the drawing board to find a new hypothesis.

You should note, however, that even the most confirmed scientific theories (special relativity would certainly qualify as one of those) are never confirmed beyond all doubt. There is always the chance that some new experimental results will come to light that do not match the predictions of the theory. In that case, as scientists, we do what we do every time results don't confirm a hypothesis.

There complications, of course. Experiments inherently have sources of error in them - random and/or systematic. Most experiments do not provide us with absolute information, but information that comes with a quantified level of uncertainty. When results do not match a prediction (within the calculated limits of random experimental error), it is not necessarily the case that the hypothesis is wrong. Maybe something is wrong with the experiment, instead. This is why we usually do lots of experiments, rather than just one. In the case of SR, literally thousands of different experiments (maybe millions, depending on how you count them) have matched the predictions of SR. That's why we have high confidence that it is correct.

No you can't.

You may be correct when it comes to direct evidence for its existence. But when it comes to indirect evidence, there's a heap of it.

In terms of the formal theory itself, length contraction is a derived consequence of the postulates, as is the rest of the theory. You can't remove it from the theory while leaving the rest intact. If length contraction doesn't occur, then one or both of the postulates of special relativity must be false. So, which one is false? Or are both of them wrong? You tell me. You also need to then explain why all the experiments that have been done verify the theory, and have done so for 116 years now.

It's like your man-at-a-distance example. Once he comes close, his thumbnail size disappears, like a "phantom effect". In both cases, this is because the effects being discussed have something to do with the observer, rather than the thing being observed.

There are many different ways to explain why that happens. It boils down to the effects of acceleration, which mean that one of the two clocks in the twin paradox spends part of its time in a non-inertial frame of reference.

Yes.

No. As you sit there in your chair reading this, your perspective is as real as mine.

 

You're introducing yet another new topic into this discussion. It would be easier if we could sort out one problem at a time, instead of trying to sort many things at once.

The main thing to say about your example here is that you're trying to appeal to how things might look from the "reference frame of a photon" or "the reference frame of a light beam". In fact, one of the motivating thoughts Einstein had, which led to his formulation of SR in the first place, is the thought that you can't ride along on a light beam. That is, a light beam has no "rest frame". Or, to put it in more stark terms, it is meaningless to talk about "the reference frame of the light".

What we can do is to consider how the world would look if we could travel very close to the speed of light. As $v\rightarrow c$, we find that $\gamma \rightarrow \infty$. In the rest frame of an observer travelling in the spaceship that is moving very close to the speed of light, "outside" distances in the direction of motion would approach zero, and "outside" clocks would appear to tick very very slowly compared to the spaceship clocks. That would mean that, from the point of view of an observer in the spaceship, the spaceship could cross any distance in a negligibly small amount of time, as measured by the spaceship clocks, as long as the spaceship was moving close enough to the speed of light.

A "pulse of light" probably consists of billions upon billions of individual photons. A pulse that is allowed through an aperture for 1 ms would have a length of 300 km from one end to the other in the "lab frame". It isn't really meaningful to ask a question like "From the point of view of a photon at the rear end of the pulse, how far away is a photon at the front end of the pulse", because that's assumes that we can ride along in the frame of a photon, which we can't. If the pulse was made up of tiny billiard balls travelling very close to, but not quite at, the speed of light, then we could ask that question. The answer would be that the distance in the "rear ball" frame could be very short, in that frame, and in the limit as $v\rightarrow c$, it would go to zero.

From a wave perspective, by the way, the frequency of a light wave is related to its speed and its wavelength by $f=c/\lambda$. We know how the frequency transforms for observers in different frames - just use the relativistic Doppler shift formula, with which you are familiar. But remember that the "frame of the light wave" is not a valid frame. You can't ride along on a light wave.

 

As I said, if you want to toss out the Lorentz transformations, that's fine. But if you still want to do relativity - i.e. look at what observers in different states of motion measure - then you still need some transformation formulas, to allow us to predict measurements in a different frame when we already know then in one frame. The most basic transformations involve the transformation of the space and time coordinates between the two frames. I've already shown you Galileo's ones, and Einstein's. Are you saying you don't know what they are for your theory?

Then you're saying there's no way, in your theory, to compare the lengths of objects in different frames of reference.

Why do you then claim that length contraction doesn't exist in your theory?

If you can't compare lengths, how do you know there is no length contraction?

Explain to me how muons can reach the ground before decaying, as in the muon experiment. Please do that (a) from the perspective (frame) of somebody standing on the ground, and (b) from somebody riding along beside one of the muons.

 

This is a response to post #194:

All rulers spew out real experimental results.

Suppose I have a 30 cm (12 inch) ruler. I can sit here at my desk and measure the length of a book, say, using that ruler. Then, I can take that ruler, jump in my car and go for a ride at 100 km/hr along the freeway. While I do that, I can take the ruler and measure the length of the book again. It doesn't matter whether I sit at my desk or in my car: the ruler still works to measure lengths.

Now, I can also measure moving lengths with my ruler, in principle. For example, I can sit my laptop in my window and take a photo of a bird as it flies past. Then, I can pull out my trusty 12 inch ruler and measure the length of the bird on the photograph. If I'm really quick, I don't even need the photo. I can just mark off the two ends of the bird on my ruler at some instant as it is flying past the window.

I can do the same thing in my moving car. I can sit the laptop in front of the car window and photograph two trees beside the road, say. Then I can take my trusty ruler and measure the distance between the trees on the photograph. Or, if I'm really quick, I can just mark off where the trees are on my ruler as they go past the window, provided I mark them both at the same time.

I am mystified as to why you think any of these examples would be magical.

You can get hold of one of these magical ruler devices yourself, if you want one. They are available in lots of different stores. You can even order them online.

We agree that Bob and Alice can use clocks beside them to measure time in their respective frames. That is not in dispute.

Now you want to introduce yet another scenario. We can discuss your "clock handoff scenario" if you like. Please post the details and we can discuss it. It will make the discussion longer, of course, because we still haven't resolved a lot of issues from earlier scenarios. Up to you.

No. It won't be the same. If Alice stops, she must accelerate to slow down from speed v to speed zero in Bob's frame. That acceleration will affect the "age difference" - it will be different to the age difference if Alice just keeps flying past Bob's position at constant speed.

I'll wait until you show me the math.

You'll have to provide a specific example that shows what you mean, I'm afraid.

Human beings have a biological age. At any given time, a given human being has only one biological age. An "age difference" would be the difference in biological ages between two human beings, compared in some reference frame at a particular time.

I don't mind if you don't like the word "permanent" in "permanent age difference". The word "permanent" would only mean, presumably, that the age difference stays the same, in some frame, after some specified event.

Proper time is always specific to a particular reference frame. There is no universal proper time, and therefore no scars on universal proper time.

You're advising me to talk to somebody else about your claims, your theory? Aren't you an expert on your own theory?

You're mistaken if you believe that proper time is universal. It isn't. Proper time is just the time in some frame that is measured by a stationary clock in that frame. Different frames all have their own proper times.

I'm trying to help you to see where you're going wrong. To do that, I need to compare your erroneous results to the correct ones from SR.

Where your results agree with SR, there is no problem, other than possibly in matters of your incorrect interpretation about what the results are telling you.

 

It would be more useful to concentrate on moving forwards in the thread, rather than backwards. We've sorted out a lot of the issues of definitions etc. that came up early in the thread. Your choice, of course. But you'll probably end up just writing "AA" for a lot of things. There are better ways you could spend your time.

 

Then why does Alice end up with a biological age 2 years younger than Bob, with Alice's elapsed time being 8 years and Bob's elapsed time being 10 years? How is that not an age difference?

Alice doesn't continue without velocity change in the twin paradox. She accelerates three times and ends up reuniting with Bob, so they can compare ages at the end of her trip.

"Velocity change" is acceleration, by definition. We agree that accelerations are associated with time differences.

If you say so. Calling it a "perspective illusion" doesn't change anything that we can measure, so it's not very important.

Luckily, you're not talking to those people here.

Who were they?

It seems to me like you're looking for excuses to ignore the comments of anybody who is willing to examine your ideas. The argument would presumably go like this: you're willing to look at my "alternative" theory of relativity; therefore it follows you do not "actually know something", because if you did you wouldn't be interested; therefore I can write off anything you have to say about my ideas because you don't "actually know something".

Yes. For instance, I've been on this forum for 20 years now. How many nuts do you think I've seen who believe they have found a fatal flaw in the theory of relativity, or who believe they have a revolutionary new alternative that works better? The answer is: lots of nuts. The usual pattern is that these people get upset at the first hint of criticism of their new and revolutionary physics. Sooner or later, the discussion devolves into name calling and claims that nobody is qualified to examine the new revolutionary theory except for its promoter.

 

No. Time dilation is a separate effect to the relativity of simultaneity. The Lorentz factor $\gamma$ in the transformation equations ought to tell you that something more is going on with the time coordinates than a mere rotation. The coordinates are not just skewed, but also re-scaled between frames.

Okay, but so far you have not presented any clock handoff scenarios - just the twin paradox, which involves acceleration.

That's fine for the twin paradox scenario.

That's a meaningless statement. No observer's proper time ever slows. All observers always see their own clocks (which measure their respective proper times) as ticking the usual rate. It is only ever time in "other frames" which is observed to slow.

Probably because it's meaningless.

If you're talking about metrics, you're essentially talking about GR, not SR, although obviously there are a number of different metrics which are "flat".

If you think the Rindler metric is important enough to discuss, you ought to discuss it, rather than making wild guesses about who may or may not have heard of it.

That's a very muddled sort of statement. I can only repeat: all observers always see their own clocks (which measure their respective proper times) as ticking the usual rate. It is only ever time in "other frames" which is observed to slow.

You and I sort of agree on this, only you use bizarre "alternative" terminology to describe it. If you were more precise with your language, we wouldn't need to keep clarifying your meanings.

For example, what is "perspective time", exactly? Can you give a concise definition of the term "perspective time"? If all it means is "the time in some frame other than the 'rest' frame of the observer", then we're in agreement that "perspective time" slows. Of course, what is "proper time" in one frame will be "perspective time" in a different frame, and vice versa. It only confuses matters to speak as if there is a universal "proper time" common to all frames. That simply isn't true, which is why you won't find it in any reputable book on relativity.

You can say it until your face turns red, but nothing in any of your calculations supports your claim that SR is wrong. On the contrary, you rely on the maths of SR every time you calculate a "proper time" or a "perspective time".

You're losing credibility here, ralfcis.

SR is a scientific theory, not a religion. There is no "dogma" involved. The scientific method applies.

If you think SR is wrong, it is up to you to come up with some experiment or example where SR gets the "wrong" answer. Alternatively, you could try to attack it to show that the theory itself makes inconsistent predictions, or something - i.e. that it is logically or mathematically flawed in some way.

Good luck with both of those projects, because expert scientists have been trying to find flaws in relativity for 116 years now, and nobody has yet succeeded in demolishing or replacing the theory with something else.*

---
* Obviously, there are ongoing efforts to develop a quantum theory of gravity, but any such theory would incorporate GR is some kind of appropriate "classical limit".

 

I responded to post #172 in post #189.

Did you miss it?

 

Yes.

I don't know why you couldn't respond to the scenario I put to you, and why you couldn't answer my questions about that scenario.

You tried instead to replace my scenario with a different one of your own making, and then you waved your hands and pretended that my questions were answered by your alternative scenario.

I'll probably get back to the train example later on.

That, by the way, would be a sort of "clock handoff" scenario, would it not?