Revenge of the Cranks by Chris Kennedy

Chris,

If you are up for some math, the good news for you is that - if you take advantage of the opportunity - you will be able in the near future to learn something pretty cool. Namely, special relativity. I know you took physics in high school that touched on the subject but it's clear that you didn't really learn SR at that time, and after all, most high school students don't.

Like I said, if you analyze it in any given inertial frame, you get the same result for the age difference.

Various different explanations you've encountered that seem so contradictory to you are actually all correct. Relativity is like that: A lot of things that you might expect to be different are equal, while a lot of things that you might expect to be equal are different.

This wikipedia article should help:

http://en.wikipedia.org/wiki/Twin_paradox

You can tell different "stories" about what happens just by choosing different inertial frames to analyze it in, or indeed by getting more fancy like Einstein did and using accelerated frames, but all observable results are the same for all such choices. You might feel that in reality there must be only one true story, and I'm inclined that way myself, but all the stories that SR tells are experimentally equivalent and that's what's at issue here.

You would need to learn the actual math to *really* make sense of it, not just read explanations. Luckily, the math is not that hard if you can handle algebra and geometry. You can derive it all yourself using Einstein's two postulates (physics is the same in all inertial reference frames, and the speed of light is fixed) but I don't recommend you try it without a textbook handy. I remember doing that exercise in school, pen and paper, and yes, I got the standard results.

One main point you are missing involves the relativity of simultaneity:

http://en.wikipedia.org/wiki/Relativity_of_simultaneity

Thus in your Fig. 1, with clock A being distributed over a long distance in the direction of motion, then if in the frame of clock A all parts of it read the same time, then in the frame at which clock B is at rest the different parts of clock A all read different times. It is exactly like the train-and-platform example in the wikipedia article. If clock B is the platform, then from the viewpoint of clock A, different parts of clock B read different times (assuming that clock B is also long). This is how they can BOTH think the OTHER guy's clocks are ones going slow: When they compare a FIXED part of one clock to the nearest part of the other clock at every moment in time, because of the motion it's a *different* part of the second clock at every moment, and it's kind of like comparing apples and oranges.

If they try to compare using only two small point clocks to get around that, then they need to send signals at light speed or less to report the time, which introduces the needed time differences, or to send one clock on a round trip by accelerating it and that's the "twin paradox". Does the math really work? Get a pen and paper and you can see that it does.

Sincerely,

Jack

Hi Chris,

I read your entire essay. I believe that in your analysis you are overlooking the fact that whenever an object accelerates, it switches to a different inertial frame. This is the crux, the most important point, to understanding the twin paradox, but I did not see it mentioned in your essay.

Perhaps it helps if you consider a simpler situation to appreciate just how important the effect of switching frames is. It would greatly help if you look at a spacetime diagram comparing two frames in relative motion while you read the situation.

Let us suppose you travel in a spaceship toward a very far away object, say, the Andromeda galaxy while I stay rest with respect to it and you just pass me by. At that instant, in my frame the Andromeda galaxy (AG) as it is right now lies in your *past*, because you are in a frame that is moving toward it, and therefore your line of simultaneity is different from mine. Say in the spacetime diagram in which my frame is taken to be at rest, you are moving right, then your line of simultaneity has an increasing slope while mine is completely horizontal. Since the AG as it is right now in my frame lies below your line of simultaneity it lies, as mentioned, in your past.

Before you proceed, make sure you really get this difference.

Now, let's say you accelerate in the opposite direction and turn around and pass me by again. Now you have switched to a different frame. You have switched to a frame in which your line of simultaneity has a decreasing slope, and as a result, the AG as it is right now in my frame lies *above* your line of simultaneity. That means it now lies in your *future*.

So just by switching frames, you can make an object that lies in my present lie either in your past or in your future as we coincide in space. This is certainly counter intuitive, but if it were different, it would be inconsistent with the rest of relativity and physics as we know it.

If you develop an intuition for this simpler scenario, it will be much easier to understand the twin paradox.

Couple of comments:

1) This scenario only works if the object is far enough in space and close enough in time to be outside our light cones. In other words, it has to be spacelike separated from us. Events that lie on either observer's line of simultaneity are always spacelike separated.

2) Spacetime diagrams are just an aid to visualization, the strength behind these applications is the mathematics of the theory which allows one to conduct experiments and compare the results

3) I intended this as sincere attempt to help you understand the twin paradox, and post this in good faith.

hope this helps,

Armin

From Thomas Garcia

To Anonymous

Your reply re: your diagram - If all 3 clocks are moving at the same speed, how can one pass one then reach the other? Seems you may have left out something?

About absolute time, I don't think physics applies "absolute" to single discrete objects. It refers to time, temperature, space and other things. I believe Newton did that, but I understand it was replaced with spacetime relativity. I am afraid I do not understand what you mean by your method for obtaining universal abs. time. We already know light's one-way speed in vacuum, but how will that give us our abs. speed? I have said all objects having the same speed will have the same time rate, with which you seem to agree, apparently, but I am unsure of that.

Your reply: "Time must slow because of round-trip light-speed invariance." Then you quote Wheeler that both time and length must contract, which is not in contention in this discussion. Are you saying time rates only decrease and never increase?

Hi Chris,

Isn't it just awesome when some self-appointed demigod comes up to you and starts clobbering you on the head with labels like "crackpot"? :) Anyway, I'm pretty sure that you have the entire thing down pat, whether or not you agree with it, and that attacker's tilting at windmills.

I believe that general relativity is the most natural way to solve the Twin Paradox, but that doesn't have to mean that a gravitational field is involved. It just means that acceleration is relative and that you should probably judge the two twins based on which one is moving with regard to the "fixed background" of the rest of the Universe. Surely the twin that accelerates with respect to the "fixed background" is the one who is moving during the journey, and so is the one that undergoes kinematic time dilation. I'm not making myself very clear... What I'm trying to sell is Mach's principle as interpreted by Einstein.

I dunno. I thought your essay was pretty awesome. I loved its spirit.

- Shawn

Jack Mallah,

I see you threw out the 'crackpot' label in your revious message. A waste of time and insult. You need to say something that makes scientific sense supported by empirical evidence. One contrary point by myself at this time:

Quoting you:

"If they try to compare using only two small point clocks to get around that, then they need to send signals at light speed or less to report the time, which introduces the needed time differences, or to send one clock on a round trip by accelerating it and that's the "twin paradox". Does the math really work? Get a pen and paper and you can see that it does."

The time that effects occur and the times reported by delayed means are not interchangeable. The delayed reports, in the relativistic instance, are for theorists who cannot relate their theory to actual time occurances. If you plug in mathematical values that result from acceptance of relativity theory, then you will have mathematical results that agree with relativity theory. So what?

By the way, crackpot crap is ignored by me. You either give empirically supportable answers or you acknowledge that you are debating in favor of your favorite theory. Nothing wrong with that unless,of course, your point is that your favorite theory is final. In that case, you are clearly mistaken.

To Garcia from absolutely Nobody:

my 3-clock reply:

The part that I omitted in my three-clock diagram was simply the left arrow for the 2-clock frame. As I said, I was trying to simplify to avoid scrambled diagrams. If you recall, I *did* note that all 3 clocks moved up by exactly the *same* amount of time (2 hours each), so this was mathematical indication that they all ran at the same absolute or intrinsic rate.

my absolute-time reply:

As Einstein said, if we use the (absolutely) synchronous clocks of classical physics to measure the one-way speed of light, then it will vary directly with frame velocity, and this is absolute motion detection. (In Einstein's simple example, light wrt the embankment went at c, whereas light wrt the carriage went at c - v (less than c due to Einstein's usage of a departing ray of light). After observers in all inertial frames have determined their own absolute speeds through space, they can then mathematically correct for intrinsic clock slowing because the formula is known, namely, sqr[1 - (s^2/c^2)], where s is absolute speed. (A clock moving at absolute speed 0.6c will intrinsically slow by 20%.) Correcting for different intrinsic clock slowing in each frame will put all frames on universal absolute time. Bingo!

my time-must-slow reply:

The fastest clocks in the universe are those which are at absolute rest. They are the only unslowed clocks, so are the only ones that can correctly measure time. (For example, only an unslowed clock can correctly measure the time it takes for a light ray to travel from point (0,0,0) to point (x,0,0).) Of course, if a fast-moving speed-wise clock slows down speed-wise, then of course it will speed up time-wise.

(It seems that we have partially hi-jacked Chris's area - sorry, Chris!)

Hi Chris,

I think that you could find debate about that topic, for sure, and probably with more learned people than I. :) All I know is that I've been told that acceleration such as that would not directly cause a time dilation effect. I've been told that the time dilation effect would result only due to the velocity gained during/by the acceleration itself.

If it were otherwise, and acceleration had an effect like such, then wouldn't the Moon undergo gravitational time dilation, kinematic time dilation, and this "acceleration" time dilation?

I ask this because (and I think you agree) that gravitational time dilation isn't really from the acceleration per se, but just from being in the gravitational field itself -- like, a test particle at the centre of the Earth would not undergo acceleration (Newton's shell theorem), but it would definitely undergo gravitational time dilation because the Newtonian potential at the centre of the Earth is non-zero.

So basically, you're proposing three kinds of time dilation? I imagine that the effect would be smaller than the kinematic time dilation, because you'd probably also have to consider a time dilations from the 1st derivative of acceleration, 2nd derivative, etc. It's an interesting thing to think about anyway, even if most people have told me "no, not possible".

Relativity theory gave us clock dilation and length contraction. The subject matter is time dilation. Without proof of it, relativists are faced with justifying their theory's basis. Since time is not revealed to relativists or anyone else in empirical evidence, there is nothing that theorists can say about time that is not pure theory.

James Putnam

Chris,

You said:" In my essay, I do address changing out of the first inertial phase and into a non-inertial frame at the bottom of page 4 and continue on to page 5. I address what changes occur from the perspective of each clock according to Einstein's own 1918 paradox resolution. Please go back and reread it and if you need clarification, I would be happy to provide further elaboration."

I read that passage, and the explanation you provide there is largely irrelevant to the explaining the twin paradox. Using a largely irrelevant explanation for a phenomenon while overlooking the most relevant one and then arguing that that phenomenon cannot be explained one is called a straw man argument.

The explanation you provide there is largely irrelevant because it does not account for switching from one *inertial* frame to another *inertial* frame, which, I repeat myself, is the important aspect of the twin paradox. Relativity of simultaneity is precisely a consequence of the importance of switching *inertial* frames. Your paragraph only discusses the switch from an *inertial* frame to a *non-inertial* frame, which is not the most salient aspect of the twin paradox, it is only relevant to the extent that you need to switch at least momentarily to a non-inertial frame (i.e. accelerate) in order to be able to switch from one inertial frame to another inertial frame (that's why it is "largely" and not "completely" irrelevant).

I thought I could help you understand the twin paradox by providing a simpler scenario where the essence of the twin paradox's explanation (switching from one *inertial* frame to another *inertial* frame) is more obvious, but I realize now that I can't help you.

Good luck and take care,

Armin

From T. Garcia

To absolutely Nobody

Your 3-clock reply does not refer to the question.

Your absolute-time reply requires a link to support it.

Your time-must-slow reply argues clocks can be at rest, yet you do not say how or why. Sure, anything is possible, in Philosophy, but in theoretical physics, some supporting remarks must be given to take ideas from fantasy to physical reality.

Clocks cannot be "at-rest" because everything in the universe is in motion. Objects cannot be observed to be in a state of absolute rest, thus we cannot see what time one would hold.

I see you agree a slower-moving clock runs faster time than a faster-moving clock, which is the point of my essay. Thanks so much for your comments. I am hoping Chris will respond to my last inquiry to him, and I too apologize to you, Chris, for using up your space here.

Okay, thanks Chris.

The 't' problem with relativity theory:

The 't' in physics equations never referred to the property of time. It referred to a number of cycles of activity with respect to an accepted standard cycle of something else. The true unwritten units of the physics' 't' are cycles(B)/cycle(A). The standard cycle (A) is certainly not time itself. We must use a recurring reliable effect for our standard and effects are always about a change of distance and/or direction with respect to a cycle of something or other.

From a message above of mine:

"The subject matter is time dilation. Without proof of it, relativists are faced with justifying their theory's basis. Since time is not revealed to relativists or anyone else in empirical evidence, there is nothing that theorists can say about time that is not pure theory."

This statement stands as fact. Relativity theory unadmittedly uses cycles(A)/cycle(B) for its 't'. Both A and B refer to activities of objects.

The unraveling of relativity theory begins with its slight of mind substitution of the word time for cycles(A)/cycle(B), and, space in place of length variation as measured by one object compared to another object. The key point to understand is that cycles(A)/cycle(B) is referring to the speeds at which one activity is occurring with respect to another activity.

The importance of this to theoretical physicists must be that it is the cause of the activity that is changing its potency and, thereby, the rate of the activity varies. Time is not a cause. No one knows what cause is. All knowledge of physics involves effects. All conjecturing about cause are theoretical with no possible empirical verification. Effects cannot explain what is cause.

It is time to put relativity theory aside and develop theory that is empirically based. All empirical evidence consists of patterns in changes of velocity of objects. All velocities are measured as distance per second. Seconds are the name assigned to cycle(A)/cycle(B). There is no empirical justification for claiming that seconds define a property that is not limited to identifying it as cycle(A). Cycle (A) refers to activity of an object.

All activity occurs in time. Seconds are a measure of activity with respect to activity. Seconds occur in time and are not time itself. Theoretical conjecture aside, neither space nor time are verified as parts of any physics equations.

James Putnam

Garcia wrote to Nobody:

>Your 3-clock reply does not refer to the question.

Here was the question:

>>>Your reply re: your diagram - If all 3 clocks are moving at the

>>>same speed, how can one pass one then reach the other?

>>>Seems you may have left out something?

Here was my reply:

>>The part that I omitted in my three-clock diagram was simply

>>the left arrow for the 2-clock frame.

My reply answers both questions because it tell what I left out (and why), and it tells you that the 2-clock frame was moving to the left at the same speed through space as was the 1-clock frame. (For example, both frames could be moving through space at half the speed of light. I honestly do not see why this is in any way confusing.)

I decided to focus on only your first objection first. Let's clear it up for sure before going on.