Examples Of Relativity In A Sentence
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These example sentences are selected automatically from various online news sources to reflect current usage of the word ‘relativity.’ Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.
The Two Primary Postulates Of Albert Einstein’s Special Theory Of Relativity
The Laws of Physics are uniform throughout
The speed of light in a vacuum is equal to the speed of light in any other space, irrespective of its source.
It counters the popular belief where universal time is dependent and represented as a reference frame and spatial position.
The principle of Galilean relativity is retained in Einstein’s special theory of relativity. This theory refers to the body , to follow the principle of inertia. For example, if you’re standing on a highway and a bus passes you by at 80km/hr, then, relative to somebody sitting inside the bus, you are traveling at 80km/hr in the opposite direction to that of the bus.
Special relativity is only constrained to objects that can move in uniform motion to each other, and cannot be discerned. The speed of light and traveling at its speed can be approached but never attained by any object. The famous Einstein equation, E=mc2, also came into being. It was expressed that mass and energy can often be interchanged, and the increased relativistic mass from its Kinetic Energy E can be divided by c2.
May 1: Lightning Strikes A Moving Train
Einsteins revelation was that observers in relative motion experience time differently: its perfectly possible for two events to happen simultaneously from the perspective of one observer, yet happen at different times from the perspective of the other. And both observers would be right.
Einstein later illustrated this point with another thought experiment. Imagine that you once again have an observer standing on a railway embankment as a train goes roaring by. But this time, each end of the train is struck by a bolt of lightning just as the trains midpoint is passing. Because the lightning strikes are the same distance from the observer, their light reaches his eye at the same instant. So he correctly says that they happened simultaneously.
Meanwhile, another observer on the train is sitting at its exact midpoint. From her perspective, the light from the two strikes also has to travel equal distances, and she will likewise measure the speed of light to be the same in either direction. But because the train is moving, the light coming from the lightning in the rear has to travel farther to catch up, so it reaches her a few instants later than the light coming from the front. Since the light pulses arrived at different times, she can only conclude the strikes were not simultaneousthat the one in front actually happened first.
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What Does This Spacetime Diagram Mean
- I don’t understand a spacetime diagram about relativty and simultaneity that I found in a book and its explaination by the author
fee_de said:First of all I don’t understand what it means that “the moment in the middle of my quarter of an hour can be considered simultaneus to your answer”.
fee_de said:Talking about the diagram, why can we say that the observer perceives the two dots as simultaneous? They don’t exit his past and enter his future at the same time, do they? In these diagrams souldn’t we find simultaneous events on the same horizontal line?
fee_de said:Honeslty I think you are right. I generally like him as a science writer but in this book he made general relativity easier to understand than special relativity ^^”
What Does Modern Physics Mean
Modern physics is a branch of physics in which matter and energy are not separate, but instead are alternate forms of one another.
The term modern physics refers to the study of facts and theories developed in this century that concern the interactions of matter, space, and time.
Moreover, one of the big dilemmas arising from 20th-century physics is that so much of modern physics is based on two pillars. In particular, which came up in the early part of the last century.
1. Theory of Relativity
The theory of relativity usually encompasses two interrelated theories by Albert Einstein. Including, the special relativity and general relativity. Whereas, special relativity applies to elementary particles and their interactions, describing all their physical phenomena except gravity.
2. Quantum Mechanics
Quantum mechanics , is also . In particular, the wave mechanical model, and or matrix mechanics. Including, quantum field theory, is a fundamental theory in physics. As an illustration, it describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Significance Of The Dot Product In Physics: Intuitive Explanation + Examples
In an intuitive sense, the dot product is a measure of how much two vectors are aligned. So, if we have two vectors, u and v, the dot product between these two would give the length of the vector v along the vector u, or if you will, the projection of v along u.
If we know the angle between the two vectors , the dot product can be calculated by the following formula:
The dot product can also be calculated in terms of the components of these vectors by using the following formula:
Now, whats the significance of all of this to physics? Well, many physical quantities are described by vectors , so it only makes sense that the dot product also has some physical significance.
In particular, the same geometric picture applies in physics as well the dot product gives the length of one vector along another vector, but now, vectors represent something physical.
The best way to explain the physics of this is through an example. Namely, the dot product between a displacement vector and a force vector, which could be described as the change in position in the direction of the force.
This quantity gives the work done by the force, which is essentially the change in energy caused by this force. More precisely, the work done along some path is actually given by a line integral of this dot product, which I explain in this article.
A nice explanation of this can be found in the video below:
For our purposes, the main properties of the dot product are:
How Does General Relativity Work
To understand general relativity, first, let’s start with gravity, the force of attraction that two objects exert on one another. Sir Isaac Newton quantified gravity in the same text in which he formulated his three laws of motion, the “Principia.”
The gravitational force tugging between two bodies depends on how massive each one is and how far apart the two lie. Even as the center of the Earth is pulling you toward it , your center of mass is pulling back at the Earth. But the more massive body barely feels the tug from you, while with your much smaller mass you find yourself firmly rooted thanks to that same force. Yet Newton’s laws assume that gravity is an innate force of an object that can act over a distance.
Albert Einstein, in his theory of special relativity, determined that the laws of physics are the same for all non-accelerating observers, and he showed that the speed of light within a vacuum is the same no matter the speed at which an observer travels, according to Wired.
As a result, he found that space and time were interwoven into a single continuum known as space-time. And events that occur at the same time for one observer could occur at different times for another.
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Gold Doesn’t Corrode Easily
The relativistic effect on gold’s electrons is also one reason that the metal doesn’t corrode or react with anything else easily.
Gold has only one electron in its outer shell, but it still is not as reactive as calcium or lithium. Instead, the electrons in gold, being “heavier” than they should be, are all held closer to the atomic nucleus. This means that the outermost electron isn’t likely to be in a place where it can react with anything at all it’s just as likely to be among its fellow electrons that are close to the nucleus.
How Did Einstein Come Up With Special Relativity
According to Einstein, in his 1949 book “Autobiographical Notes” , the budding physicist began questioning the behavior of light when he was just 16 years old. In a thought experiment as a teenager, he wrote, he imagined chasing a beam of light.
Classical physics would imply that as the imaginary Einstein sped up to catch the light, the light wave would eventually come to a relative speed of zero the man and the light would be moving at speed together, and he could see light as a frozen electromagnetic field. But, Einstein wrote, this contradicted work by another scientist, James Clerk Maxwell, whose equations required that electromagnetic waves always move at the same speed in a vacuum: 186,282 miles per second .
Philosopher of physics John D. Norton challenged Einstein’s story in his book “Einstein for Everyone” , in part because as a 16-year-old, Einstein wouldn’t yet have encountered Maxwell’s equations. But because it appeared in Einstein’s own memoir, the anecdote is still widely accepted.
If a person could, theoretically, catch up to a beam of light and see it frozen relative to their own motion, would physics as a whole have to change depending on a person’s speed, and their vantage point? Instead, Einstein recounted, he sought a unified theory that would make the rules of physics the same for everyone, everywhere, all the time.
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Albert Einstein Tug Of Gravity
Eventually, Sir Isaac Newton quantified the gravity between two objects. When he formulated his three laws of motion. The force tugging between two bodies depends on how massive each one is. And also, how far apart the two lie.
Even if the center of the Earth pulls you toward it, inasmuch as it keeps you firmly lodged on the ground, your center of mass is pulling back at the Earth. But the more massive body barely feels the tug from you.
While with your much smaller mass you find yourself firmly rooted thanks to that same force. Yet, Newtons laws assume that gravity is an innate force of an object that can act over a distance.
Albert Einstein, in his theory of special relativity, determined that the laws of physics are the same. Generally, for all non-accelerating observers, and he showed that the speed of light within a vacuum is the same.
No matter the speed at which an observer travels. Events that occur at the same time for one observer could occur at different times for another.
Build Your Own Time Machine
One of the above implications of Special Relativity is Time Dilation. What this means is due to the speed of light being invariant, and all laws being the same for constant velocities, time can slow down. Time, it turns out, is not a constant throughout the universe but is totally relative.
Imagine youre on a space ship and in youre hand you have a fancy new type of clock youve invented. Its basically two mirrors that a photon bounces between and youve set it up so that every time the photon hits one of the mirrors you hear a click. Youve also set it up so that you know how many clicks you will hear in one second, so providing you are good at counting you can measure time very accurately with this clock.
Now lets assume your space ship is currently stationary. Luckily one side is made of glass so we can see whats going on.
The photon would go up to the top mirror and set off a Click and then bounce down to the bottom mirror and set off another Click. Then it would bounce back up and back down again, over and over again. Simple and easy.
Now lets assume you decide to take the space ship for a quick spin. So now youre moving along at a constant velocity. All the laws that applied before still hold now, but as you can see form the below image, something has changed.
Using some simple trigonometry you can work out an equation for how much time differs as you move along at your constant velocity. In the case of you being stationary then the clock situation is
Machthe 7 Biggest Unanswered Questions In Physics
For example, the sun is massive enough to warp space across our solar system a bit like the way a heavy ball resting on a rubber sheet warps the sheet. As a result, Earth and the other planets move in curved paths around it.
This warping also affects measurements of time. We tend to think of time as ticking away at a steady rate. But just as gravity can stretch or warp space, it can also dilate time. If your friend climbs to the top of a mountain, youll see his clock ticking faster compared to yours another friend, at the bottom of a valley, will have a slower-ticking clock, because of the difference in the strength of gravity at each place. Subsequent experiments proved that this indeed happens.
What Does Relativity Look Like ‘under The Hood’
Special relativity is ultimately a set of equations that relate the way things look in one frame of reference to how they look in another the stretching of time and space, and the increase in mass. The equations involve nothing more complicated than high-school math.
General relativity is more complicated. Its field equations describe the relationship between mass and the curvature of space and dilation of time, and are typically taught in graduate-level university physics courses.
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Dot Product In Quantum Mechanics
The dot product in quantum mechanics is quite a bit more abstract than any of the notions we talked about before.
Besides, it usually doesnt even go by the name if a dot product, but rather the inner product .
The inner product between two vectors is denoted by sandwiching together a bra vector and a ket vector :
Now, this is equivalent to a typical dot product, except that in quantum mechanics, were usually dealing with complex numbers. So, this inner product is actually:
Now, these bras and kets are indeed vectors. However, they are not the typical vectors in 3D space, but rather they are abstract state vectors in a complex vector space.
The physical meaning of them is that they represent quantum states of a system. Now, what this practically means will depend on the particular state vector. For example, we could have a state vector that represents a particle with some momentum and this would be a perfectly valid quantum state.
The dot product also has pretty much the same meaning, except that it is now a mathematical operation in an abstract vector space, so we cannot picture it geometrically.
An important application of these inner products in quantum mechanics is for basis states. These are analogous to basis vectors, but again they are abstract complex vectors. Basis states are defined by the following inner products:
Special Relativity And Quantum Mechanics
Special relativity and quantum mechanics are two of the most widely accepted models of how our universe works. But special relativity mostly pertains to extremely large distances, speeds and objects, uniting them in a “smooth” model of the universe. Events in special relativity are continuous and deterministic, wrote Corey Powell for The Guardian, which means that every action results in a direct, specific and local consequence. That’s different from quantum mechanics, Powell continued: quantum physics are “chunky,” with events occurring in jumps or “quantum leaps” that have probabilistic outcomes, not definite ones.
Researchers uniting special relativity and quantum mechanics the smooth and the chunky, the very large and the very small have come up with fields like relativistic quantum mechanics and, more recently, quantum field theory to better understand subatomic particles and their interactions.
Researchers striving to connect quantum mechanics and general relativity, on the other hand, consider it to be one of the great unsolved problems in physics. For decades, many viewed string theory to be the most promising area of research into a unified theory of all physics. Now, a host of additional theories exist. For example, one group proposes space-time loops to link the tiny, chunky quantum world with the wide relativistic universe.
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Einstein’s Theory Of Special Relativity
Special relativity: It’s like normal relativity, but special.
Albert Einstein’s 1905 theory of special relativity is one of the most important papers ever published in the field of physics. Special relativity is an explanation of how speed affects mass, time and space. The theory includes a way for the speed of light to define the relationship between energy and matter small amounts of mass can be interchangeable with enormous amounts of energy , as defined by the classic equation E = mc^2.
Special relativity applies to “special” cases it’s mostly used when discussing huge energies, ultra-fast speeds and astronomical distances, all without the complications of gravity. Einstein officially added gravity to his theories in 1915, with the publication of his paper on general relativity.
As an object approaches the speed of light, the object’s mass becomes infinite and so does the energy required to move it. That means it is impossible for any matter to go faster than light travels. This cosmic speed limit inspires new realms of physics and science fiction, as people consider travel across vast distances.