Posts tagged albert einstein

Posts tagged albert einstein

Einstein’s Special Theory of Relativity challenges our perceptions of space and time. Through simple algebra, it can be shown that “a clock that is moving will run slower than a clock that is still.” To specify a clock that is “still” is not exactly correct when dealing with relativity because all inertial reference frames are just as valid as any other reference frame. The “specialness” of Special Relativity is that only inertial frames of reference may be considered, whereas Einstein’s General Theory of Relativity deals with accelerating frames of reference. Let’s begin!

The Twin Paradox states this: There is a set of twins, Alice and Bob. It is their 20th birthday and Alice decides to take her rocket and go on a spaceflight while Bob stays at home and waits upon her arrival. Let’s say Alice travels at 95% the speed of light (ie: 0.95c.) In Bob’s reference frame, he calculates that in 20 years, she will come back. Thus, he would have aged 20 additional years and will be 40 years old upon her arrival. While Bob is waiting for Alice’s return, he learns some Special Relativity and decides to calculate how long Alice’s flight will be in her frame of reference. For simplicity, let’s say she travels to an extraterrestrial planet 9.5 light years away, and immediately turns around and begins traveling back at 0.95c. He understands that in her frame of reference, since she is flying in her rocket at 0.95c, time will go by slower. He calculates that she would have only aged 6.25 years. Thus, while he is 40 upon her arrival, Alice will only be 26.25 years old. But what does Alice experience?

During her flight, Alice also decides to bring along some physics books and learn some Special Relativity to pass the time. While she is sitting in her rocket, she sees the Earth flying away from her and concludes that Bob’s time will pass by slower because she decides she is in an inertial frame of reference and he is the one flying away from her. Alice concludes that upon her arrival, Bob would have only aged 6.25 years and she, on the other hand, would have aged 20 years. But which one is younger upon her arrival back to Earth? They can’t both be younger, right? This is supposedly the paradox.

Somewhere, we made an assumption that lead us to a conundrum. But where did we go wrong? As noted in the beginning, only inertial reference frames are considered with Special Relativity. While Bob was sitting at home, he was certainly in an inertial reference frame. Alice, on the other hand, is not. She experiences three separate events during her flight; she accelerates away from the Earth, accelerates as she turns around as she approaches the extraterrestrial planet, and once again accelerates as she approaches Earth. She is not in an inertial reference frame and thus we can conclude that Alice’s reference frame is not as valid as Bob’s. It is Alice’s time that slows down since we can be certain that it is she that is doing the relativistic motion and it is Alice that will be younger than Bob. No paradox.

A Quantum Paradox

The idea that quantum mechanics applies to everything in the universe, even to us humans, can lead to some strange conclusions. Consider this variant of the iconic Schrödinger cat thought experiment that Nobel laureate Eugene P. Wigner came up with in 1961 and David Deutsch of the University of Oxford elaborated on in 1986.

Suppose that a very able experimental physicist, Alice, puts her friend Bob inside a room with a cat, a radioactive atom and cat poison that gets released if the atom decays. The point of having a human there is that we can communicate with him. (Getting answers from cats is not that easy.) As far as Alice is concerned, the atom enters into a state of being both decayed and not decayed, so that the cat is both dead and alive. Bob, however, can directly observe the cat and sees it as one or the other. Alice slips a piece of paper under the door asking Bob whether the cat is in a definite state. He answers, “yes.”

Note that Alice does not ask whether the cat is dead or alive because for her that would force the outcome or, as physicists say, “collapse” the state. She is content observing that her friend sees the cat either alive or dead and does not ask which it is.

Because Alice avoided collapsing the state, quantum theory holds that slipping the paper under the door was a reversible act. She can undo all the steps she took. If the cat was dead, it would now be alive, the poison would be in the bottle, the particle would not have decayed and Bob would have no memory of ever seeing a dead cat.

And yet one trace remains: the piece of paper. Alice can undo the observation in a way that does not also undo the writing on the paper. The paper remains as proof that Bob had observed the cat as definitely alive or dead.

That leads to a startling conclusion. Alice was able to reverse the observation

because, as far as she was concerned, she avoided collapsing the state; to her, Bob was in just as indeterminate a state as the cat. But the friend inside the room thought the state did collapse. That person did see a definite outcome; the paper is proof of it. In this way, the experiment demonstrates two seemingly contradictory principles. Alice thinks that quantum mechanics applies to macroscopic objects: not just cats but also Bobs can be in quantum limbo. Bob thinks that cats are only either dead or alive.

Doing such an experiment with an entire human being would be daunting, but physicists can accomplish much the same with simpler systems. Anton Zeilinger and his colleagues at the University of Vienna take a photon and bounce it off a large mirror. If the photon is reflected, the mirror recoils, but if the photon is transmitted, the mirror stays still. The photon plays the role of the decaying atom; it can exist simultaneously in more than one state. The mirror, made up of billions of atoms, acts as the cat and as Bob. Whether it recoils or not is analogous to whether the cat lives or dies and is seen to live or die by Bob. The process can be reversed by reflecting the photon back at the mirror. On smaller scales, teams led by Rainer Blatt of the University of Innsbruck and by David J. Wineland of the National Institute of Standards and Technology in Boulder, Colo., have reversed the measurement of vibrating ions in an ion trap.

In developing this devious thought experiment, Wigner and Deutsch followed

in the footsteps of Erwin Schrödinger, Albert Einstein and other theorists who

argued that physicists have yet to grasp quantum mechanics in any deep way. For decades most physicists scarcely cared because the foundational issues had no effect on practical applications of the theory. But now that we can perform these experiments for real, the task of understanding quantum mechanics has become all the more urgent. —V.V.

(Source: physics.utoronto.ca)

A human being is a part of the whole called by us universe, a part limited in time and space. He experiences himself, his thoughts and feeling as something separated from the rest, a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty.

The fairest thing we can experience is the mysterious. It is the fundamental emotion which stands at the cradle of true art and science. He who knows it not and can no longer wonder, no longer feel amazement, is as good as dead, a snuffed-out candle.

*Apparently I can still draw.*

Oddly enough, dark energy — for all the surprise around its discovery — is not an entirely new concept in physics. There is historical background for this idea, and it comes from the preeminent astronomer of the 20^{th} century, Albert Einstein.

In 1917, Einstein was applying his new theory of general relativity to the structure of space and time. General relativity says that mass affects the shape of space and the flow of time. Gravity results because space is warped by mass. The greater the mass, the greater the warp.

But Einstein, like all scientists at that time, did not know that the universe was expanding. He found that his equations didn’t quite work for a static universe, so he threw in a hypothetical repulsive force that would fix the problem by balancing things out, an extra part that he called the “cosmological constant.”

Then, in the 1920s, astronomer Edwin Hubble, using a type of star called a Cepheid variable as a “standard candle” to measure distances to other galaxies, discovered that the universe was expanding. The idea of the expanding universe revolutionized astronomy. If the universe was expanding, it must at one time have been smaller. That concept led to the Big Bang theory, that the universe began as a tiny point that suddenly and swiftly expanded to create everything we know today.

Once Einstein knew the universe was expanding, he discarded the cosmological constant as an unnecessary fudge factor. He later called it the “biggest blunder of his life,” according to his fellow physicist George Gamow.

Today astronomers refer to one theory of dark energy as Einstein’s cosmological constant. The theory says that dark energy has been steady and constant throughout time and will remain that way.

A second theory, called quintessence, says that dark energy is a new force and will eventually fade away just as it arose.

If the cosmological constant is correct, Einstein will once again have been proven right — about something even he thought was a mistake.

(Source: hubblesite.org)

How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?

A 12-year-old child prodigy has astounded university professors after grappling with some of the most advanced concepts in mathematics.

Jacob Barnett has an IQ of 170 - higher than Albert Einstein - and is now so far advanced in his Indiana university studies that professors are lining him up for a PHD research role.

The boy wonder, who taught himself calculus, algebra, geometry and trigonometry in a week, is now tutoring fellow college classmates after hours.

And now Jake has embarked on his most ambitious project yet - his own ‘expanded version of Einstein’s theory of relativity’.