Archive for the ‘Theory of Special Relativity’ Category

By Jeffrey Bennett

It has been exactly 100 years since Albert Einstein presented his theory of general relativity to an audience of scientists on November 25, 1915. While virtually everyone has heard of Einstein and his theory, very few people have any idea of what the theory actually is.

This is a shame, not only because there is a great public thirst for understanding of it, but also because relativity is important, for at least four major reasons.

General relativity provides our modern understanding of space, time and gravity — which means it’s crucial to almost everything we do in physics and astronomy. For example, you cannot understand black holes, the expansion of the universe or the Big Bang without first understanding the basic ideas of relativity. Though few people realize it, Einstein’s famous equation E = mc2 is actually part of the theory of relativity, which means that relativity also explains how the sun shines and how nuclear power works.

A second reason everyone should know about relativity lies in the way it changes our perception of reality. Relativity tells us that our ordinary perceptions of time and space are not universally valid. Instead, space and time are intertwined as four-dimensional space-time.

In our ordinary lives, we perceive only three dimensions—length, width and depth—and we assume that this perception reflects reality. However, in space-time, the four directions of possible motion are length, width, depth and time. (Note that time is not “the” fourth dimension; it is simply one of the four.)

Although we cannot picture all four dimensions of space-time at once, we can imagine what things would look like if we could. In addition to the three spatial dimensions of space-time that we ordinarily see, every object would be stretched out through time. Objects that we see as three-dimensional in our ordinary lives would appear as four-dimensional objects in space-time. If we could see in four dimensions, we could look through time just as easily as we look to our left or right. If we looked at a person, we could see every event in that person’s life. If we wondered what really happened during some historical event, we’d simply look to find the answer.

To see why this is so revolutionary, imagine that you met someone today who deeply believed that Earth is the center of the universe. You would probably feel sorry for this person, knowing that his or her entire world view is based on an idea disproven more than 400 years ago.

Now imagine that you met someone who still believed that time and space are independent and absolute — which, of course, describes almost everyone — even though we’ve known that’s not the case for a century now. Shouldn’t we feel equally sorry for all who hold this modern misconception?

It seems especially unfortunate once you realize that the ideas of relativity are not particularly difficult to understand. Indeed, I believe we could begin teaching relativity in elementary school in much the same way that we teach young children about the existence of atoms, even though few will ever study quantum mechanics.

My third reason for believing relativity is important lies in what Einstein’s discovery tells us about human potential. The science of relativity may seem disconnected from most other human endeavors, but I believe Einstein himself proved otherwise. Throughout his life, Einstein argued eloquently for human rights, human dignity and a world of peace and shared prosperity. His belief in underlying human goodness is all the more striking when you consider that he lived through both World Wars, that he was driven out of Germany by the rise of the Nazis, that he witnessed the Holocaust that wiped out more than six million of his fellow Jews, and that he saw his own discoveries put to use in atomic bombs.

No one can say for sure how he maintained his optimism in the face of such tragedies, but I see a connection to his discovery of relativity. Einstein surely recognized that a theory that so challenged our perceptions of reality might have been dismissed out of hand at other times in history, but that we now live in a time when, thanks to the process that we call science, the abundant evidence for relativity allowed for its acceptance.

This willingness to make judgments based on evidence shows that we are growing up as a species. We have not yet reached the point where we always show the same willingness in all our other endeavors, but the fact that we’ve done it for science suggests we have the potential.

Finally, on a philosophical level, relativity is profound. Only about a month before his death in 1955, Einstein wrote: “Death signifies nothing … the distinction between past, present and future is only a stubbornly persistent illusion.” As this suggests, relativity raises interesting questions about what the passage of time really means.

Because these are philosophical questions, they do not have definitive answers, and you will have to decide for yourself what these questions mean to you. But I believe that one thing is clear. Einstein showed that even though space and time can independently differ for different observers, the four-dimensional space-time reality is the same for everyone.

This implies that events in space-time have a permanence to them that cannot be taken away. Once an event occurs, in essence it becomes part of the fabric of our universe. Every human life is a series of events, and this means that when we put them all together, each of us is creating our own, indelible mark on the universe. Perhaps if everyone understood that, we might all be a little more careful to make sure that the mark we leave is one that we are proud of.

So there you have it. Relativity is necessary to comprehend the universe as we know it, it helps us understand the potential we all share when we put our brains to work for the common good, and if we all understood it we might treat each other a little more kindly.


Stephen Hawking's black hole theory
Notion of an ‘event horizon’, from which nothing can escape, is incompatible with quantum theory, physicist claims.

by Zeeya Merali

Most physicists foolhardy enough to write a paper claiming that “there are no black holes” — at least not in the sense we usually imagine — would probably be dismissed as cranks. But when the call to redefine these cosmic crunchers comes from Stephen Hawking, it’s worth taking notice. In a paper posted online, the physicist, based at the University of Cambridge, UK, and one of the creators of modern black-hole theory, does away with the notion of an event horizon, the invisible boundary thought to shroud every black hole, beyond which nothing, not even light, can escape.

In its stead, Hawking’s radical proposal is a much more benign “apparent horizon”, which only temporarily holds matter and energy prisoner before eventually releasing them, albeit in a more garbled form.

“There is no escape from a black hole in classical theory,” Hawking told Nature. Quantum theory, however, “enables energy and information to escape from a black hole”. A full explanation of the process, the physicist admits, would require a theory that successfully merges gravity with the other fundamental forces of nature. But that is a goal that has eluded physicists for nearly a century. “The correct treatment,” Hawking says, “remains a mystery.”

Hawking posted his paper on the arXiv preprint server on 22 January1. He titled it, whimsically, ‘Information preservation and weather forecasting for black holes’, and it has yet to pass peer review. The paper was based on a talk he gave via Skype at a meeting at the Kavli Institute for Theoretical Physics in Santa Barbara, California, in August 2013.

Hawking’s new work is an attempt to solve what is known as the black-hole firewall paradox, which has been vexing physicists for almost two years, after it was discovered by theoretical physicist Joseph Polchinski of the Kavli Institute and his colleagues.

In a thought experiment, the researchers asked what would happen to an astronaut unlucky enough to fall into a black hole. Event horizons are mathematically simple consequences of Einstein’s general theory of relativity that were first pointed out by the German astronomer Karl Schwarzschild in a letter he wrote to Einstein in late 1915, less than a month after the publication of the theory. In that picture, physicists had long assumed, the astronaut would happily pass through the event horizon, unaware of his or her impending doom, before gradually being pulled inwards — stretched out along the way, like spaghetti — and eventually crushed at the ‘singularity’, the black hole’s hypothetical infinitely dense core.

But on analysing the situation in detail, Polchinski’s team came to the startling realization that the laws of quantum mechanics, which govern particles on small scales, change the situation completely. Quantum theory, they said, dictates that the event horizon must actually be transformed into a highly energetic region, or ‘firewall’, that would burn the astronaut to a crisp.

This was alarming because, although the firewall obeyed quantum rules, it flouted Einstein’s general theory of relativity. According to that theory, someone in free fall should perceive the laws of physics as being identical everywhere in the Universe — whether they are falling into a black hole or floating in empty intergalactic space. As far as Einstein is concerned, the event horizon should be an unremarkable place.

Now Hawking proposes a third, tantalizingly simple, option. Quantum mechanics and general relativity remain intact, but black holes simply do not have an event horizon to catch fire. The key to his claim is that quantum effects around the black hole cause space-time to fluctuate too wildly for a sharp boundary surface to exist.

In place of the event horizon, Hawking invokes an “apparent horizon”, a surface along which light rays attempting to rush away from the black hole’s core will be suspended. In general relativity, for an unchanging black hole, these two horizons are identical, because light trying to escape from inside a black hole can reach only as far as the event horizon and will be held there, as though stuck on a treadmill. However, the two horizons can, in principle, be distinguished. If more matter gets swallowed by the black hole, its event horizon will swell and grow larger than the apparent horizon.

Conversely, in the 1970s, Hawking also showed that black holes can slowly shrink, spewing out ‘Hawking radiation’. In that case, the event horizon would, in theory, become smaller than the apparent horizon. Hawking’s new suggestion is that the apparent horizon is the real boundary. “The absence of event horizons means that there are no black holes — in the sense of regimes from which light can’t escape to infinity,” Hawking writes.

“The picture Hawking gives sounds reasonable,” says Don Page, a physicist and expert on black holes at the University of Alberta in Edmonton, Canada, who collaborated with Hawking in the 1970s. “You could say that it is radical to propose there’s no event horizon. But these are highly quantum conditions, and there’s ambiguity about what space-time even is, let alone whether there is a definite region that can be marked as an event horizon.”

Although Page accepts Hawking’s proposal that a black hole could exist without an event horizon, he questions whether that alone is enough to get past the firewall paradox. The presence of even an ephemeral apparent horizon, he cautions, could well cause the same problems as does an event horizon.

Unlike the event horizon, the apparent horizon can eventually dissolve. Page notes that Hawking is opening the door to a scenario so extreme “that anything in principle can get out of a black hole”. Although Hawking does not specify in his paper exactly how an apparent horizon would disappear, Page speculates that when it has shrunk to a certain size, at which the effects of both quantum mechanics and gravity combine, it is plausible that it could vanish. At that point, whatever was once trapped within the black hole would be released (although not in good shape).

If Hawking is correct, there could even be no singularity at the core of the black hole. Instead, matter would be only temporarily held behind the apparent horizon, which would gradually move inward owing to the pull of the black hole, but would never quite crunch down to the centre. Information about this matter would not destroyed, but would be highly scrambled so that, as it is released through Hawking radiation, it would be in a vastly different form, making it almost impossible to work out what the swallowed objects once were.

“It would be worse than trying to reconstruct a book that you burned from its ashes,” says Page. In his paper, Hawking compares it to trying to forecast the weather ahead of time: in theory it is possible, but in practice it is too difficult to do with much accuracy.

Polchinski, however, is sceptical that black holes without an event horizon could exist in nature. The kind of violent fluctuations needed to erase it are too rare in the Universe, he says. “In Einstein’s gravity, the black-hole horizon is not so different from any other part of space,” says Polchinski. “We never see space-time fluctuate in our own neighbourhood: it is just too rare on large scales.”

Raphael Bousso, a theoretical physicist at the University of California, Berkeley, and a former student of Hawking’s, says that this latest contribution highlights how “abhorrent” physicists find the potential existence of firewalls. However, he is also cautious about Hawking’s solution. “The idea that there are no points from which you cannot escape a black hole is in some ways an even more radical and problematic suggestion than the existence of firewalls,” he says. “But the fact that we’re still discussing such questions 40 years after Hawking’s first papers on black holes and information is testament to their enormous significance.”

“Our hypothesis is that the inside of a black hole — it may not be there. Probably that’s the end of space itself. There’s no inside at all.”
– Joe Polchinski, physicist

It could rightly be called the most massive debate of the year: Physicists are locked in an argument over what happens if you fall into a black hole.

On one side are those who support the traditional view from Albert Einstein. On the other, backers of a radical new theory that preserves the very core of modern physics by destroying space itself.

Regardless of who’s right, the new take on black holes could lead to a better understanding of the universe, says Leonard Susskind, a physicist at Stanford University. “This is the kind of thing where progress comes from.”

Black holes are regions of space so dense that nothing, not even light, can escape.

There’s a long-standing view about what would happen if you fell into one of these holes. At first, you’re not going to notice much of anything — but the black hole’s gravity is getting stronger and stronger. And eventually you pass a point of no return.

“It’s kind of like you’re rowing on Niagara Falls, and you pass the point [where] you can’t row fast enough to escape the current,” Susskind says. “Well, you’re doomed at that point. But passing the point of no return — you wouldn’t even notice it.”

Now you can’t get out. And gravity from the black hole is starting to pull on your feet more than your head. “The gravity wants to sort of stretch you in one direction and squeeze you in another,” says Joe Polchinski, a physicist at the University of California, Santa Barbara. He says the technical term for this stretching is spaghettification.

“It’d be kind of medieval,” says Polchinkski. “It’d be like something on Game of Thrones.”

In Einstein’s version of events, that’s the end. But Polchinski has a new version of things: “Our hypothesis is that the inside of a black hole — it may not be there,” he says.

So what’s inside the black hole? Nothing, Polchinski says. Actually even less than that. “Probably that’s the end of space itself; there’s no inside at all.”
This “no inside” idea may sound outrageous, but it’s actually a stab at solving an even bigger problem with black holes.

According to the dominant theory of physics — quantum mechanics — information can never disappear from the universe. Put another way, the atoms in your body are configured in a particular way. They can be rearranged (radically if you happen to slip inside a black hole). But it should always be possible, at least in theory, to look at all those rearranged atoms and work out that they were once part of a human of your dimensions and personality.

This rule is absolutely fundamental. “Everything is built on it,” says Susskind. “If it were violated, everything falls apart.”

For a long time, black holes stretched this rule, but they didn’t break it. People thought that if you fell into a black hole, your spaghettified remains would always be in there, trapped beyond the point of no return.

That is, until the famous physicist Stephen Hawking came along. In the 1970s, Hawking showed that, according to quantum mechanics, a black hole evaporates — very slowly, it vanishes. And that breaks the fundamental rule because all that information that was once in your spaghettified remains vanishes with it.

This didn’t seem to bother Hawking. (“I’m not a psychiatrist, and I can’t psychoanalyze him,” Susskind says.) But it has bothered a lot of other physicists since.

And in the intervening years, work by another theorist — Juan Maldacena, with Princeton’s Institute for Advanced Study — seems to show that Hawking was wrong. Information has to get out of the black hole … somehow. But nobody knows how.

So Polchinski took another look. “We took Hawking’s original argument,” he says, “and very carefully ran it backwards.”

And Polchinski and his colleagues found one way to keep things from vanishing when they fall inside a black hole — they got rid of the inside. By tearing apart the fabric of space beyond the point of no return, the group was able to preserve the information rule of quantum mechanics.

In this version, anything falling into a black hole is instantly vaporized at the point of no return, in a fiery storm of quantum particles. Particles coming from the hole collectively carry away any and all information about the object that’s falling in.

So in Polchinski’s version, when you fall into a black hole, you don’t disappear. Instead, you smack into the end of the universe.

“You just come to the end of space, and there’s nothing beyond it. Terminated,” Susskind says. All the information once contained in your atoms is re-radiated in a quantum mechanical fire.

This new version seems too radical to Susskind. “I don’t think this is true,” he says. “In fact, I think almost nobody thinks this is true — that space falls apart inside a black hole.”

Even Polchinski still feels that black holes should have insides. “My gut believes that the black hole has an interior,” he says. But, he adds, nobody’s been able to disprove his hypothesis that it doesn’t.

“Every counterargument I’ve seen is flawed,” Polchinski says.

Susskind agrees: “Nobody quite knows exactly what’s wrong with their argument — and that’s what makes this so important and interesting.”

And as crazy as it sounds, this is progress. In the year ahead, Susskind hopes someone can find the flaw in Polchinski’s argument, just the way Polchinski found a flaw in Stephen Hawking’s argument. But it will be awhile before we understand black holes inside and out.


A new study reveals the contribution of a little known Austrian physicist, Friedrich Hasenöhrl, to uncovering a precursor to Einstein famous equation.

Two American physicists outline the role played by Austrian physicist Friedrich Hasenöhrl in establishing the proportionality between the energy (E) of a quantity of matter with its mass (m) in a cavity filled with radiation. In a paper in the European Physical Journal H, Stephen Boughn from Haverford College in Pensylvannia and Tony Rothman from Princeton University in New Jersey argue how Hasenöhrl’s work, for which he now receives little credit, may have contributed to the famous equation E=mc2.

According to science philosopher Thomas Kuhn, the nature of scientific progress occurs through paradigm shifts, which depend on the cultural and historical circumstances of groups of scientists. Concurring with this idea, the authors believe the notion that mass and energy should be related did not originate solely with Hasenöhrl. Nor did it suddenly emerge in 1905, when Einstein published his paper, as popular mythology would have it.

Given the lack of recognition for Hasenöhrl’s contribution, the authors examined the Austrian physicist’s original work on blackbody radiation in a cavity with perfectly reflective walls. This study seeks to identify the blackbody’s mass changes when the cavity is moving relative to the observer.

They then explored the reason why the Austrian physicist arrived at an energy/mass correlation with the wrong factor, namely at the equation: E = (3/8) mc2. Hasenöhrl’s error, they believe, stems from failing to account for the mass lost by the blackbody while radiating.

Before Hasenöhrl focused on cavity radiation, other physicists, including French mathematician Henri Poincaré and German physicist Max Abraham, showed the existence of an inertial mass associated with electromagnetic energy. In 1905, Einstein gave the correct relationship between inertial mass and electromagnetic energy, E=mc2. Nevertheless, it was not until 1911 that German physicist Max von Laue generalised it to include all forms of energy.


The science fiction vision of stars flashing by as streaks when spaceships travel faster than light isn’t what the scene would actually look like, a team of physics students says.

Instead, the view out the windows of a vehicle traveling through hyperspace would be more like a centralized bright glow, calculations show.

The finding contradicts the familiar images of stretched out starlight streaking past the windows of the Millennium Falcon in “Star Wars” and the Starship Enterprise in “Star Trek.” In those films and television series, as spaceships engage warp drive or hyperdrive and approach the speed of light, stars morph from points of light to long streaks that stretch out past the ship.

But passengers on the Millennium Falcon or the Enterprise actually wouldn’t be able to see stars at all when traveling that fast, found a group of physics Masters students at England’s University of Leicester. Rather, a phenomenon called the Doppler Effect, which affects the wavelength of radiation from moving sources, would cause stars’ light to shift out of the visible spectrum and into the X-ray range, where human eyes wouldn’t be able to see it, the students found.

“The resultant effects we worked out were based on Einstein’s theory of Special Relativity, so while we may not be used to them in our daily lives, Han Solo and his crew should certainly understand its implications,” Leicester student Joshua Argyle said in a statement.

The Doppler Effect is the reason why an ambulance’s siren sounds higher pitched when it’s coming at you compared to when it’s moving away — the sound’s frequency becomes higher, making its wavelength longer, and changing its pitch.

The same thing would happen to the light of stars when a spaceship began to move toward them at significant speed. And other light, such as the pervasive glow of the universe called the cosmic microwave background radiation, which is left over from the Big Bang, would be shifted out of the microwave range and into the visible spectrum, the students found.

“If the Millennium Falcon existed and really could travel that fast, sunglasses would certainly be advisable,” said research team member Riley Connors. “On top of this, the ship would need something to protect the crew from harmful X-ray radiation.”

The increased X-ray radiation from shifted starlight would even push back on a spaceship traveling in hyperdrive, the team found, slowing down the vehicle with a pressure similar to the force felt at the bottom of the Pacific Ocean. In fact, such a spacecraft would need to carry extra energy reserves to counter this pressure and press ahead.

Whether the scientific reality of these effects will be taken into consideration on future Star Wars films is still an open question.

“Perhaps Disney should take the physical implications of such high speed travel into account in their forthcoming films,” said team member Katie Dexter.

Connors, Dexter, Argyle, and fourth team member Cameron Scoular published their findings in this year’s issue of the University of Leicester’s Journal of Physics Special Topics.