Can someone explain Einstein's relativity theory?

[russ_watters]

Yes, I disagree with your statement; "...there is no objective truth about whose clocks are really running slower".

I think it's quite obvious when the twins get back together that the younger twin was the one whose clock ran slower. There can be no denial of this since that is the twin that is younger upon return. What else would cause this effect if it wasn't objectively true? Really.

This is a wording issue: before they are brought back together and the situation is symmetrical, neither can be said to be running faster or slower. Once they are brought back together, you can say one went faster/slower. But that's not the issue here: the issue is what that implies about the laws of physics. The fact that the outcome is not the same does not imply the laws of physics aren't consistent, because the conditions of each twin's journey aren't the same. More on that in a sec...

Lemme try a different tack here: it seems you agree with everything except the conclusion. All of it is here:

The twin that ages less may have undergone an acceleration, however, his or her clock continues to run more slowly relative to the non-accelerated sibling even after the acceleration has ceased. Therefore, the twin who has undergone a change in an inertial frame has also undergone a change in his or her fundamental laws of physics

First off, you seem hung-up on the part about acceleration (yet you say frame of reference is unimportant?) - the acceleration is what puts them in different frames.

You also seem hung-up on the outcome (and this is probably more important): you're saying that the fact that the clocks show different times means the laws of physics are different. But that's wrong. Lemme give an example: you have two identical rocks. You throw one and your little brother throws the other. But they don't move the same distance. Why not? The rocks are identical, the laws of physics are identical - why wouldn't they go the same distance? Well, you're stronger than your little brother - you pushed harder! So too with the twins paradox: the laws of physics are the same, its just that you're doing different things to the two clocks: one is being accelerated, the other isn't. What's more, after the rocks leave your hand, they are no longer accelerating - shouldn't they then go the same distance (just like the twins who are not accelerating...)? No, the acceleration is what makes their frames different and what makes them travel different distances.

This seems self-evident, but perhaps its a symptom of another issue: what you are saying implies the desire for Time to be an absolute like C. If the laws of physics said time is abslute, then yes, certainly there'd be a contradction. But the laws of physics don't say that.

 

[Phobos]

I've read a piece on his theory and I'm having a little difficulty understanding it. I've used the famous E = MC^2 in calculations before but I want to have more understanding of the theory behind it.

Any info would be great.

The Teaching Company's "Great Lectures Series" (college lectures on tape) has a helpful one introducing Relativity (geared toward non-scientists).

no, I'm not being paid by them to say that

They're expensive to buy but your local library may have it.

 

[JesseM]

Yes, I disagree with your statement; "...there is no objective truth about whose clocks are really running slower".

I think it's quite obvious when the twins get back together that the younger twin was the one whose clock ran slower. There can be no denial of this since that is the twin that is younger upon return. What else would cause this effect if it wasn't objectively true? Really.

I'm not asking about the twin, since he switched rest frames--I'm asking about clocks in the frames themselves. If in each frame the twin is traveling alongside a clock that does not accelerate, then obviously that clock will be ticking at the same rate as his clock while he's in that frame--if you conclude that the traveling twin's clock was objectively ticking slower than the Earth twin's, would you also say that this clock moving with him while he was in that rest frame was objectively ticking slower than a clock on earth?

 

[JesseM]

The fact that either twin can be picked, randomly, to accelerate to meet the other twin and the results will be the same.

I'm sorry russ, but what you've said here simply isn't true. If you pick the twin in frame A to accelerate back to meet the other twin, then twin A would need to undergo more acceleration, and travel at a greater speed than the other twin in order to catch up to the other twin.

No, the acceleration would be the same, because the velocity difference would be the same in each twin's own previous rest frame. If a twin is traveling away from Earth at 0.6c, then turns around and heads back to Earth at 0.6c, then from the perspective of the frame in which he was at rest during the outbound trip he will be moving at about 0.88c as he returns to Earth (using the equation for addition of velocities give here). Likewise, if the twin is traveling away from the Earth at 0.6c, and then the earth-twin gets in a rocket and accelerates until he is approaching the traveling twin at 0.6c, then in the Earth's frame the earth-twin will now be going at about 0.88c. The situation is completely symmetrical. So Russ is right--the choice of which twin to accelerate so they will meet again can be made at random, and whichever one accelerates, he will be the one whose clock is behind when they meet.

 

[jcsd]

If the worldlines of two observers are coincident at events A and B which one of them experinced the longest time between the two events is depednent on the 'length' of their worldlines between the two events. The maximal proper time between two events is experinced by an observer represented by a staright worldline (i.e. an inertial observer).

 

[Janus]

What ever gave you the idea that I'm trying to grasp what SR is all about? I already know what SR is all about. I'm simply pointing out the fact that time must necessarily flow at different rates for different inertial frames. I don't think that SR denies this, on the contrary, the twin brothers paradox confirms it! If this wasn't true then time dilation would indeed just be an illusion and not at all objective. But it is objective.

The point is that you don't grasp SR. All your arguments are more in line with what Lorentzian Relativity says. In Lorentzian Relativity, time dilation is caused by motion through the aether, and thus the Clock that has the highest relative velocity with respect to the aether is the clock that runs slower. The aether provides an absolute frame of rest by which all motion could be judged. In LR is is possible to say that one of the clocks objectively runs slower than the other.

In SR, this is not the case. There is no absolute frame from which motion can be judged. And there is no way to say objectively (in a way that all frames in relative motion to each other would agree), which clock actually runs slower than the other. This is not to say that they will not agree which clock will read less time when brought back together, but they will disagree as to why this is the case. And each frame's explanation as to what caused the difference is equally valid.

 

[NeutronStar]

The point is that you don't grasp SR. All your arguments are more in line with what Lorentzian Relativity says. In Lorentzian Relativity, time dilation is caused by motion through the aether, and thus the Clock that has the highest relative velocity with respect to the aether is the clock that runs slower. The aether provides an absolute frame of rest by which all motion could be judged. In LR is is possible to say that one of the clocks objectively runs slower than the other.

In SR, this is not the case. There is no absolute frame from which motion can be judged. And there is no way to say objectively (in a way that all frames in relative motion to each other would agree), which clock actually runs slower than the other. This is not to say that they will not agree which clock will read less time when brought back together, but they will disagree as to why this is the case. And each frame's explanation as to what caused the difference is equally valid.

You may very well be right. Even though I've taken several courses on SR I've probably always viewed the problems intuitively from Lorentz's point of view.

Why isn't LR taught in college classrooms? Is there anything inherently wrong with LR, or is it just not taught because of the principle of Occam's Razor? Personally, I have never agreed with Occam's Razor. If something can be comprehended intuitively by including an idea that may not be physically detectable I have no problem with that.

Heck, scientists today are postulating the existence of strings to explain particle physics. Yet it is believed that we may never be able to detect the existence of a string. Ironically, if string theory makes a prediction that can be tested in the lab then everyone will start believing in strings.

So what if Einstein had never existed, and instead Lorentz proposed his relativistic aether. Then when his predictions came true (which would have been the same predictions as SR) everyone would start believing in his aether.

I think the whole scientific community needs to start getting their act together.

Either follow the lead of Occam or not. I wish they'd make up there minds. They just aren't being consistent. With SR they hold to Occam's Razor. But when it comes to String Theory they toss Occam's Razor out the window.

 

[ohwilleke]

Why isn't LR taught in college classrooms?

Because it is very likely wrong.

 

[NeutronStar]

Because it is very likely wrong.

Well, just for the record, John Stewart Bell doesn't agree with you for one. The following is from a book called The Ghost in the Atom by Cambridge press, ISBN 0-521-30790-2. The book is a collection of interviews with famous scientists on various topics. The following is an excerpt from an interview with John Stewart Bell:

Interviewer:

"Of course the theory of relativity has a tremendous amount of experimental support, and it's hard to imagine that we can actually go back to a pre-Einstein position without contradicting some of this experimental support. Do you think it's actually possible?"

John Bell:

"Well, what is not sufficiently emphasized in textbooks, in my opinion, is that the pre-Einstein position of Lorentz and Poincare, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether - that is a perfectly coherent point of view"

Interviewer:

"And it was abandon on the grounds of elegance?"

John Bell:

"Well, on the grounds of philosophy; that what is unobservable does not exist. And also on the grounds of simplicity, because Einstein found that the theory was both more elegant and simpler when we left out the idea of an aether. I think that the idea of the aether should be taught to students as a pedagogical device, because I find that there are lots of problems which are solved more easily by imagining the existence of an aether,…."

These are the words of John Stewart Bell, not me.

Although, I obviously agree with him.

 

[NeutronStar]

Apology to OsiriS^

I would like to apologize to OsiriS^ for contaminating his thread with my controversial view on SR. That wasn't my original intent. My original intent was to simply mention that SR is based on two very simple postulates. Everything follows from those two postulates. However, as you can see from the controversy everyone doesn't necessarily follow the same logic.

In other words, you may or may not find Einstein's approach to be the one of your choosing. I do believe that it is healthy to know that other choices are possible that are still consistent with the original hypothesis.

As someone posted earlier, "The theory is the postulates". Many people do feel that way. However, if that is indeed the case then any legitimate conclusions that you can make while maintaining the postulates of relativity, that too, is relativity theory. At least this is true if you believe that, "a theory is its postulates".

The Teaching Company's "Great Lectures Series" (college lectures on tape) has a helpful one introducing Relativity (geared toward non-scientists).

no, I'm not being paid by them to say that

They're expensive to buy but your local library may have it.

I actually purchased that video lecture and then returned for a different course. The lecture was technically correct alright. But I found it very hard to watch because of the annoying style of the lecturer. He seemed to be trying to argue the ideas by repeating trivial things over and over again as if he felt that his audience simply wouldn't believe it. At least that was my perception. Like I say, he was technically correct. But his lecture style got a huge thumbs down from me.

Just to add a positive note, I have since then bought several other video lectures from The Teaching Company. They aren't on the topic of relativity, but they are much better lectures. The professors are active in their fields, and quite popular having been on other programs like NOVA. They are also involved with popular scientific discoveries.

Some of the video lectures that I am quite happy with and highly recommend are,..

http://www.teach12.com/store/course.asp?id=178&d=Understanding+the+Universe%3A+Astronomy+2003%2FUnderstanding+the+Universe%3A+Astronomy+%28Set%29"

I found this lecturer, Alex Filippenko, to be very positive, upbeat, and knowledgeable in his field. Big thumbs up! This video set contains 56 lecture hours.

http://www.teach12.com/store/course.asp?id=1247&d=Particle+Physics+for+Non%2DPhysicists%3A+A+Tour+of+the+Microcosmos"

This follow dances around a lot while lecturing and waves his hands continuously while talking. He's a riot to watch in fast forward!

But on a serious note, he really knows his particle physics. He covers it all including the Higgs particle. I'd call it a must-see video. His excitement and love of particle physics really shows. I've already watched that video three times and learn something new every time. His lecture style is very efficient and he covers a lot of material. There are 24 lecture hours in this course.

http://www.teach12.com/store/course.asp?id=1423&d=Joy+of+Thinking%3A+The+Beauty+and+Power+of+Classical+Mathematical+Ideas"

There are two mathematicians that teach this course. What can I say? Pure mathematicians are nuts! These guys are no exception! They don't fool around, but some of these abstract ideas are pretty far-fetched. They also make fairly efficient use of the lecture time (for the most part). I wouldn't call this one a "must see", but I do give it a thumbs up.

Don't expect to see any heavy equations. This is aimed at the general public. Its more about how to think mathematically than about the technicalities of mathematics. I found it interesting and thought provoking. And perhaps most important of all I found it enjoyable to watch.

I really wish I could give that Relativity course a thumbs up. But I just can't. Like I say, the course material is technically correct if you can stand the lecture style. But I found that trying to watch that guy was more than I could bear. He just sounded more like he was arguing his points rather than teaching them from an excited point of view. I actually asked the teaching company to let me know if they ever redo that lecture with someone like Pollock or Fillipenko teaching it. Then I'd give it a thumbs up I'm sure! The course material was great. It just wasn't fun to watch. But you can always watch it and then return it for another lecture.

Or maybe it was just me. You might enjoy it. Who knows?

 

[NeutronStar]

Getting back to basics,...

I've read a piece on his theory and I'm having a little difficulty understanding it. I've used the famous E = MC^2 in calculations before but I want to have more understanding of the theory behind it.

Any info would be great.

Here's a link to contribute to the original purpose of the thread,...

http://www.karlscalculus.org/einstein.html"

 

[jcsd]

The problem with Lorentz ether theory is that it's such an ugly ad hoc theory that once you are sufficently skilled in relativity there is no way that you would want to use it. From what I understand LET originally because of the singularity in the equations when v = c it postulated that the Lonretz transformations breakdown when v is approimately equal to c (in special relativity the singularity is simply explained as the fact that light has no frame of reference) and I'm not entirely sure that all the relativstic result can be derived from the original theory without essentially 'tacking them on' to LET.

 

[NeutronStar]

The problem with Lorentz ether theory is that it's such an ugly ad hoc theory that once you are sufficently skilled in relativity there is no way that you would want to use it.

I would agree with you from a purely mathematical point of view. However, I prefer a little meat with my potatoes when it comes to ontology.

What you have said about comparing Lorentz's aether theory the with Einstein's relativity could just as easily be said about comparing Lagrangian dynamics with Newtonian mechanics.

Lagrangian dynamics considers only the energy of systems and so makes the mathematics of dynamics much easier. However, that doesn't mean that concepts like force, velocity, acceleration, and momentum don't exist. In other words, we don't abandon the underlying concepts of Newtonian mechanics just because Lagrangian methods are mathematically simpler.

In a similar way we don't need to abandon the concept of an aether altogether in order to enjoy the mathematical simplicity of SR. I'm not suggesting that the mathematical tricks of SR should be abandoned completely. I'm merely suggesting that from an intuitive point of view tossing out the concept of an aether altogether is not necessarily the greatest idea. It's also not necessary.

It appears that the aether theory is sneaking back into physics via quantum fluctuations. We are discovering that there is no such thing as a complete vacuum anywhere in the universe. So the idea of an aether may very well be ontologically correct, and possibly even be detectable on the quantum level. I personally have always believed that the universe is ontologically aetheral based so the idea of officially rejecting an aether altogether does not sit well with me.

I think that one of the biggest setbacks to aether theories is the classical notion that it somehow has to be absolute in some way. In other words, when people think of an aether they often think in terms of a Newtonian absolute space. The existence of that type of aether has been disproved. To think that way would be like thinking in terms of a Ptolemaic astronomy.

A relativistic aether, on the other hand, is not so confining. A relativistic aether is malleable and changing with the expansion of the universe, it's not an absolute space, it's more like the dynamic fabric of an expanding universe.

In any case, I just wish that this idea of a relativistic aether would have been better explored by young bright university students during the last few decades. Unfortunately, when the classical aether was disproved that kind of put a lid on every mention of any type of aether theory. Personally I think that was a bad thing.

But just to recap,... I'm not suggesting that we toss out the mathematics of SR. That is certainly a valid mathematical framework just like Lagrangian dynamics is a valid mathematical framework. But just because Lagrangian mathematics works doesn't mean that we should toss out all of the fundamental Newtonian concepts that preceded it. The same goes for SR. Just because SR works doesn't mean that there can't be an aether description beneath it.

 

[jcsd]

The problem is I really don't see any advanatge at all from teaching LET and you might as (quantum fluctuations are unrelated to any concept of ether), but I see plenty of adavnatges in teaching special relativity and to avoid confusion it is much better to be consitent and to use common conventions.

 

[NeutronStar]

The problem is I really don't see any advanatge at all from teaching LET,…

Well, actually I agree with you that colleges shouldn't actually teach the aetheral theory in all its gory mathematical detail. Heaven forbid! Modern pedagogical thinking seems to be aimed at the concept that torturing students by making them work out every conceivable mathematical relationship is "teaching". I have a real bone to pick with that particular pedagogical method. But that's another story.

I'm not suggesting that the mathematics of an aetheral theory be taught in all its gory detail. All I'm suggesting, like John Stewart Bell had suggested in the interview that I posted earlier, is that the basic notion of a relativistic aetheral theory should be included in courses on Modern Physics. At least to the point of making sure that the students are aware that it is still a viable option without contradicting the postulates of SR.

(quantum fluctuations are unrelated to any concept of ether)

I strongly disagree with this statement,…

Let's see,… How can I show how strongly I disagree with it?

How about,…

 

[Hurkyl]

What you have said about comparing Lorentz's aether theory the with Einstein's relativity could just as easily be said about comparing Lagrangian dynamics with Newtonian mechanics.

It would be nice if they were analogous -- however, it seems the major impetus for believing an aether theory is precisely because one doesn't want to believe SR. The same is not true for your example of Lagrangian and Newtonian dynamics.

I'm merely suggesting that from an intuitive point of view tossing out the concept of an aether altogether is not necessarily the greatest idea. It's also not necessary.

I disagree. Virtually every person I've ever seen touting aether theories had a very poor grasp of the things that let you take advantage of the mathematics of SR. For instance, they tend not to grasp relativity of simultaneity. If you don't grasp that, then you have no chance of properly analyzing a problem in different frames.

The evidence suggests that adopting this "intuitive" (ha!) point of view seems to increase one's difficulty doing problems, rather than decrease it.


Quite frankly, I don't see how

Here is how I'm going to do measurements. It turns out that the equations of physics will be valid for any inertial observer who does measurements my way.

is any less intuitive than

I'm not going to tell you how I do measurements, but they're affected by the aether. I'm not going to tell you anything about the aether, except that it affects measurements. Oh, and it all conspires to make that SR guy over there think he's right.

 

[NewLocality]

Hi everyone

Can I invite you to visit: -
www.electrodynamics-of-special-relativity.com[/URL]

Let me know what you think.

NL

 

[NeutronStar]

It would be nice if they were analogous -- however, it seems the major impetus for believing an aether theory is precisely because one doesn't want to believe SR. The same is not true for your example of Lagrangian and Newtonian dynamics.

I can assure you that my reasons for believing in an aether have absolutely nothing to do with not wanting to believe in SR. What exactly does SR offer that could or couldn't be believed anyway? I mean, it really doesn't offer a mechanism for time dilation. There's nothing to believe or disbelieve. It's just a mathematical trick.

Besides, any aether theory that maintains the postulates of relativity is going to also predict all of the same conclusions. The only difference is that it will also offer a physical mechanism for how these phenomenon arise.

I mean seriously. You can use SR to make calculations of how things will behave. But can you use SR to explain the actual physical mechanism of time dilation? I think not. SR doesn't explain the mechanism of time dilation, it simple says that it must occur. However, an aether theory, coupled with some concepts in quantum mechanics, can actually offer an explanation of the physical mechanism of time dilation. To me, that is much more attractive than just doing engineering calculations using SR.

 

[russ_watters]

I can assure you that my reasons for believing in an aether have absolutely nothing to do with not wanting to believe in SR. What exactly does SR offer that could or couldn't be believed anyway? I mean, it really doesn't offer a mechanism for time dilation. There's nothing to believe or disbelieve. It's just a mathematical trick.

Wanting to believe that time dilation is "just a mathematical trick" (ie, not physically real), is, in my experience the primary reason ether theorists don't want to believe relativity (and length contraction second). They want to believe that time and space are absolute and SR takes that away. Trouble is, it can't be wished away by getting rid of Relativity: its data - its a real phenomena that needs to be dealt with via theory.

However, an aether theory, coupled with some concepts in quantum mechanics, can actually offer an explanation of the physical mechanism of time dilation.

So far I have seen no evidence of that: most ether theory is two steps behind - still trying to match observations with the desire for an ether.

 

[NeutronStar]

Wanting to believe that time dilation is "just a mathematical trick" (ie, not physically real),...

You obviously haven't been reading my posts in this thread. I completely accept the reality of time dilation. I have no problem accepting the conclusion of SR. I'm simply not satisfied that SR has given any physical explanations for the mechanisms of what physically causes these things to happen.

here's the stance of SR,…

1. Accept these postulates
2. You must accept these conclusions.

Period amen! SR doesn't offer any mechanisms for why they occur. In a very real sense this isn't much different from Newton's law of gravity that was also a mathematical description, but didn't offer an explanation for a mechanism.

Perhaps I shouldn't have called it a mathematical trick. Perhaps I should simply call it a mathematical description rather than an ontological explanation.

I think it's ironic that Einstein was so bent on explaining Newton's gravity in intuitive terms yet he didn't seem to be concerned about explaining his very own SR in the same way.

However, an aether theory, coupled with some concepts in quantum mechanics, can actually offer an explanation of the physical mechanism of time dilation.

So far I have seen no evidence of that: most ether theory is two steps behind - still trying to match observations with the desire for an ether.

First, when you refer to most aether theories I fear that you are including many classical aether theories which obviously aren't going to work. Classical aether theories are as dead as perpetual motion machines.

Secondly, far beyond the scope of this thread, there is the topic of Quantum Mechanics. Just like there is the aether theory controversy surrounding SR, there are also controversial concepts surrounding QM.

For example, do you believe that all of time and space are quantized? Or do you believe that only bound systems are quantized and space and time are a continuum in general. Just like the aether theory in SR, these two different schools of thought associated with QM have not been fully resolved either.

Just for the record, I am of the school that all of time and space is indeed quantized. Only this school of thought is useful for explaining time dilation (from my point of view). If you believe that time and space are continuums then believing in an aether probably isn't going to be of any use to you.

 

[selfAdjoint]

Einstein derived his SR in operational terms. He showed why the Lorentz transforms result from the assumption of Galilean relativity and the invariance of light speed. He showed this by exhibiting observers trying to coordinate their measurements with clocks and measuring sticks.

Source invariance of light speed in what is unexplained. The postulates are well motivated.

 

[NeutronStar]

Einstein derived his SR in operational terms. He showed why the Lorentz transforms result from the assumption of Galilean relativity and the invariance of light speed. He showed this by exhibiting observers trying to coordinate their measurements with clocks and measuring sticks.

Source invariance of light speed in what is unexplained. The postulates are well motivated.

So in other words, you're agreeing with me.

Special Relativity is basically the following:

1. If you accept these postulates.
2. Then you must accept these conclusions.

I accept both!

So in a sense I accept SR.

But at the same time I'd like to have a deeper explanation dog gone it!

 

[JesseM]

You obviously haven't been reading my posts in this thread. I completely accept the reality of time dilation. I have no problem accepting the conclusion of SR. I'm simply not satisfied that SR has given any physical explanations for the mechanisms of what physically causes these things to happen.

here's the stance of SR,…

1. Accept these postulates
2. You must accept these conclusions.

Period amen! SR doesn't offer any mechanisms for why they occur. In a very real sense this isn't much different from Newton's law of gravity that was also a mathematical description, but didn't offer an explanation for a mechanism.

Modern physicists don't really believe that "mechanisms" are important any more. Any mathematical rule we can describe could be a rule that nature uses in her "program". Check out chapter 2 of Feynman's book The Character of Physical Law, "The Relation of Mathematics to Physics", for a good articulation of the way most physicists think about this (also note that internet physics guru John Baez, on his Crackpot Index, awards 10 points 'for arguing that while a current well-established theory predicts phenomena correctly, it doesn't explain "why" they occur, or fails to provide a "mechanism"').

Secondly, far beyond the scope of this thread, there is the topic of Quantum Mechanics. Just like there is the aether theory controversy surrounding SR, there are also controversial concepts surrounding QM.

For example, do you believe that all of time and space are quantized? Or do you believe that only bound systems are quantized and space and time are a continuum in general. Just like the aether theory in SR, these two different schools of thought associated with QM have not been fully resolved either.

Just for the record, I am of the school that all of time and space is indeed quantized. Only this school of thought is useful for explaining time dilation (from my point of view). If you believe that time and space are continuums then believing in an aether probably isn't going to be of any use to you.

All quantum field theories so far have had the property of Lorentz-symmetry, and this is also true of string theory. Loop quantum gravity explicitly says that space and time are quantized, and in this article by LQG expert Lee Smolin, he discusses whether Lorentz-invariance would be preserved:

Instead, the predictions of loop quantum gravity concern the structure of space and spacetime at very short distances. In particular, loop quantum gravity predicts that the smooth picture of spacetime in classical general relativity is actually only a coarse grained approximation to a discrete structure, in which surfaces and regions can have only certain, discrete quantized values of areas and volume[10, 18, 74, 75, 17]. Loop quantum gravity makes specific predictions for the discrete quantum geometry at short distances. Furthermore, these predictions are derived from first principles, hence they are not adjustable. In this way loop quantum gravity is different from previous approaches which postulate some form of discrete structure as a starting point, rather than deriving it as a consequence of the union of quantum theory and general relativity.

It turns out that this has consequences for the question of whether special relativity, and lorentz invariance, is exactly true in nature, or is only an approximation which holds on scales much longer than the Planck scale[28]-[40]. Several recent calculations, done with different methods[36]-[38], yield predictions for modifications to the energy momentum relations for elementary particles. These are of the form,
$$E^2 = p^2 + M^2 + \alpha l_{Pl}E^3 + \beta l^2{}_{Pl}E^4 + ...$$

where predictions have been found for the leading coeffcients $$\alpha$$, which generally depend on spin and helicity[36]-[38].

This is then an area of disagreement with string theory. Further, these modifications appear to be testable with planned experiments[28, 30, 39, 40]. Hence the different predictions of string theory and loop quantum gravity concerning the fate of lorentz invariance offer a possibility of experimentally distinguishing the theories in the near future.

4 The near term experimental situation

The most important development of the last few years in quantum gravity is the realization that it is now possible to probe Planck scale physics experimentally. Depending on dynamical assumptions there is now good experimental sensitivity to the $$\alpha$$ terms in (2) for photons, electrons and protons. Increased sensitivity is expected over the next few years from a number of other experiments so that it is not impossible that even if the leading order $$E^3$$ terms are absent, it will be possible to put order unity bounds on $$\beta$$, the coefficient of the $$E^4$$ term.

However it is crucial to mention that to measure $$\alpha$$ and $$\beta$$ one has to specify how lorentz invariance is treated in the theory. There are two very different possibilities which must be distinguished.

• Scenario A) The relativity of inertial frames is broken and there exists a preferred frame. In this case the analysis has to be done in that preferred frame. The most likely assumption is that the preferred frame coincides with the rest frame of the cosmic microwave background. In such theories energy and momentum conservation are assumed to remain linear.

• Scenario B) The relativity of inertial frames is preserved, but the lorentz transformations are realized non-linearly when acting on the energy and momentum eigenstates of the theory. Such theories are called modified special relativity or doubly special relativity. Examples are given by some forms of non-commutative geometry, for example, $$\kappa$$-Minkowski spacetime[32]. In all such theories energy and momentum conservation become non-linear which, of course, effects the analysis of the experiments. In some, but not all, cases of such theories, the geometry of spacetime becomes non-commutative.

He then lists some experiments which could potentially measure $$\alpha$$ and $$\beta$$ by 2010, and concludes:

We may summarize this situation by saying that a theory of quantum gravity that leads to Scenario A) and predicts an energy momentum relation (2) with $$\alpha$$ order unity is plausibly already ruled out. This is shocking, as it was commonly said just a few years ago that it would be impossible to test any physical hypotheses concerning the Planck scale.

Anyway, you can see that Scenario B) preserves the idea that there is no preferred frame, even though it is discrete.

 

[pervect]

My $.02 on "LR". It's possible to do "LR" correctly and get the same answers as standard relativity theory, in which case it's just an interpretation of special relativity and not a different theory, as it makes the same predictions.

However, because LR focuses on what changes (space and time) rather than what does not change (the Lorentz interval), it is more difficult to get the correct answers with the "LR" approach than the one that is usually taught. This is a good enough reason for not teaching the "LR" approach, in my opinion.

Furthermore, many of the "LR" proponents you see in the newsgroups or on the webpages are seriously confused (probably, in part, due to the fact due to the aforementioned difficulties). They get results that conflict with standard relativity theory. To make matters worse, they don't always seem to realize when their results are different than standard results (even when this is pointed out to them very directly) - probably because they don't understand the standard approach.

The fact that many LR proponents don't realize when they are wrong has to a certain extent "poisoned" the name. There is at least a 50% chance that when someone talks about relativity in terms of "LR" that they are making predictions that are not compatible with standard relativity without realizing it -(or at least without admitting it) - a typical false claim of an LR enthusiast is that the ether can be detected.

 

[NeutronStar]

Modern physicists don't really believe that "mechanisms" are important any more. Any mathematical rule we can describe could be a rule that nature uses in her "program". Check out chapter 2 of Feynman's book The Character of Physical Law, "The Relation of Mathematics to Physics", for a good articulation of the way most physicists think about this

Yes, I know that this is true, and I'm not happy about it.

Just seems to me that physicist are giving up on physics and simply becoming philosophers instead.

(also note that internet physics guru John Baez, on his Crackpot Index, awards 10 points 'for arguing that while a current well-established theory predicts phenomena correctly, it doesn't explain "why" they occur, or fails to provide a "mechanism"').

So why should their be any argument? Whose arguing the other side? In other words who's arguing that science does explain anything. Why don't physicists just respond to the so-called crackpots by saying, "Oh we don't bother trying to explain anything anymore, we've all become nothing more than engineers. There are no physicists left. Physics has died and engineering is all that survived from it."There also seems to be a double standard here. I mean, everyone claims that Newton's mathematical description of gravity wasn't actually an explanation but Einstein's General Relativity explains gravity in terms of warped spacetime. Physicists seemed to like Einstein's explanation better than Newton's mere description, not merely because it is more correct, but also because it offers an intuitive mechanism.

Particle physics proposed the theory of quarks to explain particle physics. Now String theory is proposing the existence of strings to explain particle physics. But anytime someone wants to explain relativity all of a sudden explanations aren't important?

I don't get it. Seems to me like there are some real inconsistencies here on the attitude of the scientific community.

Seems like scientists don't need to explain things anymore. If someone insists on an explanation just call them a crackpot!

 

[JesseM]

So why should their be any argument? Whose arguing the other side? In other words who's arguing that science does explain anything. Why don't physicists just respond to the so-called crackpots by saying, "Oh we don't bother trying to explain anything anymore, we've all become nothing more than engineers. There are no physicists left. Physics has died and engineering is all that survived from it."

Engineering is about applying existing laws to technologies, physics is about finding new laws, so they're pretty different regardless of whether you believe in "mechanisms" or not.

There also seems to be a double standard here. I mean, everyone claims that Newton's mathematical description of gravity wasn't actually an explanation but Einstein's General Relativity explains gravity in terms of warped spacetime. Physicists seemed to like Einstein's explanation better than Newton's mere description, not merely because it is more correct, but also because it offers an intuitive mechanism.

Aside from the fact that GR gives more accurate predictions, I think physicists like GR better because it follows uniquely from a few basic assumptions like the equivalence principle, while Newtonian gravity doesn't. Similarly, SR is elegant because it follows from Einstein's two postulates. While modern physicists don't look for "mechanisms", they may want to find a few set of basic assumptions which can be used to derive a more complex-looking theory.

Particle physics proposed the theory of quarks to explain particle physics. Now String theory is proposing the existence of strings to explain particle physics. But anytime someone wants to explain relativity all of a sudden explanations aren't important?

Well, again, you're talking about a different sort of explanation than a search for a "mechanism". Physicists may try to explain some set of laws as a limit of some more fundamental laws, like with thermodynamics or with the search for more fundamental particles. If you want to derive SR from some more fundamental theory, though, that's not the same as looking for a "mechanism" which accords with our ordinary physical intuitions.

 

[NeutronStar]

My $.02 on "LR". It's possible to do "LR" correctly and get the same answers as standard relativity theory, in which case it's just an interpretation of special relativity and not a different theory, as it makes the same predictions.

I agree.

I never meant to imply that SR is incorrect. All I've ever said is that there are other interpretations that are just as correct and that in the case of LR this interpretation can include a concept of an aether.

However, because LR focuses on what changes (space and time) rather than what does not change (the Lorentz interval), it is more difficult to get the correct answers with the "LR" approach than the one that is usually taught. This is a good enough reason for not teaching the "LR" approach, in my opinion.

I also agree that the precise mathematics of LR should not be taught in colleges. That would just be a waste of everyone's time. But I believe that more emphasis should be given to the theoretical possibility. At least let the students know that it's a viable description. Too many students come out of Modern Physics courses thinking that any concept of an aether is completely forbidden. That's actually incorrect, and should be frowned upon.

Furthermore, many of the "LR" proponents you see in the newsgroups or on the webpages are seriously confused (probably, in part, due to the fact due to the aforementioned difficulties). They get results that conflict with standard relativity theory. To make matters worse, they don't always seem to realize when their results are different than standard results (even when this is pointed out to them very directly) - probably because they don't understand the standard approach.

With all due respect,… there are a lot of people out there who are seriously confused about SR and get results that conflict with relativity.

I mean, just because some people can't do math is no reason to toss out a whole theory is it?

The fact that many LR proponents don't realize when they are wrong has to a certain extent "poisoned" the name. There is at least a 50% chance that when someone talks about relativity in terms of "LR" that they are making predictions that are not compatible with standard relativity without realizing it -(or at least without admitting it) - a typical false claim of an LR enthusiast is that the ether can be detected.

Well, I agree that the whole concept of an aether has been "poisoned". This is why I feel that colleges should address the issues a little better in their Modern Physics courses. Try to clear things up a little bit one class at a time.

While, we are talking about educational formalism I'd like to mention that I actually took Modern Physics twice in my lifetime (almost 20 years between those classes). Nothing has changed! I'm mean from a pedagogical point of view. They still don't make it crystal clear at the beginning of the course that relativity is just a description and not an explanation of what's going on. And they still don't touch the word "aether" with a ten-foot pole other that to say that it died with Michelson and Morley.

The thing that I really don't understand is why colleges do this to people? I looked around me at all the younger students trying to beat their heads against the wall to comprehend the explanation. I felt like screaming at the top of my lungs, "There is no explanation! Just do the math and accept the results!". I mean really. That's the only way they are really going to survive the course. Why don’t the textbooks and professors make that clearer to make it easier on everyone?

Personally I think that the professors get a kick out of watching the students bang their heads against the wall trying to understand the explanations of relativity. Also, if they made these things crystal clear at the onset everyone might pass with an "A" and that would make the course look too easy.

So they like to keep the students in the dark about these things.

 

[Hurkyl]

I can assure you that my reasons for believing in an aether have absolutely nothing to do with not wanting to believe in SR.

I didn't say they're you're reasons (but I probably meant it) -- just that it's a common reason people have.

I mean, it really doesn't offer a mechanism for time dilation.

Sure it does -- as soon as you stop viewing measurements as a black box. It follows from the constancy of c, which was proven by the fact Maxwell's equations are not frame dependent. (One of) the first example(s) people learn about SR is that of the light clock formed as light bounces between two mirrors. If that doesn't satisfy your definition of "[offering] a mechanism", then nothing will.

The only part that's interesting is why all clocks should agree with light clocks. But, given that macroscopic matter is shaped by electromagnetic forces, it's no stretch for me to believe one could actually prove it for mechanical clocks as well.

To me, that is much more attractive than just doing engineering calculations using SR.

Again, I'll counter with my own experiences. I agree that sometimes, understanding from where an equation comes can help with solving a problem, but I find the exact opposite is more frequently helpful -- specifically, by eliminating any biases I might have formed from knowing the origin of the equation.

But, both tools are in my bag of tricks. Sometimes I'll add biases that might help me work through a problem (which usually only works when I'm not very familiar with a subject), and sometimes I'll abstract away to try and eliminate biases that are preventing me from seeing the solution.



Anyways, my question to you is this: what is the gain from assuming an aether? Unless I'm missing something, having a "preferred" frame nets you nothing more than a label for a special frame, but raises questions that have no relevance to solving the problem, like "why is that one preferred?"

Whenever I knowingly add biases to a problem, I have a specific reason. For example, when working with a particular (finite-dimensional) vector space V, I'll write its vectors as matrices with a single column (coordinates with respect to an unspecified basis, of course), and I'll write vectors in V*, the dual space, as matrices with a single row. (aka column vectors and row vectors, respectively) This approach assists me with organizational issues, and allows me the to use the familiar matrix multiplication syntax. As such, adding this bias helps me solve problems, and I know why, but I know enough to avoid this approach when it will confuse an issue.

 

[NeutronStar]

Modern physicists don't really believe that "mechanisms" are important any more. Any mathematical rule we can describe could be a rule that nature uses in her "program". Check out chapter 2 of Feynman's book The Character of Physical Law, "The Relation of Mathematics to Physics", for a good articulation of the way most physicists think about this.

By the way, thanks for pointing to this information. I'm definitely interested in reading Feynman's thoughts.

That doesn't mean that I'll agree with the direction that physics has taken. I'll probably just conclude that physics has been infiltrated by the pure mathematicians and that all the real physicists have been secretly murdered and buried in empty sets.

 

[jcsd]

If you really must have 'mechanisms', you could view time dialtion in special relattvity as simply the result as farirly intutive result of a 'rotation' in spacetime.

 

[yogi]

A couple of comments by Posters which I believe are incorrect. Specifically it is implied that LR is the same as classical Lorentz Ether Theory. It is not the same - LR is based upon a local geogravitational effect. I simply says that in the Earth's gravitational field, light is one way isotroptic and therefore the Lorentz transforms hold for measurements of time dilation relative to Earth clocks, and it comports with those measurments. It is not based upon physical contractions of the type originally introduced by Fitzgerald and Lorentz to explain MMx. Secondly, since the transforms are only applied one way, it is simplier than SR - none of the so called SR paradoxes arise (I know, they are not paradoxes to relativists - just to everyone else).

 

[Garth]

I felt like screaming at the top of my lungs, "There is no explanation! Just do the math and accept the results!".

What! Who taught you relativity? I must admit that at undergraduate level, with so much thrown at me all at once, as a student I felt the same way. But that was because at the time I failed to appreciate the deep truths of SR space-time.

The mechanism is the metric with signature (-1,+1,+1,+1) or with the opposite convention if you prefer.
1. Is time a dimension like space, and should be treated with it in a space-time continuum?
This can be considered the basic postulate of SR.

If so then:

2. Is the metric, which connects events with their neighbours and gives a structure to the space-time manifold, given by an extension of Pythagoras' theorem:
dtau² = dt² - [dx² + dy² + dz²]/c²?
[In which case time is a dimension like the space dimensions, but it is not exactly the same. Mathematically time has the same relationship to length as the imaginary numbers have to the real numbers. The suggestion that if time is a dimension then it is subtly different from the others is, in my opinion, intuitively obvious.]
This can be considered the second postulate of SR.

If so, then:

SR is all about answering the question, "What is the nature of time, and how does it relate to space?" All flows from this metric and this concept of time. If an object is stationary in the coordinate system of the observer then
dtau² = dt²
and tau, proper time, is seen to be that time as measured in the rest frame of the object. Four-momentum follows immediately as a 4D equivalent of ordinary Three-momentum, with Four-velocity being the rate of displacement across space-time wrt the proper time tau.

Consideration of the Four-momentum of a stationary object in the rest frame of the observe leads immediately to
E = mc².

Consideration of the fact that t is not the same as tau for objects moving relative to the observer leads to the realisation that simultaneity is realtive to the observer and hence to the resolution of the Twin Paradox and the other paradoxes of SR.

The question is, "Does the theory work experimentally?" I think it does. Others may properly argue on the basis that the disputed results of various experiments may, or may not, agree with its predictions, but to argue on the basis that the theory cannot be understood and you have to, “Just do the math and accept the results“ only exposes your ignorance.

Garth

 

[yogi]

Garth: ..."only exposes your ignorance" The reciprocal nature of the of the transforms in SR have created many dissidents who have spend years trying to visualize its implications. NeutronStar is one such person - that does not justify a personal attack.
That SR is confusing, can be seen by the many conflicting descriptions of its consequences: I recently came across the following:

The reciprocal effect of length contraction and time dilation, which appears by logical necessity to emerge from the kinematic part of the special theory of relativity, has been variously explained as
1. true but not really true (guess who)
2. real
3. not real
4. apparent
5. the result of the relativity of simultaneity
6. determined by measurement
7. a perspective effect
8. mathematical.
Here is a small selection from the literature; Unless placed in quotation marks, authors' assessments are summarized.
1. Effects are true but not really true:
Pride of place goes to Eddington [1928, 33-34]:
"The shortening of the moving rod is true , but it is not really true."
2. Effects are real:
Arzelies [1966, 120-121]:
The Lorentz Contraction is a Real Phenomenon. ...
Several authors have stated that the Lorentz contraction only seems to occur, and is not real. This idea is false. So far as relativistic theory is concerned, this contraction is just as real as any other phenomenon. Admittedly ... it is not absolute, but depends upon the system employed for the measurement; it seems that we might call it an apparent contraction which varies with the system. This is merely playing with the words, however. We must not confuse the reality of a phenomenon with the independence of this phenomenon of a change of system. ... The difficulty arises because we have become accustomed to the geometrical concept of a rigid body with a definite shape, whatever the measuring system. This idea must be abandoned. ... We must use the term "real" for every phenomenon which can be measured ... The Lorentz Contraction is an Objective Phenomenon. ...
We often encounter the following remark: The length of a ruler depends upon its motion with respect to the observer. ... From this, it is concluded once again that the contraction is only apparent, a subjective phenomenon. ... such remarks ought to be forbidden.
Krane [1983, 23-25]:
It must be pointed out that time dilation is a real effect that applies not only to clocks based on light beams but to time itself. All clocks will run more slowly as observed from the moving frame of reference. ...
The length measured by the moving observer is shorter. It must be emphasized that this is a real effect.
Matveyev [1966, 305]:
The dimensions of bodies suffer contraction in the direction of motion ... A body is, therefore, "flattened" in the direction of motion. This effect is a real effect ...
Møller [1972, 44]:
Contraction is a real effect observable in principle by experiment. It expresses, however, not so much a quality of the moving stick itself as rather a reciprocal relation between measuring-sticks in motion relative to each other. ... According to relativistic conception, the notion of the length of a stick has an unambiguous meaning only in relation to a given inertial frame. ... This means that the concept of length has lost its absolute meaning.
Pauli [1981, 12-13]:
We have seen that this contraction is connected with the relativity of simultaneity, and for this reason the argument has been put forward that it is only an "apparent" contraction, in other words, that it is only simulated by our space-time measurements. If a state is called real only if it can be determined in the same way in all Galilean reference systems, then the Lorentz contraction is indeed only apparent, since an observer at rest in K' will see the rod without contraction. But we do not consider such a point of view as appropriate, and in any case the Lorentz contraction is in principle observable. ... It therefore follows that the Lorentz contraction is not a property of a single rod taken by itself, but a reciprocal relation between two such rods moving relatively to each other, and this relation is in principle observable.
Schwinger [1986, 52]:
Each will observe the other clock to be running more slowly. This is an objective fact. It is not a property of clocks but of time itself.
Tolman [1987, 23-24]:
Entirely real but symmetrical.
3. Relativistic effects are not physically real:
Taylor & Wheeler [1992, 76]:
Does something about a clock really change when it moves, resulting in the observed change in the tick rate? Absolutely not! Here is why: Whether a clock is at rest or in motion ... is controlled by the observer. You want the clock to be at rest? Move along with it. ... How can your change of motion affect the inner mechanism of a distant clock? It cannot and it does not.
4. Relativistic effects are apparent:
Aharoni [1985, 21]:
The moving rod appears shorter. The moving clock appears to go slow.
Cullwick [1959, 65, 68]:
[A] rod which is at rest in S' ... appears to the observer O to be contracted ... Similarly, a rod at rest in S will appear in S' to be contracted...
Jackson [1975, 520]:
The time as seen in the rest system is dilated.
Joos [1958, 243-244]:
The interval appears to the moving observer to be lengthened. A body which appears to be spherical to an observer at rest will appear to a moving observer to be an oblate spheroid.
McCrea [1954, 15-16]:
The apparent length is reduced. Time intervals appear to be lengthened; clocks appear to go slow.
Nunn [1923, 43-44]:
A moving rod would appear to be shortened. An interval is always less than measured by the other observer.
Whitrow [1980, 255]:
Instead of assuming that there are real, i.e. structural, changes in length and duration owing to motion, Einstein's theory involves only apparent changes, and these are independent of the microscopic constitution and hidden mechanisms controlling the structure of matter. [Unlike]... real changes, these apparent phenomena are reciprocal.
5. Relativistic effects are the result of the relativity of simultaneity:
Bohm [1965, 59]:
When measuring lengths and intervals, observers are not referring to the same events.
French [1968, 97],
Rosser [1967, 37],
Stephenson & Kilmister [1987, 38-39]:
Measurements of lengths involve simultaneity and yield different numerical values.
6. Relativistic effects are determined by measurements:
Schwartz [1972, 113]:
Each observer determines distances to be foreshortened.
7. Relativistic effects are comparable to perspective effects: Rindler [1991, 25-29]:
Moving lengths are reduced, a kind of perspective effect. But of course nothing has happened to the rod itself. Nevertheless, contraction is no illusion, it is real. Moving clocks go slow, a 'velocity-perspective' effect. Nothing at all happens to the clock itself. Like contraction, this

 

[jcsd]

That's silly, as I said, evryone knows that time dialtion and length contraction are the result of changing basis in spacetime

Until 'real', 'not real', 'apparent', etc, are well-defiinde physical concepts then it's just a matter for that age old question of ontology as the actual predictions of relativity are unambiguous. Personally I have to say within the rleativstic paradigm length contraction etc must be described as 'real' as cleraly if you take a spatial slice from a givcen cordinate system then there is no objevctive way to tell whether the lengths of objects are due to length contraction or not (though you could argue that by only examing a single spatila slice we're not looking at the bigger picture).

 

[Janus]

This thread has drifted off the initial question to the point that I'm just going to lock it.