Relativity: A steep ascent of physics

Journal name:
Nature
Volume:
549,
Pages:
331–332
Date published:
DOI:
doi:10.1038/549331a
Published online
Corrected online

Robert P. Crease applauds the third volume of a thrilling guide to a special pursuit.

Special Relativity and Classical Field Theory: The Theoretical Minimum

Leonard Susskind and Art Friedman Basic: 2017. ISBN: 978-0465093342

Buy this book: US UK Japan

Marchipatrick via Flickr/CC by 2.0

Negotiating the peaks and crevasses of the strange world of special relativity is akin to scaling the Matterhorn.

Since 2007, physicist Leonard Susskind has regularly delivered a lecture series called the Theoretical Minimum, on the foundations needed to study different areas of physics (http://theoreticalminimum.com/home). Companion volumes have emerged, the first on classical mechanics and the second on quantum mechanics. Special Relativity and Classical Field Theory is the third volume. Like the book on quantum mechanics, it is co-authored by Art Friedman and aimed, in Susskind's words, at “physics enthusiasts” or “people who know, or once knew, a bit of algebra and calculus, but are more or less beginners”.

The latest volume concerns the strange world that Albert Einstein discovered by combining James Clerk Maxwell's field theory with Isaac Newton's mechanics — a world in which moving fast makes time compress and lengths shorten. To understand it, challenging mathematical tools are required. In this volume, as in the others, you get the sense of being led up a legendary mountain by a trained guide. The guide knows you are an amateur, but wants you to get to the top on your own, without being airlifted over risky terrain. You do not hike through some of the hardest passes or peaks, nor past some of the most magnificent vistas. It's a peculiar route, and you encounter many sites in a different order from the one early explorers adopted, or in the way experts are used to teaching. But it's accessible. And you do get to the top. As an amateur myself, I found it thrilling.

The path starts with the first lecture, a discussion of reference frames. These are tools for labelling the positions of objects in your immediate space, and in spaces moving with respect to yours (such as on a train), that allow you to go back and forth between the spaces. Understanding them is an important skill for traversing rough spots ahead. Other essential tools include space-time, in which the reference frame includes time as well as space; proper time; and four-vectors, special kinds of paths and objects in space-time.

In a book on special relativity, you might expect to meet Einstein's mass–energy equivalence, E = mc2, close to the beginning. Yet you don't encounter it until Lecture 3, about 100 pages in, where it is refreshingly derived from first principles. You don't get the important Euler–Lagrange equation, which describes particle motion, until Lecture 4. Poisson's equation, for the electrostatic potential of a particle, and the Klein–Gordon equation, which describes a particle as a wave and relativistically, don't show up until Lecture 5. Gauge invariance, the basis of modern field theory, appears first in Lecture 7; Maxwell's equations, which provide the foundation of classical electromagnetism, materialize in Lecture 8; and the Poynting vector, which describes the flow of energy in electromagnetic waves, surfaces first in Lecture 11.

From a historian's point of view, therefore, the path is topsy-turvy. But Susskind's approach is to subject the novice to an ahistorical mathematical boot camp to make the path seem natural, and ultimately easier.

He appeals to the reader's evolving understanding to stay motivated, rather than airing his own expertise. Whenever you are puzzled by the famous conundrums of special relativity — the twin paradox, for instance, in which a sibling journeying on a light-speed rocket ages less than one who stays at home — he instructs you to “draw a spacetime diagram”. Such visual representations, he notes, make most of the weirdness in relativistic events go away.

Friedman pops up as the most vocal hiker on this at-times steep slope. He is not averse to making protests: “I don't recognize any of this. I thought you said we were going to get the Lorentz force law.” (“Lenny” replies: “Hang on, Art, we're getting there.”) Such jousts are infrequent, yet preserve the book's informal tone. In that vein, the narrative is rich in remarks at once witty and insightful. Modifying physicist John Wheeler's quote on relativity — “space-time tells matter how to move; matter tells space-time how to curve” — Susskind remarks, “Fields tell charges how to move; charges tell fields how to vary.”

Understanding the theoretical minimum in special relativity and classical field theory, however, itself demands a certain minimum of preparation and research. The book occasionally bumps up against this problem, referring the reader to earlier volumes; or Susskind might impatiently write, “If you don't know what a cross product is, please take the time to learn.”

The last few chapters are the steepest. You meet landmarks that would have been encountered much earlier in a historical approach, such as the laws of Maxwell, Charles de Coulomb, André-Marie Ampère and Michael Faraday — and even Maxwell's discovery that light is composed of electromagnetic waves, not mentioned until close to the end. But these conclusions fall right out of the tools you have been given in your intensive training — which Susskind calls the “cold shower” approach.

So why buy the book when the lectures are online? The online course consists of ten lectures, each anywhere up to two hours long, whereas the book is orderly and concise. You can go at your own pace, make notes and appreciate where Friedman — a former student of the course — becomes your stand-in and asks the questions that nag at you. You can refer back to something you read earlier and locate it quickly, rather than try to remember how far into the lecture it was and skip around until you find it. Finishing the book, you the physics enthusiast may not have a more profound view of any particular landmark in physics than before. But you will surely have a much more reliable map of the territory.

Change history

Corrected online 03 October 2017
An earlier version of this article incorrectly stated that Special Relativity and Classical Field Theory is the last book in the Theoretical Minimum series, and described it as “historical” rather than “ahistorical”. The text and title have been corrected.

Comments

  1. Report this comment #70657

    Pentcho Valev said:

    Leonard Susskind fraudulently teaches that the constancy of the speed of light is a consequence of the principle of relativity:

    Leonard Susskind 10:26 : "The principle of relativity is that the laws of physics are the same in every reference frame. That principle existed before Einstein. Einstein added one law of physics – the law of physics is that the speed of light is the speed of light, c. If you combine the two things together – that the laws of physics are the same in every reference frame, and that it's a law of physics that light moves with certain velocity, you come to the conclusion that light must move with the same velocity in every reference frame. Why? Because the principle of relativity says that the laws of physics are the same in every reference frame, and Einstein announced that it is a law of physics that light moves with a certain velocity."

    Also, Leonard Susskind fraudulently teaches that Maxwell's 19th century theory showed that the speed of light is the same for all observers, and that the Michelson-Morley experiment confirmed this:

    Leonard Susskind : "One of the predictions of Maxwell's equations is that the velocity of electromagnetic waves, or light, is always measured to have the same value, regardless of the frame in which it is measured. [...] So, in Galilean relativity, we have c'=c-v and the speed of light in the moving frame should be slower than in the stationary frame, directly contradicting Maxwell. Scientists before Einstein thought that Galilean relativity was correct and so supposed that there had to exist a special, universal frame (called the aether) in which Maxwell's equations would be correct. However, over time and many experiments (including Michelson-Morley) it was shown that the speed of light did not depend on the velocity of the observer measuring it, so that c'=c."

    Ninety-nine percent of the Einsteinians teach those lies, and yet the truth does show up sometimes, even though this remains unnoticed in the post-truth world:

    John Norton : "That [Maxwell's] theory allows light to slow and be frozen in the frame of reference of a sufficiently rapidly moving observer."

    John Norton : "The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

    Pentcho Valev

  2. Report this comment #70659

    Xinhang Shen said:

    Robert P. Crease, please let Leonard Susskind know that Einstein's relativity is wrong.

    It has been more than one year since Einstein's relativity theory got disproved both logically and experimentally (see "Challenge to the special theory of relativity", Volume 29: Pages 142-148, 2016, Physics Essays and a press release: "Special Theory of Relativity Has Been Disproved Theoretically" on Eurekalert: https://www.eurekalert.org/pub_releases/2016-03/ngpi-tst030116.php ), but many physicists in the world seem still not aware of that and continue teaching relativity to students and working on projects based on relativity. Therefore, I feel obliged to remind all those physicists. In case you don't have the access to the paper, please read the following simplified reasoning that can also let you know the problem of relativity.

    Einstein's relativity has redefined time and space through Lorentz Transformation. The newly defined time is no longer the physical time measured with physical clocks, which can be easily demonstrated by the following thought experiment of candle clocks:

    There are a series of vertically standing candles with the same burning rate and moving at different constant horizontal velocities in the inertial reference frame of (x, y, z, t). At any moment t, all candles have the same height H in the frame of (x, y, z, t) and the height has been calibrated to physical time. Therefore, we have the simultaneous events of the observation measured in both relativistic times t and physical time H in the frame of (x, y, z, t): (Candle1, x1, y1, H, t), (candle2, x2, y2, H, t), ?, (CandleN, xN, yN, H, t) in the frame of (x, y, z, t). When these events are observed on anther horizontally moving inertial reference frame (x?, y?, z?, t?), according to special relativity, these events can be transformed to the frame of (x?, y?, z?, t?) through Lorentz Transformation: (Candle1, x1?, y1?, H, t1?), (Candle2, x2?, y2?, H, t2?), ? , (CandleN, xN?, yN?, H, tN?) where t1?, t2?, ?, and tN? are relativistic times of the events in the frame of (x?, y?, z?, t?). It is seen that these events have different relativistic times after Lorentz Transformation in the frame of (x?, y?, z?, t?), i.e., they are no longer simultaneous measured with relativistic time in the frame of (x?, y?, z?, t?), but the heights of the candles remain the same because the vertical heights here do not experience any Lorentz contraction. Since the heights of the candles are the measures of the physical time, we can see these events still have the same physical time, i.e., they are still simultaneous measured with the physical time. Therefore, the physical time is invariant of inertial reference frames, which is different from relativistic time. As relativistic time is no longer the physical time we measure with physical devices, the des cription of special relativity is irrelevant to the physical world.

    Now let's have a look at the symmetric twin paradox. Two twins made separate space travels in the same velocity and acceleration relative to the earth all the time during their entire trips but in opposite directions. According to special relativity, each twin should find the other twin?s clock ticking more slowly than his own clock during the entire trip due to the relative velocity between them because acceleration did not have any effect on kinematic time dilation in special relativity. But when they came back to the earth, they found their clocks had exact the same time because of symmetry. Thus, there is a contradiction which disproves special relativity. This thought experiment demonstrates that relativistic time is not our physical time and can never be materialized on physical clocks.

    Now let's look at clocks on the GPS satellites which is thought as one of the strong evidences of Einstein's relativity as many physicists claim that clocks on the GPS satellites are corrected according to both special relativity and general relativity. This is not true because the corrections of the atomic clocks on the GPS satellites are absolute changes of the clocks, none of which is relative to a specific observer as claimed by special relativity. After all corrections, the clocks are synchronized not only relative to the ground clocks but also relative to each other, i.e., they become universally synchronized after correction. Thus, we can conclude that time is absolute and special relativity is wrong.

    This is a fact as shown on Wikipedia. But some physicists argue that the clocks on the GPS satellites are only synchronized in the earth centered inertial reference frame, and are not synchronized in the reference frames of the GPS satellites. If it were true, then time difference between a clock on a GPS satellite and a clock on the ground observed in the satellite reference frame would monotonically grow due to their relative velocity while the same clocks observed on the earth centered reference frame were still synchronized. If you corrected the clock on the satellite when the difference became significant, the correction would break the synchronization of the clocks observed in the earth centered frame. That is, there is no way to make a correction without breaking the synchronization of the clocks observed in the earth centered frame. Therefore, it is wrong to think that the clocks are not synchronized in the satellite frame.

    Hefele-Keating experiment is also considered as another evidence of relativistic effects. It is clear that all the differences of the clocks after flights in Hefele-Keating experiment were absolute (i.e., they were the same no matter whether you observe them: on the earth, on the moon or on the space station). But according to relativity, if the clocks were observed on the earth, the two clocks after flights had experienced the equivalent paths of same velocity and same distance in same elevation, and thus should generate the same kinematic time dilation and the same gravitational time dilation, which is directly contradicting the experimental result. Therefore, the differences of the clocks were nothing to do with the velocities relative to each other or relative to the earth as claimed by special relativity, but the result of the velocities relative to one medium which seems fully dragged by the earth on its surface and partially dragged on the altitude of the airplanes. It is wrong to interpret the differences of the displayed times of the clocks as the results of relativistic effects.

    The increase of the lives of muons in a circular accelerator or going through the atmosphere are also absolute changes which are the same observed in all reference frames.

    If you carefully examine all so-called evidences of relativistic effects, you will find that they are just misinterpretations of experiments and observations without exception, and thus, all what relativity describes is irrelevant to physical phenomena, including the speed of light which in special relativity is constant in all inertial reference frames, but which in real physical world still follows Newton's velocity addition formula (see the paper for detail).

    Therefore, we can safely conclude that time is absolute and space is 3D Euclidean and Einstein's relativity is wrong.

  3. Report this comment #70663

    Abed Peerally said:

    The whole of humanity benefits from Einstein's relativity from the GPS. Otherwise all critical motion- based systems in civil and military uses will fail. My relativity paper: 104;221 proves that in both SR and GR, time dilation is due to acceleration, not velocity. The connection of acceleration is critical and Einstein often wondered why we should have acceleration. Acceleration is the reason why we have relativity and gravitation and our universe. My TOE will explain a lot further on this issue. A TOE is a very complex concept, which will clear a lot of our mysteries of physics, and make science more logical and understandable. In fact all forms of knowledge follow universal rules, which basically are all linked to the reality of entropy.

  4. Report this comment #70669

    Ralph Knight said:
    • @Xinhang Shen, the thought experiment you cite is fundamentally flawed because it assumes the conclusion – namely that Einstein's relativity is wrong. From your post above:

    "At any moment t, all candles have the same height H in the frame of (x, y, z, t) and the height has been calibrated to physical time."

    Candles moving at different velocities will (eventually) have different heights in frame (x,y,z,t), unless relativity is wrong. This by itself doesn't prove relativity is right, but it does invalidate the experiment.

  5. Report this comment #70671

    Pentcho Valev said:

    @Ralph Knight, actually there is no need to devise new experiments – relativity is unequivocally refuted by the old ones – Michelson-Morley, Doppler, Pound-Rebka. See this:

    Wikipedia : "Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson?Morley experiment of 1887. [...] The name most often associated with emission theory is Isaac Newton. In his corpuscular theory Newton visualized light "corpuscles" being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v)."

    Since c' = c ± v (the speed of light varies with the speed of the emitter) was "explaining the results of the Michelson?Morley experiment of 1887", then the antithesis, c' = c (the speed of light is independent of the speed of the emitter), was contradicting those results. In 1905 c' = c became one of Einstein's postulates, so it is fair to say that Einstein's relativity was experimentally refuted before it was created.

    See also this:

    Albert Einstein Institute : "The frequency of a wave-like signal – such as sound or light – depends on the movement of the sender and of the receiver. This is known as the Doppler effect. [...] Here is an animation of the receiver moving towards the source:

    Stationary receiver

    Moving receiver

    By observing the two indicator lights, you can see for yourself that, once more, there is a blue-shift – the pulse frequency measured at the receiver is somewhat higher than the frequency with which the pulses are sent out. This time, the distances between subsequent pulses are not affected, but still there is a frequency shift: As the receiver moves towards each pulse, the time until pulse and receiver meet up is shortened. In this particular animation, which has the receiver moving towards the source at one third the speed of the pulses themselves, four pulses are received in the time it takes the source to emit three pulses." [END OF QUOTATION]

    "Four pulses are received in the time it takes the source to emit three pulses" means that the speed of the pulses relative to the moving receiver is greater than their speed relative to the source, in violation of Einstein's relativity.

    Pentcho Valev

  6. Report this comment #70677

    Xinhang Shen said:

    @Ralph Knight, "Candles moving at different velocities will (eventually) have different heights in frame (x,y,z,t), unless relativity is wrong. This by itself doesn't prove relativity is right, but it does invalidate the experiment."

    You just mixed up what we set and what we derived from. The candles here in the frame of (x, y, z, t) were set to be the same height and same burning rate. Then what we found is that such candles, through Lorentz Transformation, would have the same height in all other horizontally moving inertial reference frames too. Therefore, special relativity is disproved.

  7. Report this comment #70679

    Xinhang Shen said:

    Abed Peerally said:
    "The whole of humanity benefits from Einstein's relativity from the GPS. Otherwise all critical motion- based systems in civil and military uses will fail. My relativity paper: 104;221 proves that in both SR and GR, time dilation is due to acceleration, not velocity. "

    Then you yourself have denied special relativity which claims the relative velocity generates kinematic time dilation.

  8. Report this comment #70681

    Pentcho Valev said:

    If taught correctly, the Doppler effect directly refutes Einstein's 1905 constant-speed-of-light postulate:

    Albert Einstein Institute : "We will start with a very simple set-up, which you can see in the following animation. On the right-hand side, drawn in green, there is a sender that emits pulses in regular succession. On the left-hand side there is a receiver, drawn in blue. The pulses themselves are drawn in red, and they all travel at the same speed from right to left. Everytime the sender emits a new pulse, a yellow indicator light flashes once. Likewise, a flashing light indicates when a pulse has reached the receiver:

    stationary source

    Next, let us look at a slightly different situation, where the source is moving towards the detector. We assume that the motion of the sender does not influence the speed at which the pulses travel, and that the pulses are sent with the same frequency as before. Still, as we can see in the following animation, the motion influences the pulse pattern:

    moving source

    The distance between successive pulses is now smaller than when both sender and receiver were at rest. Consequently, the pulses arrive at the receiver in quicker succession. If we compare the rates at which the indicator lights at the receiver and at the sender are flashing, we find that the indicator light at the receiver is flashing faster. [END OF QUOTATION]

    Einsteinians make the following assumption above, which is essentially identical to Einstein's 1905 constant-speed-of-light postulate:

    Assumption 1: "The motion of the sender does not influence the speed at which the pulses travel."

    Assumption 1 goes hand in hand with another assumption:

    Assumption 2: "The distance between successive pulses is now smaller than when both sender and receiver were at rest."

    Assumption 2 is false – the pulses do not bunch up when the source (sender) is moving. If they did, by measuring the (variable) distance between the pulses, an observer associated with the source would know whether he is moving or at rest, which contradicts the principle of relativity.

    Since Assumption 2 is false, Assumption 1 is false as well. If the speed of the moving source is v, the speed of the light relative to the receiver is c'=c+v, in violation of Einstein's relativity.

    Pentcho Valev

  9. Report this comment #70683

    Abed Peerally said:

    Zinghang`s comment: "Then you yourself have denied special relativity which claims the relative velocity generates kinematic time dilation."

    Actually, we can say that velocity and acceleration have the same physical truth in relation to relative motion. Please read my SAJS paper carefully and compare special and general relativity, and you will see that behind every velocity there is a fundamental explanation due to acceleration. In several ways and in relation to a TOE and to the meaning of mass and gravity, I am afraid that acceleration has a critical role. In fact it is not velocity that generates time dilation, it is acceleration and gravitation. That is very clear.
  10. Report this comment #70687

    Xinhang Shen said:

    Abed Peerally said: In fact it is not velocity that generates time dilation, it is acceleration and gravitation. That is very clear.

    You are rewriting relativity!

    All special relativity tells us is that time dilation is dt' = dt/? where ? is the function of the relative velocity only. Period!

  11. Report this comment #70689

    Xinhang Shen said:

    Abed Peerally said: In fact it is not velocity that generates time dilation, it is acceleration and gravitation. That is very clear.

    You are rewriting relativity!

    All special relativity tells us is that time dilation is dt' = dt/? where ? is the function of the relative velocity only. Period!

  12. Report this comment #70721

    Eric Katz said:

    Despite the ire that Dr. Susskind has drawn for daring to promote a theory that works better than nearly any other in physics, I want to discuss something far more egregious: bad formatting.

    If you are interested in reading this series (which is enjoyably written), I warn you not to purchase the Kindle version of the first volume. The formatting is terrible, and (most importantly) the equations are reduced to a little images so tiny that I got a headache when I tried to make them out. I could enlarge them, but I would have to do so separately for every single one in the book, which sort of breaks the flow of the reading experience. I even sent the publisher (Basic Books ) a snippy little note about it and told them to be ashamed. I believe I even used the word "monkey".

    Fortunately, it looks like the second and third in the series were formatted by somebody more (ahem) experienced.

    My recommendation: borrow the first volume from the library, in paper format. Then, buy the second and third in Kindle format if you wish.

    Cheers!

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