Boy of Age 16 Asks Me about Relativity, etc. 21. Does Time Really Exist? What Is Time?

Relativity of simultaneity: Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and occurs later in the red frame (Ref. 1). The original PNG file of the figure was created by Army1987; Acdx converted it to SVG. (GFDL or CC-BY-SA-3.0), via Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: Do we control in time? Or does it control in us?

Ted: I do not understand what you exactly mean by the words "control in" in your question. The question sounds like a philosophical one rather than that of physics. But I can say this: Time is one of physical dimensions connected to the Universe or Nature. Therefore, human being can do nothing to affect it. However, "psychological time" (duration of time one feels about a definite length of physical time under different situations) can be controlled by the adjustment of one's mind. Am I talking in the wrong direction than you expected?

Aaron: Sorry, I want to know if time really exists. In relativity, time also seems to be relative, right? A body that travels at a speed close to that of light can slow time, right? So, what is time?

Ted: I see, Aaron. Time is one of dimensions of the physical framework of the Universe, "spacetime," and is the measure of durations of events and the intervals between them. It has a definite meaning when we consider the movement of something. If there were nothing moving around in the Universe, time would be meaningless and could be said that it does not exist. However, the real Universe includes a lot of moving things. So, time is a meaningful and useful concept. Duration of events and simultaneity depend on the coordinate system (reference frame) on which it is measured (see the figure above), but this does not deny the reality of time.

By the way, the slowing-down of the passage of time (time dilation) occurs for the fast-moving body, as you mentioned, but this occurs for the moving system as a whole, i.e., your biological activity and ability also slow down. So, you cannot do much more thing during the high-speed flight in a rocket compared with what you can do on the earth in the same duration of time. You cannot be the master of time but remain to be its slave.

It would be another problem to ask if time is a fundamental concept. There is a growing movement to create a theory that shows spacetime is emergent, i.e., not fundamental (see for example Ref. 1). In this respect, time is one of things still mysterious.

References

1. "Time," Wikipedia: The Free Encyclopedia (February 19, 2013, at 06:41).
2. Graeme Stemp-Morlock, Melting Spacetime, Web site FQXi Community (April 30, 2012).

(Originally written on October 14, 2011)

Boy of Age 16 Asks Me about Relativity, etc. 20. Have You Heard about Naruto?

Cover of the first Japanese Naruto manga volume.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: I just wanted to ask you if you have heard about Naruto.

Ted: What I think of from the word "Naruto" is tidal whirlpools in the Naruto Strait, Japan. However, this is probably not what you mean. Perhaps, you mean this (though it is not related to the physics of relativity): Naruto (ナルト), an ongoing Japanese manga series written and illustrated by Masashi Kishimoto. I don't know about it. So, I quote a passage from a Wikipedia page (Ref.1): "The plot tells the story of Naruto Uzumaki (note by Ted: Uzumaki means tidal whirlpools), an adolescent ninja who constantly searches for recognition and dreams to become the Hokage, the ninja in his village who is acknowledged as the leader and the strongest of all. The series is based on a one-shot comic by Kishimoto that was published in the August 1997 issue of Akamaru Jump."

Aaron: Yes, it's one of the best Japanese anime series. Ninjas can travel near the speed of light.

Ted: Oh, Naruto has then a relationship to relativity. Ha-ha!

Reference

1. Naruto, Wikipedia: The Free Encyclopedia (January 24, 2013 at 19:01).

(Originally written on October 7, 2011)

Boy of Age 16 Asks Me about Relativity, etc. 19. Do All the Forces in Nature Travel at the Same Speed as That of Light?

The Feynman diagram for the beta-minus decay of a neutron (n) into a proton (p) , due to the weak force, i.e., via an intermediate heavy W⁻ boson. One of down quarks (d) in the neutron decays into an up quark (u) to make a proton, emitting an electron and an electron anti-neutrino. By Joel Holdsworth (Joelholdsworth) [Public domain], via Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: Do all the forces in nature travel at the same speed as that of light?

Ted: There are four known fundamental interactions in nature to cause fundamental forces in the universe: gravitational, electromagnetic, strong nuclear, and weak nuclear interactions. Among these interactions, the mediators of three interactions, i.e., the gluon for the strong interaction, the photon for electromagnetic interaction and the graviton for the gravitational interaction, have (or assumed to have) zero mass. Therefore, the forces based on these interactions are transmitted by the speed of light. The remaining one interaction, weak interaction, is mediated by the heavy W and Z bosons and cannot be transmitted by the speed of light. However, the effective range of the weak force is quite short (around 10⁻¹⁷–10⁻¹⁶; Ref. 1), so that we can regard that the weak force is transmitted almost instantaneously for it actually to work.

Reference

1. J. Christman. The Weak Interaction, Physnet (Michigan State University, 2001) p. 2.

(Originally written on October 1, 2011)

Boy of Age 16 Asks Me about Relativity, etc.18. Why Is the Speed of Light Constant?

Albert Einstein in 1931 by Doris Ulmann [Public domain], via Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: Why doesn't the speed of light change?

Ted: It is gratifying that you think so deeply as to want to know the reason for the constancy of the speed of light in vacuum. However, no one knows the reason. It was initially Albert Einstein's assumption in developing the special theory of relativity. Then, many experiments have confirmed the correctness of the theory, and the assumption has been accepted as one of true facts. So, presently there is no reason or cause to which physicists attribute the constancy of the speed of light.

By the way, I have learned, on Twitter this morning, the Reuters news that neutrinos were found to break the speed of light by a group of physicists working on an experiment dubbed OPERA, which was run jointly by the CERN particle research center and the Gran Sasso Laboratory in Italy. If this experiment be confirmed to be correct, it will make an immense challenge to theoretical physicists.

Aaron: The news is extremely serious. The title of the report says, "Finding could overturn laws of physics." But it would not invalidate the theory of relativity, right?

Ted: Yes, it would do so, to some extent. Namely, if the neutrino experiment were correct, it would require a correction of the theory of relativity. However, many experiments and observations have been consistent with that theory. Further, neutrinos produced by the explosion of the 1987 supernova arrived at the earth not earlier than light from the same source. So, I highly doubt the correctness of the experiment just reported.

(Originally written on September 23 and 24, 2011, except for "Note" below)

Note about "faster-than-light neutrino" measurements:

In March 2012, the OPERA team confirmed that the measurements first announced in September 2011 were skewed by a combination of a faulty cable and flawed timing in the experiment’s master clock (Ref. 1). The group repeated its measurement and have reported the final results that are consistent with the special theory of relativity (Ref. 2; see also Ref. 3 for the whole story about the measurement of the neutrino speed).

I was not surprised at reading the news of possibly wrong measurements because I had once encountered a paper that reported the results of erroneous measurements in the prestigious journal Physical Review (the author's name was Dressel). The results were inconsistent not only with many previous authors' but also with my own that had just been obtained. Thus, I was able timely to publish my results in the same journal, pointing out possible causes of errors in Dressel's measurements. (You can see the abstract of my paper here.) Later, Dressel found the real cause of errors by himself. Some or many scientists believe "it is right to release an 'uncomfortable' result for scrutiny and then seek an instrumental or methodological effect that might explain it," as the OPERA spokesman Antonio Ereditato is reported to have said (Ref. 1).

References

1. E. S. Reich, "Embattled neutrino project leaders step down," Nature (April 2012).
2. The OPERA Collaboration, "Measurement of the neutrino velocity with the OPERA detector in the CNGS beam using the 2012 dedicated data," arXiv:1212.1276 [hep-ex] (December 2012).
3. "Faster-than-light neutrino anomaly," Wikipedia, The Free Encyclopedia (15 December 2012 at 14:07).

(Originally written on September 23 and 24, 2011)

Boy of Age 16 Asks Me about Relativity, etc.17. What Is Golden Physics?

Carl Sagan's The Demon-Haunted World explains methods to help distinguish between ideas that are considered valid science, and ideas that can be considered pseudoscience. — "The Demon-Haunted World," Wikipedia: The Free Encyclopedia (November 12, 2012 at 02:36).

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: I just wanted to ask you about golden physics. What is it?

Ted: I have never heard of the phrase "golden physics" and would like to confirm if you mean "golden age of physics." If you mean any other thing, please let me know where, or in relation to what, you got the phrase.

Aaron: Have you heard about the physicist Mohamed El Naschie? It is his theory.

Ted: I have heard the name Mohamed El Naschie for the first time and made a search on the Internet. The "Mohamed El Naschie" page (Ref. 1) of RationalWiki gives useful information. The essence is given below:

—Mohamed El Naschie is an Egyptian mathematician, physicist and engineer. He served as editor-in-chief of the journal Chaos, Solitons & Fractals. His research centers on a theory of everything called "E-infinity theory", a "fractal cosmology model" which he developed in 1994. El Naschie characterizes his theory as follows: "This models a harmonic production of quarks and elementary particles through a golden section [Note by Ted: Here "golden" appears] centered Cantorian fractal spacetime." El Naschie's theories are regarded as not even wrong by almost all physicists and mathematicians.—

The page mentioned has the link to the El Naschie Watch Web site (Ref. 2). This is the blog site that describes critically about this man in detail and includes the words, 'Dr. Mohamed El Naschie is pseudoscientist crackpot who makes grandiose claims about being a "paradigm-shifting" high-energy physicist' (Ref. 3). From the descriptions of his work on Ref. 1, I believe that the words "pseudoscientist crackpot" is quite true and do not recommend you to learn about his physics.

(See also Ref. 4, which probably appeared after my original reply had been written.)

References

1. "Mohamed El Naschie," RationalWiki (August 21, 2012, at 16:56).
2. El Naschie Watch, Blog site.
3. "Introduction to Mohamed El Naschie," El Naschie Watch (May 6, 2010).
4. "Mohamed El Naschie," Wikipedia: The Free Encyclopedia (December 13, 2012 at 12:58).

(Originally written on September 16 and 17, 2011)

Boy of Age 16 Asks Me about Relativity, etc.16. What Is the Paradox about Time Travel?

Hand colored etching Mr. Fezziwig’s Ball by John Leech from A Christmas Carol by Charles Dickens. [Public domain], via Wikimedia Commons.
A Christmas Carol is considered to be one of the first depictions of time travel in both directions, as the main character, Ebenezer Scrooge, is transported to Christmases past, present and yet to come.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: I think they say that there is a paradox about time travel. What is it?

Ted: Any theory that would allow time travel would require that problems of causality (the relationship between the cause and effect that the former should come before the latter) be resolved. From this viewpoint, the concept of time travel seems to give contradictions, examples of which are stated as paradoxes. One of the best examples is the grandfather paradox.

The grandfather paradox is a hypothetical situation in which a time traveler goes back in time and attempts to kill his grandfather at a time before his grandfather met his grandmother. If he did so, then his mother or father never would have been born, and neither would the time traveler himself. In that case, the time traveler never would have gone back in time to kill his grandfather. This is in contradiction to the assumption at the start.

This paradox has been used to argue that backwards time travel must be impossible. A number of hypotheses have been postulated to avoid the paradox, such as the idea that the past is unchangeable. However, any of those hypotheses has not become an accepted theory because the theoretical possibility of time travel itself is unknown.

To write the above explanations, I referenced the Wikipedia pages of "Time travel" (Ref. 1) and "Grandfather paradox" (Ref. 2). So, if you want to learn in more details, you can consult those pages.

Aaron: It's amazing. Now, I have an idea about how to go backwards in time. Time is like a line and flows in one direction, like a river, and we can go in both directions, in a river. This means that we can also control ourselves in time. If we can go back in time, we can kill Hitler and make the future without stupid World War II. But, I have to find how this is possible in a theoretical way. What do you think? Is it funny?

Ted: Your idea is appealing. However, it does not seem to be a physical idea about how to go backwards in time, but I'm afraid that it is an idea about what you would like to do if you could go backwards in time. Further, only killing Adolf Hitler would not prevent the World War II totally. You may need to kill also Benito Mussolini in Italy and Hirohito in Japan and to change all the factors related to nationalism or imperialism and international tensions of those days.

[Next day, Ted again wrote to Aaron, writing as follows:]

However, your idea also included a good point. If you go backwards in time not to kill your grandfather but to kill Hitler, you can escape the paradox of your not being born. Thus, your idea is a good step toward the solution of the paradox.

I compared your idea with Novikov self-consistency principle. This principle was proposed by a Russian (and former Soviet) theoretical astrophysicist and cosmologist, Igor Dmitriyevich Novikov, in the mid-1980s and have been regarded as an important contribution to the theory of time travel (Ref. 3). I have just learned it from Wikipedia.

According to this hypothetical principle, the only possible time lines are those entirely self-consistent. So, anything a time traveler does in the past must have been "part of history all along." Your idea is partly similar to this principle, in the successful removal of the inconsistency about the time traveler's birth, though killing Hitler is inconsistent with the real history. You can have confidence in your ability of thinking about physics.

References

1. Time travel, Wikipedia, The Free Encyclopedia (December14, 2012 at 23:29).
2. Grandfather paradox, Wikipedia, The Free Encyclopedia (December17, 2012 at 08:09).
3. Novikov self-consistency principle, Wikipedia, The Free Encyclopedia (November 26, 2012 at 03:04).

(Originally written from July 29 to 31, 2011)

Boy of Age 16 Asks Me about Relativity, etc.15. What is String Theory?

Different levels of magnification of matter, ending with the string level: 1. Macroscopic level – Matter. 2. Molecular level. 3. Atomic level – Protons, neutrons, and electrons. 4. Subatomic level – Electron. 5. Subatomic level – Quarks. 6. String level. [By MissMJ (CC-BY-3.0), via Wikimedia Commons.]

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: What is string theory? I have read a little about it. It seems to be the theory of everything that Einstein was working on. Dr. Michio Kaku is probably working on how to find it. However, there are many equations in this theory. How can I understand it?

Ted: "What is string theory?" is a difficult question for me. In my student days, this theory was not yet born. So, some years ago I wanted to learn a little bit of it and bought a graduate level text book on this theory written by the physicist you just mentioned, i.e., Michio Kaku. However, it was pretty difficult for me to learn it by myself, and I have not read the book yet.

The essential idea of string theory is that all of the different "fundamental" particles are different manifestations of one basic object, a string (see the figure above). I hear that the equations of this theory gives a lot of solutions, and presently it is difficult to determine which of those solutions reflect the laws of physics in the real world. In this situation, there is the supposition that there may be many worlds, in each of which one of many solutions is applicable. (However, it is a vexing problem how we can verify the applicability of solutions in other worlds). A number of gifted physicists are studying this theory, but some famous physicists do not think that this is the right direction to advance the study of theoretical physics. Further, it is said that we humans don't yet have enough mathematical methods fully to explore this theory.

String theory is such a complex and difficult thing. You had better learn it after enough mastering of quantum mechanics and relativity. Taking such a step is indispensable also considering the fact that string theory aims at the unification of quantum mechanics and general relativity. However, there are a number of Web pages explaining string theory for non-scientists. See, for example, Ref. 1 and links given in it.

Reference

1. Alberto Güijosa, What is String Theory?

(Originally written on July 18, 2011)

Boy of Age 16 Asks Me about Relativity, etc.14. Relations among the Expansion of the Universe, Gravity, Relativity Theory and Dark Energy

George Gamow's book My World Line, in which Einstein's words "the biggest blunder
I had ever made in my life" were first written.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: Why is the universe expanding? Where is gravity? What about Einstein's relativity? Some scientists say that the universe is expanding because of dark energy, don't they?

Ted: The expansion of the universe is considered possibly due to the initial condition of the Big Bang, with which our universe started. In 1998, two teams of astronomers suggested on the basis of their observations of Type Ia supernovae that the expansion of the universe had been accelerating. (Saul Perlmutter and Adam Riess of the U.S. and Brian Schmidt of Australia contributed to this finding and won Nobel Prize in Physics in 2011.) Until this discovery, physicists were convinced that gravity should be causing the expansion rate of the universe to slow. To explain the accelerated expansion, dark energy, which produces the mysterious force to repel gravity, was proposed and has been constituting the most accepted theory. Scientists are still trying to find what dark energy exactly is (Ref. 1).

As explained above, dark energy is the notion that appeared after the discovery of the accelerated expansion. With regard to the relation between the expansion of the universe found earlier and the relativity theory, there is a fascinating history. After formulating the equation of general relativity, Einstein tried to find the distribution of masses that would lead to a stable universe unchangeable with time (a static universe was the prevailing hypothesis those days). He found that the equation was incorrect to produce such a universe. Therefore, he added a term to the equation, which became known as the "cosmological term" or the "cosmological constant."

The Russian mathematician Alexander Friedmann found that Einstein's treatment had been wrong and that the original equation of general relativity was correct to predict time-dependent universes as well including an expanding one, which became the observational fact by Edwin Hubble's work, in the late 1920s, of measuring the redshifts of light from galaxies. Thus, changing the original equation was a mistake, and Einstein once told Gamow that the introduction of the cosmological term was the biggest blunder he had ever made in his life (Ref. 2).

One possible source of dark energy, supposed to explain the accelerated expansion, is the "cosmological constant," a constant energy density filling space homogeneously, and the other is scalar fields (Ref. 3). Therefore, Einstein's biggest blunder has become a central concept of the present cosmology.

Note: Earlier, Aaron asked what would happen to the relativity theory if dark energy were true (see here). I took this as the question about a possible failure of general relativity under the presence of the accelerated expansion. So, I quoted from Ref. 4 the description of some theorists' thought that a failure might happen on scales larger than superclusters. However, the equation of the general relativity with the cosmological constant might prove to be an excellent theory except for such an extreme case.

References

1. Physics Nobel Explainer: Why Is Expanding Universe Accelerating? National Geographic, Daily News (October 2011).
2. George Gamow, My World Line: An Informal Autobiography (Viking, New York, 1970) p. 44.
3. Dark energy, Wikipedia, the free encyclopedia (November7, 2012 at 00:22).
4. 3 Alternative Ideas, ibid.

(Originally written on June 27 and July 5; modified to a large extent.)

Boy of Age 16 Asks Me about Relativity, etc. 13. Mass and Weight

Illustration of the first experiment performed by Eötvös to determine whether the inertial mass equals the gravitational mass. If the ratio F1 to F2 of centrifugal forces depending on inertial masses would differ
from the ratio G1 to G2 of gravitational forces depending on graviattional masses, the rod
would rotate. The mirror is used to monitor the rotation. Subsequent experiments used
a different setup for improved accuracy. For details, see the "Eötvös experiment"
page of Wikipedia. Image by Petteri Aimonen (Own work)
[Public domain], via Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: When a body travels at the speed of light, it's mass will be much bigger than at rest. But what about its gravity or weight? It will also be much bigger than at rest. Is this correct?

Ted: It is an excellent question, but I have to correct the expression of your question a little bit before answering it. The body of non-zero mass cannot travel with just the speed of light but can only approach that speed. So, you should say, "When a body travels near the speed of light, …" You're right to expect that when a body's mass becomes larger with increasing speed, the body's weight or the gravitational force acting on the body also becomes larger compared with its weight when it was at rest in the same gravitational field. This is the result of "the equivalence principle" of general relativity, i.e., the law of the equality of the inertial and gravitational mass. Since the 17th century, repeated experiments demonstrated that inertial and gravitational mass are equivalent. One of the methods of such experiments is shown above. In 1915, Einstein included this observation a priori in the equivalence principle of general relativity.

Aaron: Thank you so much for your answer. By the way, Have you heard about Dr. Who?

Ted: No, I have not. I am not so much interested in science fiction stories except for old ones. However, I have learned from Wikipedia the followings about it: Doctor Who is a science fiction television program produced by the BBC and originally broadcast from 1963 to 1989. The program depicts the adventures of a mysterious, time-traveling humanoid alien who is known only as the Doctor and explores time and space in the "TARDIS," a sentient machine for four-dimensional traveling. (There is further information about its history, episodes, characters, etc. in the Wikipedia page) Thanks for your mentioning of Dr. Who.

Further reading

1. "Mass versus weight," in Wikipedia, the free encyclopedia.
2. "Mass," ibid.
3. "Gravitation," ibid.
4. "Equivalence principle," ibid.

(Originally written on June 9 and 20, 2011.)

Boy of Age 16 Asks Me about Relativity, etc. 12. If Dark Energy Is Real, What Will Happen to the Relativity Theory?

Estimated distribution of dark matter making up 22% of the mass of the universe and dark energy making up 74%, with 'normal' matter making up only 0.4% of the mass of the universe. By PeteSF at en.wikipedia [Public domain], via Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: If dark energy* is true, what will happen to the relativity theory?

* In 1998, observations of Type Ia supernovae by the High-z Supernova Search Team followed in 1999 by the Supernova Cosmology Project suggested that the expansion of the universe is accelerating. (This work was awarded by the Nobel Prize in Physics in 2011.) Dark energy is a hypothetical form of energy that permeates all of space and causes this accelerating expansion of the universe. The exact physics behind dark energy is yet unknown. (Adapted from Ref. 1.)

Ted: It is a difficult question for me, so that I have consulted Ref. 1. We see the following explanation there:

"Some theorists think that dark energy and cosmic acceleration are a failure of general relativity on very large scales, larger than superclusters. However, most attempts at modifying general relativity have turned out to be either equivalent to theories of quintessence, or inconsistent with observations."

Thus, we can assume that, at the worst, general relativity might be necessary to be supplemented by a new theory for extremely large distances beyond the size of superclusters. Even in that case, however, it would not mean that general relativity was wrong but that it was a highly accurate approximation to the true theory of gravitational phenomena.

References

1. "Dark energy," Wikipedia: The Free Encyclopedia (11 February 2012 at 02:02).

(Originally written on June 9, 2011)

Boy of Age 16 Asks Me about Relativity, etc. 11. How Do We Prove a=F/m?

Newton's first and second laws, in Latin, from the original 1687 Principia Mathematica. Source: http://www.loc.gov/exhibits/world/images/s123.jpg
[Public domain], via Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: How do we prove a=F/m?

Ted: Your question is considered to be equivalent to this: Can we derive Newton's second law of motion F=ma from a more fundamental principle? (Here, F is the net external force acting on a body, m is the mass of the body and a is the acceleration the body obtains.) We cannot derive this equation from any other principle. Newton assumed it and presented it as a law. The validity of the equation can experimentally be confirmed. For example, we measure accelerations of the bodies of different masses by applying the same force to find that the result is inversely proportional to the known masses. Another confirmation comes from the application of the law to planetary motion. The law combined with Newton's law of universal gravitation neatly explains Kepler's laws of planetary motion empirically found. Thus, the equation is certainly a law. This law can be considered equivalently as a fundamental postulate in the (classical) mechanics of a particle* or as a definition of force and mass [1].

* The mechanics of a particle treats the motion of bodies (objects) which are considered or idealized as a particle, in the sense that the extent of the body is neglected in the evaluation of its motion, i.e., the object is small compared to the distances involved in the analysis, or the deformation and rotation of the body is of no importance in the analysis [2].

By the way, April 18 was the anniversary of Albert Einstein's death, so that I made a short blog post about it. Please enjoy the article here.

References

1. H. Goldstein, Classical Mechanics (Addison-Wesley,1950) p. 1.
2. "Newton's laws of motion," Wikipedia: The Free Encyclopedia (19 February 2012 at 09:36).

(Originally written on April 20 and 22, 2011)

Boy of Age 16 Asks Me about Relativity, etc.10. Body's Mass Increases with Increasing Speed. Then, Why Is Light Mass Zero?

The diagram of Ole Roemer's method, used in 1676, to determine the speed of light by observing the eclipse (D) and reappearance (C) of (B) Jupiter's moon Io from different locations (E, F, G, H, L, K) in Earth orbit around the Sun (A). By Roemer.jpg: Ole Roemer derivative work: Gregors (Roemer.jpg) [Public domain], via Wikimedia Commons. (This diagram is not directly related to the present question, but is put here by the reminiscence from the speed of light.")

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron's question of this time is closely related to the question made in the fifth story of this series, "The object's mass is zero when it is traveling at the speed of light, right? Where does its mass go?" Ted's answer to that question seems to have been insufficient for his understanding.

Aaron: According to Einstein's relativity, the mass of a body will increase when its speed approaches the speed of light, right? Then, how does it come that light has zero mass?

Ted: The relativistic increase of mass is caused, so to speak, as a result of "prohibiting" the acceleration of a body with a finite rest mass to a speed equal to or larger than the speed of light in vacuum. The light quantum, or the photon, has zero mass and always has the maximum constant speed without getting acceleration, so that no "prohibition" works on light. Light is a distinct entity in the Universe.

The above explanation is quite metaphorical. Physicists' understanding is just that the photon always has zero mass and light speed without suffering any change, even independently of relative velocity of the observer to the photon, because this hypothesis proposed by Einstein is consistent with every observation.

(Originally written on April 8 and 9, 2011)

Boy of Age 16 Asks Me about Relativity, etc.9. Recommended Books on and by Einstein for Young People

Books recommended.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

This time, Aaron does not pose a question, but write about Einstein as follows by appending many photos of Einstein to his email message:

Aaron: Oh my God! That smile of Einstein! I'm gonna die. I want a hug from him! He's cute, isn't he?

Ted: You have a sizeable collection of photos of Einstein and talk about him like a lover. Now there are a lot of biographies of him for people from young to adult ages (a search of paperbound books by the key words "biography Einstein" at Amazon.com gives a list of about 500 titles). Have you read any of those for adults?

I liked a book written in a relatively early year (first published in 1972). It is entitled "Albert Einstein, Creator and Rebel." The author is Einstein's close collaborator Banesh Hoffmann. Another book about Einstein I recommend to young people is "Einstein: A Centenary Volume" edited by A. P. French (published by Heinemann for the International Commission on Physics Education, 1979). You may find copies of these books at a library or an old-book shop.

As for books by Einstein, "The Evolution of Physics" written together with one of his co-workers Leopold Infeld (Touchstone, 1967, still available; first edition 1938; my copy, Cambridge University Press, 1978) is one of the most excellent books for young people to learn about the development of ideas in physics from early concepts to relativity and quanta.

By the way, it is Einstein's birthday and is also π day, today. The reason for the latter is that it is March (the 3rd month) 14th. So, his birthday is especially convenient to remember. Do you have any party for this day at your home?

(Originally written on March 11 and 14, 2011)

Boy of Age 16 Asks Me about Relativity, etc.8. "I Can't Get Gauss's Flux Theorem"

Gauss's portrait published in Astronomische Nachrichten 1828.
By Siegfried Detlev Bendixen [Public domain],
from Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: I have a problem with Maxwell's equations. We don't learn them at school, and there're a lot of math. I'm not ready for that level of math. So, I can't get Gauss's flux theorem. But I want to understand it.

Ted: You are quite ahead of school lessons. Gauss's flux theorem was formulated by Carl Friedrich Gauss in 1835 and is also known as Gauss's law. I learned it only at university.

Concepts of physics can be learned to some extent without the use of math. For example, Gauss's law is stated by words as follows: The electric flux through any closed surface is proportional to the enclosed electric charge (quoted in Ref. 1 from Ref. 2).

However, true understanding of working and beauty of physics and practical application of physical laws require mathematics. Especially, if you want to become a physicist, early study of essential mathematics together with physics would be useful. Gauss's law can be expressed either by the equation of the integral form or by the equation of the differential form. The equivalence of the two equations can be shown by the use of the divergence theorem in vector calculus. Doesn't this sound interesting? (See, for example, Ref. 1.)

In The Feynman Lectures on Physics (Ref. 3), Gauss's law appears in Chapter 4 of Volume II after necessary mathematical preparation of "Vector Integral Calculus" in Chapter 3. Why don't you learn by the use of that fine textbook of Feynman? If you want to understand Maxwell's equations before studying Feynman's hefty books, however, Daniel Fleisch's A Student's Guide to Maxwell's Equations (Ref. 4) might be useful. Fleisch also explains the equations after giving the preparation of necessary mathematics.

References

1. "Gauss's law," Wikipedia: The Free Encyclopedia (5 January 2012 at 13:53).
2. Raymond A. Serway, Physics for Scientists and Engineers with Modern Physics, 4th edition (1996).
3. Richard P. Feynman, edited by Robert B. Leighton and Matthew Sands, The Feynman Lectures on Physics, Boxed set: The New Millennium Edition (Basic Books, 2011).
4. Daniel A. Fleisch, A Student's Guide to Maxwell's Equations (Cambridge University Press, 2008).

(Originally written on March 5–12, 2011)

Boy of Age 16 Asks Me about Relativity, etc.7. Would Einstein Have Liked Harry Potter or High School Musical?

Albert Einstein in 1893 (age 14).
By Kenosis at en.wikipedia [Public domain],
from Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: Would Einstein have liked Harry Potter or High School Musical, if he were alive now? What do you think about these fiction stories?

Ted: Oh, these are not questions about physics but fascinating ones. I have never been well acquainted with those. However, I believe that I would have liked to read the book of Harry Potter and to watch High School Musical on TV, if I were now at your age. This is because I hear that these stories contain some flavor of science fiction and because, at the age of fifteen, I enjoyed reading Mark Twain's The Adventures of Tom Sawyer (in Japanese translation) and a science fiction series about space travel in a magazine for children.

As for Einstein, it is extremely difficult to assess whether he would have liked Harry Potter or High School Musical. In his childhood, Einstein is said to have read and discussed many books with Max Talmey, a medical student from Poland. Those books are reported to have included a series of popular science books (Ref. 1). Einstein's mother was a talented pianist and ensured the children's musical education (Ref. 2). From these facts, it would not be totally wrong to think Einstein would have liked Harry Potter and High School Musical, if he were now at your age.

Additional message written by Ted: Last evening, I was reading the book on the theory of time written, without using equations, by Sean Carroll (Ref. 3) and found that he, a theoretical cosmologist at the California Institute of Technology, mentions Voldemort and Professor Trelawney from the Harry Potter books. So, this famous scientist seems to have liked Harry Potter as you do. Isn't this a happy report to you?

References

1. Banesh Hoffmann, Albert Einstein (New american Library, New York, 1972). p. 24.
2. "Albert Einstein," in Wikipedia, The Free Encyclopedia (2 January 2012 at 19:05) footnote 1.
3. S. Carroll, From Eternity to Here: The Quest for the Ultimate Theory of Time (Plume, London, 2010) p. 184.

(Originally written on March 2 and 9, 2011)

Boy of Age 16 Asks Me about Relativity, etc.6. What Is Dark Matter?

Strong gravitational lensing as observed by the Hubble Space Telescope in Abell 1689 indicates the presence of dark matter (Ref. 1). Image by NASA, N. Benitez (JHU), T. Broadhurst (Racah Institute of Physics/The Hebrew University), H. Ford (JHU), M. Clampin (STScI), G. Hartig (STScI), G. Illingworth (UCO/Lick Observatory), the ACS Science Team and ESA [Public domain], via Wikimedia Commons

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: What is dark matter? How did they know about it?

Ted: It is difficult for me to give my own, accurate description of dark matter. So, here I write a summary of the excellent Web page written by Professor Martin White at Lawrence Berkeley National Laboratory (Ref. 2).

Dark matter is "stuff" which cannot be seen directly. Its existence is inferred indirectly from observations of motions of astronomical objects, specifically, stellar, galactic, and galaxy cluster/supercluster observations. The basic principle of these observations is that if we measure velocities in some region, then there has to be enough mass there for gravity to stop all the objects flying apart. Such measurements done on large scales indicate that the amount of inferred mass is much more than can be explained by the luminous stuff. Hence, we infer that there is dark matter in the Universe.

Dark matter candidates are usually divided into two broad categories, with the second group being sub-divided:

• Baryonic*
• Non-Baryonic
• Hot dark matter and
• Cold dark matter.

For more details, see Ref. 2 and links there.

* Baryonic matter is matter composed mostly (with regard to mass) of baryons, which in turn are composite particles made up of three quarks, and includes atoms of any sort.

References

1. "Dark Matter," Wikipedia, The Free Encyclopedia (2 January 2012 at 17:44).
2. Martin White, Dark Matter.

(Originally written on March 2, 2011)

Boy of Age 16 Asks Me about Relativity, etc.5. Object's Mass at Speed of Light

Abstract image reminiscent of light rays flying past.
Image: jscreationzs / FreeDigitalPhotos.net.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: The object's mass is zero when it is traveling at the speed of light, right? Where does its mass go? Does it turn into energy?

Ted: Surely, what is traveling with the speed of light, i.e., the photon (the quantum of light and all other forms of electromagnetic radiation), has zero mass. It is to be noted that the photon always has zero mass and always flies with the seed of light. This property is known to belong to the photon only.*

Particles with masses different from zero, when they are at rest (rest masses), can be accelerated to speeds fairly close to the speed of light by the use of large accelerators such as the Large Hadron Collider in CERN. When the particle get higher speeds, the mass of the particle does not approach zero, contrary to your supposition, but becomes larger to make the total energy higher. As a result, no body with a nonzero rest mass can be accelerated to reach just the speed of light. This is explained below by the use of a few equations (clicking on the image, you can see a larger one). Thus, the situation in your question that an object with a finite rest mass would reach the speed of light does not happen.

* Neutrinos were once thought to have zero mass, but the experimentally established phenomenon of neutrino oscillation requires neutrinos to have nonzero masses. As for the experiment that suggested the possibility of neutrinos traveling faster than light, mention will be made in a later story of this series.

(Originally written on February 28, 2011)

Boy of Age 16 Asks Me about Relativity, etc.4. Newton vs Einstein

Isaac Newton. By Sir Godfrey Kneller [Public domain],
via Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: It seems that Newton did not know exactly how gravity worked. Then, there came Einstein to find the answer. Why do they still write about Newton's law of gravity in textbooks?

Ted: Newton's law of gravity and equation of motion are highly accurate approximations to Einstein's general and special theories of relativity. Einsteinian mechanics did not make Newtonian mechanics useless but expanded the scope of the latter. The latter is quite simple and yet is useful for doing calculations of the motion of materials being situated in a weak gravitational field and having a speed much smaller than the speed of light. Therefore, we first study Newtonian mechanics at high schools.

Note Added later: An educational blog post on the relation between Einstein's relativity and Newton's mechanics has appeared: Matt Strassler, "How did Einstein do it?" Blog site Of Particular Significance (2012).

(Originally written on February 24, 2011)

Boy of Age 16 Asks Me about Relativity, etc.3. Space and Time

Diagram showing space and time in space-time. Here space is depicted as a two-dimensional entity in three-dimensional spacetime. Time from the observer's viewpoint is represented as a vertical line. Image by K. Aainsqatsi (Own work) [Public domain], via Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: Will there be time, if there is no space?

Ted: Your question does not seem to be a valid one in physics. Physics is the branch of natural science to study matter and its motion through spacetime; and these, i.e., matter, motion and spacetime, are inseparable from space.* From this viewpoint, physicists are not expected to think about the circumstance in which there is no space. In treating a complex problem, physicists often assume a simplified model of the situation, but elimination of space would make the problem non-physical.

However, the following should be noted in relation to your question: Approaches to quantum gravity, being studied for uniting quantum mechanics with general relativity, suggest the possibility that space and time are not fundamental entities but emergent phenomena (see, for example, Ref. 1). If such is the case, the phrase in your question, "there is no space," would have physical meaning in the sense that equations of quantum gravity would dispense with space and time variables.

* Especially in the theory of relativity, space and time (to say precisely, imaginary time) are treated symmetrically, and it can happen that part of time duration of one observer is part of spatial length of the other observer.

Reference

1. Luboš Motl, Emergent space and emergent time, The Reference Frame (2004).

(Originally written on February 23, 2011)

Boy of Age 16 Asks Me about Relativity, etc.2. Einstein and Black Holes

Albert Einstein during a lecture in Vienna in 1921.
By Ferdinand Schmutzer [Public domain],
via Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit of the boy and me as well as that of other readers.

Aaron: I read in some books that Einstein did not believe in black holes. Then, why did he publish the work of general relativity that predicted black holes?

Ted: When he developed the theory, Albert Einstein did not notice that it would predict the existence of black holes. Only after the publication of the paper on general relativity, other physicists studied solutions of Einstein field equations to find the possible existence of black holes. (For the detailed history of finding black hole solutions, see Ref. 1.)

Einstein's disbelief in the black hole solution is explained in Ref. 2 as follows:

It seems that Einstein always was of the opinion that singularities in classical field theory are intolerable. They are intolerable from the point of view of classical field theory because a singular region represents a breakdown of the postulated laws of nature. I think one can turn this argument around and say that a theory that involves singularities and involves them unavoidably, moreover, carries within itself the seeds of its own destruction.

In other words, Einstein's belief in his own theory combined with his opinion about physical theories in general did not allow the existence of the black hole. However, his theory was cleverer than his opinion and predicted what was confirmed by (indirect) observations. A physical theory or an equation can sometimes be more reliable than the philosophical opinion even of the greatest man.

References

1. "Section 1. History" in "Black hole", Wikipedia, The Free Encyclopedia (19 December 2011 at 11:28).
2. Quoted in Philosophical Problems of the Internal and External Worlds: Essays on the Phylosophy of Adolf Grünbaum edited by John Earman (University of Pittsburgh Press, 1993), as written by Peter Bergmann (1980, 156).

(Originally written on February 21, 2011)