I got issues. Here’s one. I don’t like what people say about special relativity. Because we’re friends, special relativity and I.

I got issues with certain people in particular, those writing popular science books. Sometimes I feel like have to thank every physicist who takes the time to write a book. But, well, I got issues. Also, I got sunglasses and a haircut, see photo.

I presently read “The Universe in the Rearview Mirror” (disclaimer: free copy) and here we go again. Yet another writer who gives special relativity a bad name.

Here’s the issue.

Ask some theoretical physicist what special relativity is and they’ll say something like “It’s the dynamics in Minkowski space” or “It’s the special case of general relativity in flat space”. (Representative survey taken among our household members, p=0.0003). But open a pop science book and they’ll try to tell you special relativity applies only to inertial frames, only to observers moving with constant velocities.

Now, as with all nomenclature it’s of course a matter of definition, but referring to special relativity as being only good for inertial frames is a bad terminology, and not only because it doesn’t agree with the modern use of the word. The problem is that general relativity is commonly, both among physicists and in the pop sci literature, referred to as Einstein’s theory of gravity, rubber sheet and all. Einstein famously used the equivalence principle to arrive at his theory of gravity and that principle says essentially: “The effects of gravity are locally indistinguishable from acceleration in flat space.” With the equivalence principle, all you need to do is to take acceleration in flat space and glue it locally to a curved space, and voila there’s general relativity. I’m oversimplifying somewhat, all right, but if you know a thing or two about tensor bundles that’s essentially it.

The issue is, if you don’t know how to describe acceleration in flat space then the equivalence principle doesn’t gain you anything. So if you’ve been told special relativity works only for constant velocities, it’s impossible to understand all the stuff about angels pulling lifts and so on. You also mistakenly come to believe that to resolve the twin paradox you need to take into account gravity, which is nonsense.

Yes, historically Einstein first published special relativity for inertial frames, after all that’s the simplest case, and that’s where the name comes from. But the essence of special relativity isn’t inertial frames, it’s the symmetry of Minkowski space. It’s absolutely no problem to apply special relativity to accelerated bodies. Heck, you can do Galilean relativity for accelerated bodies! All you need is to know what a derivative is. You can also, for that matter, do Galilean relativity in arbitrary coordinate frames. In fact, most first semester exercises seem to consist basically of such coordinate transformation, or at least that’s my recollection. So don’t try to tell me that the ‘general’ of relativity has something to do with the choice of coordinates.

So yes, historically special relativity started out being about constant velocities. But insisting – more than 100 years later – that special relativity is about inertial frames, and only about inertial frames, is like insisting a telephone is a device to transfer messages about cucumber salad, just because that happened to be the first thing that ever went through a phone line. It’s an unnecessarily confusing terminology.

Since special relativity is busy boosting your rocket ships with laser cannons and so on, on her* behalf I want to ask you for somewhat more respect. Special relativity is perfectly able to deal with accelerated observers.

*German nouns come in three genders: male, female and neuter. Special relativity, or theory in general, is a female noun. Time is female, space is male. The singularity is female, the horizon is male. Intelligence is female, insanity male. Don’t shoot the messenger.

## 88 comments:

Defending (as I must!) popular science writers, defining special relativity as a special case of general relativity is useless for popular science, as it only works as a definition if you know what general relativity (and flat space) is - i.e it is a totally useless definition for anyone coming to the whole business afresh. I agree a lot of popular science treatments get it wrong over inertial frames/acceleration, though.

Brian,

I agree - I'm not saying you should 'define' it this way in a pop sci explanation. I was just saying that's what most physicists would say. I don't see what's wrong with explaining eg special relativity is 'without gravity' and general relativity is 'with gravity'. Which is not strictly speaking correct, but it's good enough and certainly better than saying special relativity is for observers at constant velocity. Best,

B.

For me. Special Relativity is the extension of galilean relativity based on the following two postulates:

1) The laws of Mechanics and electromagnetism satisfy the "special" relativity principle, meaning that they are both invariant under the same set of symmetry transformations.

2) The lightspeed is the maximum attainable velocity and the same for every inertial frame (inertial frame is defined as the reference system which moves with relative constant speed with respect to another).

1)+2) <---> Invariance under the Lorentz group (really the Poincaré group if we say that there is no preference between any origin, so we can translate it to any point in the universe).

Going beyond Special Relativity in the sense that we accept the equivalence principle (the weak equivalence principle) and the "general covariance", we have General Relativity. The name is unfortunated, as many people, even Einstein himself, were aware that really what "General Relativity" is has nothing of "relative" but with invariance! This misnomer of what should be called "(special) relativistic invariant theory of gravity" on "curved spacetime", or maybe "relativistic gravity" for short.

Old popular physics and divulgation of relativity, Einstein's theory of gravity or even not so old explanations of this theory were not clear about this point. Of course, after one century, Einstein's gravitational theory face yet the challenge to handle with the quantum idea/postulates and viceversa, quantum mechanics raises some questions on the foundations and postulates of relativity (specially those related to "locality" or the notion of rest and the issue of the "uncertainty" principle applied to the spacetime).

Defining special relativity as a special case of "relativistic gravitation" when the spacetime is flat can be confusing for the unexpert eye AND it requires the knowledge a priori of one version of the equivalence principle (or the geodesic equation) and the issue of reducing the GL(D,R) to the SR group SO(D-1,1). It is a massive "group contraction" somehow, since D²-> D(D-1)/2...Or D(D+1)/2=D(D-1)/2+D if you take the Poincaré group. Passing from the general linear group (as representative of the diffeomorphism group) to the Poincaré group reduces the dimension of the group in D²-D(D+1)/2=D(D-1)/2 or D(D+1)/2 if you stop at the Lorentz group. So, in my opinion, the definition of "special relativity" should not be done in the top-bottom approach from curved spacetime but in the pure postulational realm. Otherwise, you introduce issues unrelated with the pure essence of special relativity as a kinematical/dynamical extension of relativity to electromagnetism.

Then, I prefer my 1)2) or 1)+2) definition of SR above.

We deal with acceleration with a continuous series of co-moving inertial frames. Is that simple enough to explain?

It's a surprizing fact that many physicists make the same mistake (of thinking special relativity only applies in inertial frames).

Love the great new look - glamour with an edge.

You and relativity might be friends, Sabine, but relativity and I are more than just good friends. You rightfully take issue with pop-science writers who talk only about SR inertial frames, but I'm afraid there's far bigger issues than that.

“The effects of gravity are locally indistinguishable from acceleration in flat space.”OK. An accelerated charge radiates. An accelerated charge at rest in a gravitational field does not. Does this violate the principle of equivalence? Discuss.

Correction:

OK. An accelerated charge radiates. A charge at rest in a gravitational field does not. Does this violate the principle of equivalence? Discuss.

Sabine, I agree and I would go in a sense even farther. To me special relativity represents just a special point of enlarged symmetry within the larger space of possible field theories of nature. All field theories will exhibit "relativity-like" dynamics, whether or not they have exact Lorentz invariance, so it is a little misleading to attribute the various motion-dependent effects solely to the symmetry, let alone to "spacetime". I have written a paper, Arxiv 1305.3022, and book called "Relativity Made Real", expounding on this viewpoint.

Special Relativity is physics on a topologically trivial Lorentzian manifold with a zero curvature tensor metric. No particular coordinate choice is required. Its metric's group of isometries is the Poincaré group that

excludes chirality.Parity violations, chiral anomalies, symmetry breakings are diagnostics for matter (not photons). Local opposite shoes vacuum free fall along trace non-identical minimum action trajectories, falsifying the Equivalence Principle, spacetime geometry versus test mass geometry: chemically and visually identical, single crystals of alpha-quartz in

P3(1)21 versusP3(2)21 enantiomorphic space groups. gamma-Glycine, test mass space groupsP3(1) versusP3(2), is better. Theory must respect orthogonal observation, not forbid it.@Philip Helbig -

If you were right that a stationary charge in a gravitational field did not radiate (for example, a charge at rest on the surface of the earth), it would violate equivalence.

But you are not right on this question: http://arxiv.org/abs/physics/9910019

Philip, re

"An accelerated charge radiates. A charge at rest in a gravitational field does not. Does this violate the principle of equivalence?"No. See this quote from J.L. Synge'sRelativity; The General Theory:"...I have never been able to understand this principle ...Does it mean that the effects of a gravitational field are indistinguishable from the effects of an observer’s acceleration? If so, it is false. In Einstein’s theory, either there is a gravitational field or there is none, according as the Riemann tensor does not or does vanish. This is an absolute property; it has nothing to do with any observers world line ...The Principle of Equivalence performed the essential office of midwife at the birth of general relativity, but, as Einstein remarked, the infant would never have gone beyond its long clothes had it not been for Minkowski’s concept. I suggest that the midwife be buried with appropriate honours..."

See the plot of gravitational potential on wikipedia. That’s Newtonian, but it’s like the bowling ball. The curvature you can see relates to Riemann curvature. If you make that vanish, your plot doesn’t get off the flat and level in the middle, so you’ve made the gravitational field vanish too. The principle of equivalence was only a guiding principle, one that applies to an infinitesimal region only. Which means it doesn’t apply to your charged particle.

@johnduffieldblog

Two words: "locally indistingusihable"

How Synge could be confrused on such a fundamental point of GR and the geometry of manifolds astounds me.

Two more words: spelling, oops

He wasn't confused, Capital. Honest. In the "few inferences" section of

Relativity The Special And General TheoryEinstein said this:"This is by no means true for all gravitational fields, but only for those of quite special form. It is, for instance, impossible to choose a body of reference such that, as judged from it, the gravitational field of the earth (in its entirety) vanishes".I'm sorry but that paper you quoted was wrong. If matter down in a gravitational potential had been radiating energy for 13.8 billion years, some electrons would be more massive than others.Thanks for the reference. I'll have to read it and compare it to the arguments in http://arxiv.org/abs/gr-qc/9303025.

Phil: also check out http://arxiv.org/abs/physics/0204044 . It isn't peer-reviewed, but as far as I can tell it's right. At least more right than a paper that says some rock sitting on the ground has been radiating energy and losing mass for billions of years. A rock gains mass when you do work on it and lift it. We call it potential energy, but it is real, and it's in the rock*. Some of that mass-energy is converted into kinetic energy when it falls. After that's dissipated and radiated away the rock has lost mass. But after that, it doesn't radiate any more, and it doesn't lose any more mass.

* You detonate an explosion where momentum is directed at the Earth and the rock, but the rock gets the lion's share of the kinetic energy by virtue of KE=½mv². As the rock slows down the KE is converted to PE. In the rock.

johnduffieldblog: Suppose you accelerate an atom up and down a tube by some means. Will it radiate?

Not really, because positive and negative charges are balanced, and their radiation cancels. Likewise, the electrons on Earth are matched by corresponding protons.

Another equivalence principle problem: does a an observer supported in a gravitational field experience Unruh radiation? Maybe not, and that might be relevant to the question of the supported charge.

Maybe radiation depends on the global structure of the of t6he spacetime, not just the local structure.

As was mentioned, the really shocking thing is that plenty of people with PhDs suffer from this and allied mental disorders. For example, Lubos Motl still doesn't believe that special relativity is "generally covariant".

I really believe that this is a serious problem for physics research right now. For example, it's very clear that a lot of the recent firewall stuff arises from people who are unable to let go of things they picked up in old-fashioned undergraduate courses on relativity and quantum mechanics.

The way to teach relativity is as follows. "Long ago, Minkowski, using some half-digested ideas from Einstein and Poincare, realised that spacetime is a flat semi-Riemannian manifold. Later Einstein, again using silly but effective heuristics like the Principle of Equivalence [this is the last time you are ever going to hear this phrase in this course] discovered that spacetime is not flat after all, and that our failure to recognise this is the phenomenon called "gravity". Now for some equations......"

Although the discussion about what SR is and what it is not is purely semantic I think one should respect the traditional view spelled out in the best textbooks, eg. Taylor&Wheeler, Landau&Lifshitz. Therefore for me SR is, like Newtonian mechanics, about inertial frames ONLY. Accelerated observers are tricky already in the Newtonian physics and I do not think you can handle them in the relativistic theory without understanding GR. Of course you can say that SR is a special case of GR on Minkowski spacetime but the relation is rather subtle (if you understand SR in my way). Cheers J

Jerzy,

"I think one should respect the traditional view spelled out in the best textbooks..."I disagree. I think popular science writing should respect the most common use of the word in the modern literature on the topic. Otherwise they'll just contribute to misunderstanding between scientists and the public. (Also, a classic textbook isn't necessarily the 'best' textbook.) Best,

B.

Phillip,

I'm not sure what you mean with 'in rest'. A particle that is stationary in a gravitational field has to accelerate to remain stationary. I don't know why you think an accelerated charge doesn't radiate. Yes, such an observer experiences Unruh radiation, that's the whole point of Unruh radiation: place the observer at a black hole horizon, wave your hands and say equivalence principle, et voila, black holes have a temperature. As somebody said above, the word "locally" is crucial. A freely falling observer does not notice anything "locally", but he would on distances larger than the curvature radius. Best,

B.

Sabine,

I agree with most of your posting. If one is to endorse the most consistent and accurate description of SR according to Einstein himself, then for two bodies to experience special relativistic effects, they can experience something as simple as a relative position change which will indicate relative velocity. When one of the bodies experiences acceleration, there is still relative velocity, just with a continuous rate of change. How any Einstein-endorsing scientist would think that SR effects are somehow magically disengaged during non-inertial motion because an added phenomenon is at work has always puzzled me.

Having said all that – I am troubled by your specific quote:

“You also mistakenly come to believe that to resolve the twin paradox you need to take into account gravity, which is nonsense.”

I am troubled because, technically it is a separate issue from your point raised previous to that one. While it is true that physicists such as J.A. Wheeler have developed mathematical resolutions that can rely on SR alone, they, in no way describe (within the confines of relativity defined by Einstein) what could possibly happen to real physical objects experiencing an out-and-back journey. Max Born clarified Einstein’s position perfectly when he said in his book (titled: Einstein’s Theory of Relativity): “The clock paradox is due to a false application of the special theory of relativity, namely, to a case in which the methods of the general theory should be applied.” Here Born provides a simple mathematical explanation that describes the twin paradox in a series of steps. (More detailed treatments are out there as well – see Daniel Styer, Am. J. Phys. 75 (9), Sept. 2007 for example.) This is based on Einstein’s own rare twin paradox discussion found in his paper: Dialog about objections against the theory of relativity (found in: Die Naturwissenschaften, November 29, 1918).

One often hears that if the twins meet up then one of them must accelerated and thus GR must be involved. (This implies that one believes that GR is needed whenever acceleration comes into play.) However, the effect depends on the length of the journey, not on the acceleration. That is, double the length of the journey and the effect is larger, even though the acceleration at turnaround is the same. This indicates that it is an SR effect, not a GR effect.

Chris,

See! That's exactly why I am saying the terminology is not helpful. The clock paradox *is* due to a false application of special relativity, namely due to treating something as inertial frames which isn't inertial frames. You have to apply special relativity correctly, taking into account acceleration. I am pretty sure that in the quote that you mention 'general theory' does not refer to gravity, but to a more general use of (what we today call) special relativity.

Yes, if you want an accurate result you should probably take into account background expansion and such, but just to resolve the paradox you do *not* need gravity.

Best,

B.

Phillip,

"One often hears that if the twins meet up then one of them must accelerated and thus GR must be involved"Yes. And at the same time you're being told that GR is Einstein's theory of gravity, that's the problem with this terminology. Best,

B.

I think you should provide the excerpt from the book because I don't think authors' intention was to imply that you can't treat accelerating objects in SR.

When we say that SR applies only to inertial frames we mean that the principles of SR (constancy of speed of light, physical laws) are valid only to inertial frames which is evidently true and a tautology. But this does not prevent us from dealing with acceleration in SR.

Also we shouldn't go to the other end and think that SR is general covariant like Rastus implied above (you didn't correct him BTW, I don't suppose you accept this position. SR is not general covariant i.e. diffeomorphism invariant, coordinate transformations are not a gauge in SR.

The twin paradox can be explained even without accelerations, as it comes to my mind in a brief thought experiment.

Imagine an aligned set of spaceships, S', like a "train" of ships, with their clocks all synchronized, passing each ship by earth at v=0.96c, and away from it. When the 1st spaceship passes by earth, it sets t'= 0. Each ship has an observer who must take note of the time t passed on earth since t'=0, when the observer's ship passes by the planet. Now imagine another similar "train" of ships, S", traveling towards earth at opposite direction, with v=-0.96c.

Now, Mr. Spock, who is on board the first set of ships on S', decides to teletransport himself instantaneously to one of the ships on the other set, S", when his clock is, say, t'= 7. When materializing on the other ship, he instantaneously synchronizes all the clocks on S" by setting t"=7.

Then he compares the time passed on earth, as registered by the ship on S' that was passing by earth on t'=7, to that ship on S" which was also passing by earth on t" = 7. The first one will say that t on earth was 14 years, while the other, 50 years.

So you see, we have both systems of inertial frames, no accelerations involved, and yet the time passed on earth at an instant of time t'= t" = 7 does not match.

The issue is solved by noticing that the axis of simultaneity of S' is completely different to that of S", so both ships are not making a simultaneous measurement of the time passed on earth since the first ship on S' passed by it, they are not seeing earth at the same instant. Drawing a diagram makes it easy to see this.

Of course, no one knows if teletransportation is possible, so we must admit that you must have accelerations in order to turnaround back to earth. But my example emphasizes the need to take care of changing frames properly.

Best,

Christine

So If SR is about inertial frames, the we should be able to measure lightspeed differences on fast rotating masses in the lab and also masses rotating around the sun like Venus and the Earth right? See;

Experiments to determine the mass related Lightspeed extinction volume

around the Earth and around spinning objects in the Lab.

http://vixra.org/pdf/1102.0056v2.pdf

Sabine,

I want to make sure we are not mixing up two different things: Using the correct application of special relativity during all portions of a twin paradox journey will achieve an acceptable mathematical result. But it is an alternate mathematical process and not an accurate physical description of what is experienced by each twin leading to the final clock discrepancy according to Einstein’s theory.

Einstein described the inertial (SR) phase of the journey as a reciprocal clock-slowing phase (each twin sees the other’s clock running slower than their own) and stated that an induced gravitational field during the accelerated turnaround is absolutely necessary to undo the paradox by creating additional time dilating effects for the traveler in a non-reciprocal manner. Max Born (along with many others afterward) used the simple equation introduced in Einstein’s 1911 Principle of Equivalence: gh/c^2 where g is the acceleration value and h is the distance between the clocks. This explanation also addresses Phillip Helbig’s concern about the varying lengths of a journey with the same g value. As you can see – a longer journey will have a larger h value during the turnaround and produce a larger necessary compensating effect for the longer reciprocal buildup during the inertial phase.

I’m not saying that I agree with that explanation but it is the one that you must endorse if you think Einstein’s relativity is correct.

The Twin Paradox without acceleration: Three identical toggle switch mechanical clocks are kits. Three spaceships carry a kit each. Build clocks after the experiment is set up. Toggle touch switches states, on-off. CLOCK 1 is in vacuum free fall, our inertial reference frame, with its toggle exposed, off and zeroed. CLOCK 2's spaceship travels at 0.999c relative to CLOCK 1. It is far to our left. CLOCK 2, off and zeroed, has always been in vacuum free fall. It skims past CLOCK 1, toggles touch, both clocks are on, locally synchronized by touching.

CLOCK 3's spaceship travels at 0.999c relative to CLOCK 1, far far to our right. CLOCK 3 is off and zeroed. CLOCKs 2 and 3, in vacuum free fall, touch toggles. CLOCK 2 is off, CLOCK 3 is on. CLOCK 2's duration is written down. CLOCK 3 reflects CLOCK 2's path to touch toggles with CLOCK 1. Both clocks are off. Write down elapsed times.

Numbers on paper are invariant. Three clocks were passive observers in vacuum free fall (zero acceleration). Compare elapsed times. The Twin (Triplets) Paradox obtains. (No comment on quartz clocks.)

Bee,

I'm not so sure about the Unruh radiation (for a particle on, say Earth). In the QFT calculation for both Unruh and Hawking, the existence of a horizon is a crucial element. Where is the horizon in the case of Earth?

Similar considerations may apply to the case Philip considers.

There is also the question of where the energy comes from.

From some of the quotes I've seen here, it's not clear that science writers are much more confused that distinguished physicists, including a Nobel prizewinner or two.

Dear Giotis, for the "general covariance" of SR, see Misner Thorne and Wheeler.

Case closed.

Bee,

Beautiful! Reminds me why I should visit your blog more often. (Love the hair and glasses, hon.)

Tom

Capital: like I said, there are issues. For example in SR, what you usually don't read about is WHY you always measure the speed of light to be the same, and WHY Einstein was right to propose his postulate.

Giotis,

For what I am concerned, SR is GR in flat space (vanishing curvature tensor). It has the added benefit of global Poincare invariance. But that explanation is of course backwards, both historically as well as conceptually, so it doesn't work as a pop sci explanation. Best,

B.

Chris,

I would really suggest you read some modern textbook on the topic, you're just reinforcing your misconceptions. You say "an induced gravitational field during the accelerated turnaround". An acceleration in flat space does not 'induce a gravitational field.' Space is either flat or it isn't. That's an observer-independent statement. I repeat: you do not need gravity to solve the twin paradox. All you need is to know how to deal with accelerated observers in special relativity (flat space). And, yes, this acceleration is *locally* indistinguishable from a gravitational field, but that doesn't mean there are suddenly sources for an actual gravitational field (curvature of space-time). Best,

B.

Giotis,

I don't have the book here, sorry, and it's not on Amazon search inside. It'll have to wait till next week. Best,

B.

Hi CIP,

I'm not sure what you're not sure about, but possibly this answers your question. Best,

B.

John,

It's not an "issue" it's an axiom. It leads to a theory that is in excellent agreement with observation. Best,

B.

Hi Christine,

Yes, they both measure different time axis. But I don't see how your explanation solves the problem when you create a situation that really does not allow for an answer of the type "both are right", but an "either or". When they meet again, either the first twin is younger than the second or he isn't. Best,

B.

Rastus Odinga Odinga,

"Long ago, Minkowski, using some half-digested ideas from Einstein and Poincare, realised that spacetime is a flat semi-Riemannian manifold."

Not true. It was Einstein who adopted Minkowski space for general relativity as a physically real model, because of the impossibility of reconciling Newton's absolute space and absolute time as independent physically real measures, with real physical experiment. You can find this explained clearly and explicitly in Einstein's *The Meaning of Relativity* (Princeton Press 1956) in his introduction to general relativity.

Spacetime is not " ... a flat semi-Riemannian manifold ..." (a common mistake) -- it is a pseudo-Riemannian manifold of Lorentzian metric properties. That's what reconciles special relativity with general relativity; the mostly flat global curvature is a special case of uniform motion.

"Later Einstein, again using silly but effective heuristics like the Principle of Equivalence [this is the last time you are ever going to hear this phrase in this course] discovered that spacetime is not flat after all, and that our failure to recognise this is the phenomenon called 'gravity.'"

No, gravity is called gravity, and in general relativity it is described simply as the curvature of space along a time metric of reverse sign in a coordinate system. The equivalence principle is neither silly nor a heuristic. It is the consequence of observer dependence -- in this mostly flat (Euclidean) space of ours an observer cannot *in principle* distinguish between free fall in a gravitational field (Galilean relativity) and some force pushing in the opposite direction.

"Now for some equations......"

If one learns well the equations of classical mechanics leading to relativity, one should have little trouble comprehending special and general relativity.

Tom

Historically, I think Einstein did not come to special relativity through incompatibility of absolute space and time with 'real physical experiment' but via the difficulty of reconciling Maxwell's equations with Galilean relativity. (Zur Elektrodynamik bewegter Körper.)

Bee,

" ... Einstein did not come to special relativity through incompatibility of absolute space and time with 'real physical experiment' but via the difficulty of reconciling Maxwell's equations with Galilean relativity."

I stand corrected on the technical point. However, it amounts to the same thing -- Galileo demonstrated that the free fall of a body is indifferent to a straight or curved trajectory to the plane. The spacetime field concept follows.

Best,

Tom

Sorry, I meant the electrodynamic field.

Sabine,

Thank you for the advice but I’m actually pretty familiar with resolutions modern and old that use a variety of methods to solve this problem. I am new to your blog and therefore not sure what your area of expertise is but I would suggest that you familiarize yourself with the history of relativity according to Einstein. In his 1918 paper that I referenced in an earlier post, Einstein described the turnaround segment of the twin paradox journey with the following: “A homogenous gravitational field appears, that is directed towards the positive x-axis. Clock U1 is accelerated in the direction of the positive x-axis until it has reached the velocity v, then the gravitational field disappears again. An external force, acting upon U2 in the negative direction of the x-axis prevents U2 from being set in motion by the gravitational field.”

He then goes on to tie this to the principle of equivalence by designating the traveling clock to have a Lower gravitational position and therefore experiencing a required and additional time dilation separate from any SR effects. Whether you consider it induced gravity, homogenous gravity or acceleration is really no concern of mine, but please know that this is an important step in the official resolution. As I also said in an earlier post – I don’t necessarily agree with this resolution but I find that when I discuss my issues with Einstein’s own resolution, I first have to see if the person I’m chatting with is even familiar with it before I can continue, because in many cases, even physicists who are working on the most exciting and cutting-edge stuff do not have a handle on the fundamentals.

Hi Sabine,

No, my example was not intended to solve the paradox, which does need accelerated frames to solve it.

I wondered about the issue with no accelerations, a limiting situation on the turnaround, where you change frames through a teleportation.

So in the original situation, you had to deccelerate and then accelerate (using the same frame), now you change instantaneously the frames. By "solved" I just mean that in this limit, both cases (original twin problem and the teleportation twin problem) are kinematically equivalent.

So the latter kinematic calculations agree with the original one and lead to the same paradox. But the instantaneous "teleportation" of the observer from one frame to the other creates a difficulty, and the paradox is not solved. I wonder now if we use a quantum teleportation thought experiment something weird in SR turns up??

Best,

Christine

In addition: of course, there are many issues in quantum teleportation, such as the no-cloning theorem, etc. Maybe there is a much "better" thought experiment than that which I suggested above, using entanglement or something of the sort, which might cause difficulties with the twin paradox, in the sense of a physically possible situation not involving accelerations...

@Uncle Al: if I understood you correctly, you have a physically possible situation involving no accelerations, leading to a twin paradox. How do you solve it?

Thanks.

Sabine, there's no problem with the theory. But re "it's not an issue it's an axiom". Sorry, but an axiom doesn't cut it. We demand a reason, not an axiom. And the reason is the wave nature of matter. THAT'S why you always measure the speed of light to be the same. Everything consists of waves, moving. You, your clocks, your rods, everything. So you calibrate your rods and clocks rods using the motion of those waves. Then you use them to measure the motion of those waves. Duh!

Check this out:

http://www.classicalmatter.org/ClassicalTheory/OtherRelativity.pdf

Rastus, you confuse change of coordinates with ‘General covariance’ i.e. passive with active diffeomorphisms. Only GR is generally covariant i.e. laws invariant under active diffeomorphisms.

It’s a classic mistake. Please check the literature again.

Christine, it doesn't matter if he accelerates or not. The crucial point is that you change inertial frames (and planes of simultaneity) and thus you introduce the asymmetry.

Giotis,

In the limit, everything proceeds as if the twin experiences a change from an inertial frame with velocity +v to another inertial frame with -v. So, in the *limit*, I do agree that the kinematical description of a twin fixed to a frame and turning around at some point is equivalent to that of a change of frames. The asymmetry is introduced either way. But to solve the paradox, one does indeed need acceleration, no?

I mean, physically the traveling twin is necessarily fixed to a *single* non-inertial frame (having an acceleration near turnaround which results in the change from +v to -v, therefore a single frame with a variable velocity).

I mean, how would the traveling twin physically move from one inertial frame (+v) to the other (-v) otherwise? His worldline would be "cusped" in that case, so the point is: is this a physically acceptable thought experiment? Because then you have another example of twin paradox relying only on the asymmetry of the frames +v and -v, no accelerations involved. A "rounded" worldline at turnaround seems necessarily implied to solve the twin paradox, but if you bypass the argument through such a "teletransport" argument, is it really solved as well? If not, what is wrong?

Christine

Bee,

Thanks for the paper you referenced, but I don't think Earth or any other non collapsing body meets its peeling re17638 ndrente4quirements (but I'm not a good enough geometer to be sure)

Consensus in literature seems to be that the electron neither radiates nor experiences Unruh (or Hawking) radiation. The stack exchange article was written by Lubos;-)

What if you simply have two clocks sitting next to each other and one runs faster. Does it travel into the future quicker? No. Since it ages quicker, it would fall into the past more rapidly.

Does the earth travel a vector from yesterday to tomorrow, or does tomorrow become yesterday because the earth rotates?

Time is an effect of action, just like temperature. Time is to temperature what frequency is to amplitude.

Its just that each of us are one of those molecules of water, bouncing through a series of events and and so we model time as a narrative sequence, but there is no overall direction, as context pushes back. It is just events coming into being and dissolving. Probability collapsing into actuality.

It's just that our causal logic and narrative imagination are based on that sequence of events.

Temporal sequence isn't even causal. Yesterday doesn't cause today, anymore than one wave causes the next. Cause is transfer of energy, as the sun radiating on a rotating planet causes the sequence of events called days and wind across the water causes waves.

Of course there are innumerable ways to correlate measures of duration and distance, but just because measuring the distance between two waves seems little different than the rate they pass a marker, large factors can hide in small differences.

You mentioned German nouns and his (?), her (?), their (?) genders, so let me comment on your English grammar:

"I got issues. Here’s one."

This is grammatically incorrect, but, of course captures American English idiomatic use perfectly. I can't imagine how long it would take me to learn enough German to use idioms so fluently.

You sometimes flub a few a few minor expressions, but generally your blog is written as if it's by a native American English speaker. For better or for worse. This is maybe why you're successful with a widely-read blog by a non-native speaker. (I assume there are successful German, French, Chinese, etc. blogs, even on physics topics, but they don't get much exposure.

Here's video clip from an important mid-60s band, from San Francisco, which uses the "I got" idiom repeatedly:

http://www.youtube.com/watch?v=29uNvGHsRlc

This was one of my favorite songs from 1965, as a young teen. The voice track is slightly out of sync from the several videos, as it was the norm then (and still often is) to lip-sync to the released single.

--Tim

Tim,

I guess I spent too much time sitting in campus cafes :p More seriously, if you speak enough German to understand pop song lyrics, you'd pick up idioms pretty quickly. You'd also probably, much like I, be left terribly confused at some points, but then there's Google to help you out. Alas, there's more English pop songs in Germany than there are German pop songs in America, which probably explains why it's easier for me than for you. Best,

B.

Hi Christine

Sorry I don’t get it. Why it is so important for you to find a physical way for the traveller to return to earth without accelerating. Just assume in your thought experiment that he reverses instantaneously or use a second incoming traveller and let the first pass the clock reading to him. It’s irrelevant.

Again as you correctly said acceleration has nothing to do with the paradox. The asymmetry is introduced due to change of planes of simultaneity (inertial frames); time is just a coordinate in SR.

I’m not sure why you have second thoughts on this.

Giotis,

Well, what is the single, necessary and sufficient physical explanation to solve the paradox?

I think we all agree that the resolution must involve an asymmetry between the twins. Physically, one then needs a single non-inertial frame. But then that can be described, in the limit, by two inertial frames (different time axis). Yes, sure, you may put two observers on each, and the results will agree in the limit!

The limit is what is bothering me now, but maybe it's not that important. I'm not sure right now, because I was thinking on what Sabine replied above (that's why I thought I needed to have just one traveller):

"Yes, they both measure different time axis. But I don't see how your explanation solves the problem when you create a situation that really does not allow for an answer of the type "both are right", but an "either or". When they meet again, either the first twin is younger than the second or he isn't. Best,"

Christine

Sorry Christine, I have no clue of what exactly Sabine is trying to say here. The important things to follow in the experiment are the clock readings and the change of frames. The other stuff e.g. who holds them (twins or not) is just a story.

@Christine Triplet clocks illustrate defective assumption. No clock accelerated, no clock reoriented, but durations do not linearly sum. Respective

inertial frameswere manipulated before the experiment began.(Quantum) gravitation, SUSY, dark matter; the Shroud of Turin falsely assume symmetries that also exclude falsifications. Paradox and miracle obtain. Cartography falsifies the Shroud. The others fall to five classes of chiral Equivalence Principle experiments.

arxiv:1308.3213, "Tests of the universality of free fall" therein. Yukawa interaction is untenable: 1.74 solar-mass 465.1 Hz pulsar PSR J1903+0327 in a solar star binary. "...a reasonable approximation for scalar fields" is falsified by 2.01 solar mass PSR J0348+0432 in a 0.172 solar mass Fermi-degenerate white dwarf binary: arxiv:1304.6875,

Science340(6131) 448 (2013),Physics Today66(7) 14 (2013).SR is tight. GR is superset ECKS (ECSK) gravitation. The rest are falsified by massed geometric tests of spacetime geometry. Problems cannot be solved with assumptions that created them.

I have to say that this whole discussion reminds me of that early Arnold Schwarzenegger movie where all the bodybuilders are preening and flexing for the cameras, trying for a little "umphf" on their bodybuilding competitors. Who says physicists and wannabes are only interested in the life of the mind?! BY GOD, we've got egos too!

I think the most important thing is to always try to stand back a little and not get emotionally involved in the semantic details of the conflict.

In this case that detail involves the origin of time flow and what causes it to change, as in the twin case. It is just a fact that the rate of time flow locally is controlled by the energy density of the vacuum. Just because we do not know all the permutations of and details of the spectrum of that energy density and how it relates to time flow does not mean that one EVER has an excuse to ignore it in these types of discussion. It is just a given.

Similarly, one simply has to accept as a given that the total vacuum energy is finite. One can deduce this just from the fact that high concentrations of energy near one particular point in space causes time to slow down. In other words, a high energy density in one place causes a low density, or low pressure vacuum energy density in proximity to it. This fact is only even possible if the vacuum energy is finite.

So it is just a matter of semantic details as to the origin of gravity being in SR or GR. GR explicitly accounts for that vacuum energy decreasing locally at an object at the center increases energy density. It does not matter whether that vacuum energy density decreases locally due to accretion of massive particles at the center of that low pressure system, or whether that low vacuum pressure occurs due to the high energy in a single accelerated object. It has the same effect, a low vacuum energy density surrounding it.

So Bee is wrong when she say an accelerated object has nothing to do with gravity. It does. The seeds of the that are in SR but they are only implicit, because two objects with varying velocities has the technical problem of looking at a system AFTER the accelerations have already occured.

Christine,

If you don’t mind me butting in your conversation, I think I can help: Einstein divided the twin paradox journey into 5 simple steps. The initial acceleration when the traveling twin leaves earth, followed by the inertial motion away from the Earth, followed by the turnaround/reacceleration, followed by the inertial motion back toward the Earth and finally the deceleration upon return to Earth. Einstein recognized that in order to preserve Galileo’s principle (which is the 1st part of SR) that neither twin’s INERTIAL PHASE motion would be considered absolute and therefore any time dilating clock effects would actually be seen by each twin when viewing the other’s clock. It sounds crazy that my clock would appear to run slower from your perspective, while at the same time, your clock would appear to also run slower from my perspective. But that’s what his theory indicates. He stated an additional time dilation would be experienced by the traveling twin during the turnaround. This is due to the acceleration itself and produces a separate dilation not experienced by the Earth twin which completely accounts for the traveler’s clock running behind his brother’s upon reunification. This is not a special relativistic effect. Personally – I have some big problems with his theory but if you’re looking for what Einstein’s own resolution is – there it is! Hope that helps.

CIP,

I'm just saying it's not a local effect. Best,

B.

Chris,

You're just making it worse by quoting 100 years old literature and taking it literally. You cannot create a gravitational field by 'turning around' in any sensible modern interpretation of these terms. As I told you previously, space-time is either flat or it isn't. There is either a gravitational field or there isn't. The sentence that you quote is an early attempt to capture what would later become the equivalence principle, but the math wasn't there at that point. As much as I think it is important to know the historical development, you'll understand the theory much better if you use a modern reference.

"I am new to your blog and therefore not sure what your area of expertise is..."Google will help. Or if that's too complicated, read the "about". Best,

B.

@Giotis -- ok.

@Uncle Al -- thanks, interesting as always.

@Chris Kennedy -- thanks, but my issue is quite ahead of that! It also seems you are missing modern day interpretations. BTW, I hope I do not sound that novice. I was already solving SR/GR problems some ~30 years ago...

Best.

@Sabine, oops, only now I see you already answered to Chris Kennedy... I agree with you.

Best.

It is clear that an asymmetry between the twins is mandatory to solve the paradox. The asymmetry arises from the need of accelerations in the traveler's fram (that it, treatment of non-inertial frames within flat spacetime!) to solve the twin paradox.

Now, in the limit, one non-inertial frame can be described by two inertial frames at opposite velocities, this just exacerbates the issue of non-simultaneity which necessarily will come up in the non-inertial frame.

My issue was with respect to Sabine's previous question, but that is all right, no need to make further issues about it... :D

Christine, IMHO it's best to think in terms of the wave nature of matter wrt the twins "paradox". Reduce each twin down to one electron, and remembering electron diffraction and atomic orbitals where "electrons exist as standing waves", imagine the electron is some kind of wave going round in a circle. Then turn it on its side so it looks like this |. Then apply that to the simple inference of time dilation due to relative velocity. See wiki:

http://en.wikipedia.org/wiki/Time_dilation#Simple_inference_of_time_dilation_due_to_relative_velocity

Run the twins scenario, and in both cases the light-path-lengths are the same, so the Lorentz interval is invariant. The time experienced is the number of reflections between the event1 departure and event2 meetup. This is a "fundamental" approach that hopefully gets you past any issues with frames. It's not as if a reference frame exists as something in its own right. You can't look up to the clear night sky and point one out. It's an abstract thing related to your "state of motion".

Sabine wrote:

"A particle that is stationary in a gravitational field has to accelerate to remain stationary. I don't know why you think an accelerated charge doesn't radiate."

If you have a charged ball sitting on your desk it doesn't radiate, even though it's "stationary in a gravitational field" and thus in some sense accelerating upward. People love to discuss this, and there are lots of papers on this, including plenty of bad ones.

Dear Sabine:

The problem with blogs is that misunderstandings are so easy to occur, and propagate like hell. Also, some people are putting words in my mouth. Words I've never written. Anyway, I'm leaving this discussion and all discussions here on your blog for now on... You know that I enjoy your blog, for years now, but I have to leave discussions. I'll keep on reading with interest. Thanks.

Best,

Christine

@John Baez. Well said.

Sabine,

In response to your comment to me:

“You're just making it worse by quoting 100 years old literature and taking it literally. You cannot create a gravitational field by 'turning around' in any sensible modern interpretation of these terms. As I told you previously, space-time is either flat or it isn't. There is either a gravitational field or there isn't.”

As I said twice before – I am just quoting Einstein (since, after all it is his theory). I’m not the only one to recognize this dusty old literature. There are plenty of legitimate physicists who understand the use of the equivalence principle in solving the twin paradox problem. For example: In addition to Styer’s Am J. Phys paper from 2007, It’s use is explained in detail by Cornell Professor N. David Mermin in 2005 and even more recently – Oyvind Gron in 2010: http://arxiv.org/ftp/arxiv/papers/1002/1002.4154.pdf (By the way, Gron provides an analysis in both flat-space and curved-space models). I hope this is modern enough for you!

You then said:

“The sentence that you quote is an early attempt to capture what would later become the equivalence principle, but the math wasn't there at that point.”

Actually, the math used in all of the very recent references I cited above, originated in Einstein’s 1911 equivalence principle paper – which was published 7 years previous to his 1918 paper on the twin paradox. So your comment makes no sense. The great thing about all of this is – thanks to particle acceleration and atomic clocks on GPS satellites, actual time dilation effects have been, and continue to be studied and compared to all of the various relativity theories new and old. This is moving relativity out of the abstract and into a more fact-based part of physics that will continue to be tested with experiment. Perhaps you prefer physics in the abstract? In any event – best of luck!

Ah, Bee, you were supposed to answer the question about radiation from an accelerated particle in terms of classical electromagnetism (which does not have a fully consistent theory of radiation, but who cares)? Otherwise, allegedly, it shows your lack of understanding of basic physics.

Arun: don't be too hard on Sabine. If everybody got everything right physics would have been done and dusted long ago.

Chris: note John Baez's comment. And note the distinction between curved space and curved spacetime on this page from his website.

Christine: don't let Motl put you off. He doesn't understand relativity at all, and conceals this with BS and arrogance. He also has a habit of deleting comments from people who explain why he's wrong. We all get things wrong, but hopefully by talking about them we get them less wrong, and in the end, we get them right.

John,

I might be misreading Arun, but I think he was being sarcastic. As I said above, it's not a local effect (wavelength too long) and thus the equivalence principle doesn't say anything about it, which was my reading of Phillip's question. Best,

B.

Chris,

"thanks to particle acceleration and atomic clocks on GPS satellites, actual time dilation effects have been, and continue to be studied and compared to all of the various relativity theories new and old. This is moving relativity out of the abstract and into a more fact-based part of physics..."No shit, really?! They can now actually *test* a century old theory, how amazing.

PS: I give up, I don't have the patience to repeat myself endlessly. I still recommend you buy a textbook and look up 'riemann tensor, vanishing of'. Sean Carroll's book for example is pretty good.

"If you have a charged ball sitting on your desk it doesn't radiate, even though it's "stationary in a gravitational field" and thus in some sense accelerating upward. People love to discuss this, and there are lots of papers on this, including plenty of bad ones."John, what is the

bestpaper on this topic?You might recall some extensive discussion on s.p.r with Parrott and Bunn back in the proto-blogger (not to say

homo erectusdays. :-)@Philip Helbig

Re the best paper: I found the last chapter in Rudolf Peierl's "Surprises in Theoretical Physics" to have a pretty good discussion

Bee read me right :).

John Duffield:

Thanks. My Gron reference was provided in response to Sabine's comment - "As I told you previously, space-time is either flat or it isn't."

The Gron reference actually does examine twin paradox resolutions in both flat and curved spacetime. I erroneously typed "space."

Fair enough Chris. Aw, I'm fussy about people saying "curved space" instead of "curved spacetime" because it usually isn't a typo. You know how Ricci curvature represents volume deviation? Here's a depiction of a gravitational field. Plot the volumes of one column of cells and you'll find yourself drawing a curve. Like John Baez's website said, space isn't curved in a gravitational field. Instead it's inhomogeneous. The motion of light through it over time is curved as a result.

John D:

Thanks for the reference. I quickly scanned Baez's site and found this on the twin paradox:

"Terence, on the other hand, does not stay motionless in Stella's frame. The field causes him to accelerate, but he feels nothing new since he's in free fall (or rather, Earth as a whole is). There's an enormous potential difference between him and Stella: remember, he's light years from Stella, in a pseudo gravitational field! Stella is far "down" in the potential well; Terence is higher up. It turns out that we can apply the idea of gravitational time dilation here, in which case we conclude that Terence ages years during Stella's turnaround. Short and sweet, once you have the background! But remember, this is not an explanation of the twin paradox. It's simply a description of it in terms of a pseudo gravitational field. The fact that we can do this results from an analysis of accelerated frames within the context of Special Relativity."

My first comment on that is that - as far as I can tell, it certainly was Einstein's explanation. Like I stated before. It was Einstein's explanation in 1918 and nowhere in the collected papers of AE or any of his later popular books (Relativity - the Special & General Theory, The Evolution of Physics, etc.) have I been able to find an alternate explanation on the twin paradox by him. My second comment is that there should be more discussion on the consequences of solving the paradox with SR alone.

Point taken re the Einstein explanation. I'm forever pointing out what Einstein said and how it's different to what some textbook says. But I have to say I wasn't fond of that particular article and preferred this one. Even then I still prefer the "fundamental" approach as per my response to Christine where you boil it down to one electron and use the wave nature of matter with the parallel-mirror light-clock. Part of the reason for that is that I've read A World without Time: the forgotten legacy of Gödel and Einstein. There's no time flowing in that parallel-mirror light clock, it's just light, moving.

Mostly good points, Bee, but you didn't clarify about the difference between SRT treatment of *accelerating objects* (which is fine) versus whether SRT can properly and clearly construct the "world" of the reference frame of an accelerated *observer* - they are not the same issue and there are problems getting the later to work. (More on that later if you are interesting in hearing what I've learned and my views.)

Just in case anybody had still doubts that non-inertial frames can be treated in Special Relativity, here's a recent paper on Non-Inertial Frames in Special and General Relativity.

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