OFF TOPIC!!
Hi! За Max-а - в момента правя тъториалите и много се кефя (стигнал съм до този за материалите). Не ми се струва сложно и не мисля да се отказвам, само дето имам чувството, че никога няма да науча всички възможности на програмата и да мога да ги използвам пълноценно.
ON TOPIC!!
Нещо ново... ами не. Напоследък не ме е "спохождало вдъхновение" да разсъждавам по този въпрос. Мисля, че каквото казах дотук е всичко по темата "Какво представлява за мен 4Д светът?", но това не пречи да продължим да обсъждаме други научно-фантастични въпроси.
Според това, което казах по-горе, нашият свят се намира на повърхността на една четириизмерна сферна, следователно ние можем да си живеем в нашия три-пространствено-измерен свят, но дефакто живеем в четири-пространствено-измерен и просто още не сме открили кое е четвъртото измерение.
За статията - напоследък (покрай 3D Studio-то и покрай домашните) нямам нито време, нито ми идва желание да превеждам. Затова поствам статията на английски и евентуално после ще променям съобщението в процеса на превеждане.
Ето го и продължението:
2.0 - Специална теория на относителността
Вече сте запознати с главните "играчи"(буквално - има се предвид свойства) на Вселената: пространство, време, материя, движение, маса, гравитация, енергия и светлина. Тънката част в Специалната теория на относителността е, че много от дискутираните в секция 1 свойства с държат по много неочакван начин в някои специфични "релативистични" ("relativistic") ситуации. Ключът към разбирането на СО е да разберете (повторено е и в статията, дане останете с впечатление, че аз го правя така
)ефектите, които относителността има на всяко едно от свойствата.
Frames of Reference ("гледни точки", от SA Dict - "основни критерий")
(това между многото кавички е допълнение, сложено отстрани на статията)
""""""Lorentz Transformations (Лоренцови трянсформации)
Лоренцовите Трансформации са математически уравнения, които ни позволяват да преминаваме от една координатна система в друга (да преобразуваме координати). Защо бихме искали да правим това? Защото СО се занимава с гредни точки(frames of reference). Когато анализирате свойствата на едно тяло първо от една гледна точка, а после от друга,е нужно първо да трансформирате едната координатна система в другата. Така можем да нагласим Лоренцовите трансформации, че да преобразуваме координати за дължина и време от една гледна точка към друга. (convert length and time from one frame of reference to another.) Например, ако си на самолет, а аз седя неподвижно на земята, можеш да използваш трансформациите, за да трансформираш моята гледна точка в твоя, и аз бих могъл да направя същото за твоята гледна точка. Предишните твърдение намекват(имат за цел да покажат), че дължината и времето не са едни и същи за обекти, които се намират в движение спрямо един-друг. Колкото и невероятно да изглежда, това е резултат от СО. Einstein utilized the transformations because they provide a method of translating the properties from one frame of reference to another when the speed of light is held constant in both. """""
Einstein's special theory of relativity is based on the idea of
reference frames. A reference frame is simply "where a person (or other observer) happens to be standing". You, at this moment, are probably sitting at your computer. That is your current reference frame. You feel like you are stationary, even though you know the earth is revolving on its axis and orbiting around the sun. Here is an important fact about reference frames:
There is no such thing as an absolute frame of reference in our universe. By saying absolute, what is actually meant is that there is no place in the universe that is completely stationary. This statement says that since everything is moving, all motion is relative. Think about it - the earth itself is moving, so even though you are standing still, you are in motion. You are moving through both space and time at all times. Because there is no place or object in the universe that is stationary, there is no single place or object on which to base all other motion. Therefore, if John runs toward Hunter, it could be correctly viewed two ways. From Hunter's perspective, John is moving towards Hunter. From John's perspective, Hunter is moving towards John. Both John and Hunter have the right to observe the action from their respective frames of reference. All motion is relative to your frame of reference. Another example: If you throw a ball, the ball has the right to view itself as being at rest relative to you. The ball can view you as moving away from it, even though you view the ball as moving away from you. Keep in mind that even though you are not moving with respect to the earth's surface, you are moving with the earth.
The First Postulate of the Special Theory of Relativity
The first postulate of the theory of special relativity is not too hard to swallow:
The laws of physics hold true for all frames of reference. This is the simplest of all relativistic concepts to grasp. The physical laws help us understand how and why our environment reacts the way it does. They also allow us to predict events and their outcomes. Consider a yardstick and a cement block. If you measure the length on the block, you will get the same result regardless of whether you are standing on the ground or riding a bus. Next, measure the time it takes a pendulum to make 10 full swings from a starting height of 12 inches above its resting point. Again, you will get the same results whether you are standing on the ground or riding a bus. Note that we are assuming that the bus is not accelerating, but traveling along at a constant velocity on a smooth road. Now if we take the same examples as above, but this time measure the block and time the pendulum swings as they ride past us on the bus, we will get different results than our previous results. The difference in the results of our experiments occurs because the laws of physics remain the same for all frames of reference. The discussion of the Second Postulate will explain this in more detail. It is important to note that just because the laws of physics are constant, it does not mean that we will get the same experimental results in differing frames. That depends on the nature of the experiment. For example, if we crash two cars into each other, we will find that the energy was conserved for the collision regardless of whether we were in one of the cars or standing on the sidewalk. Conservation of energy is a physical law and therefore, must be the same in all reference frames.
The Second Postulate of the Special Theory of Relativity
The second postulate of the special theory of relativity is quite interesting and unexpected because of what it says about frames of reference. The postulate is:
The speed of light is measured as constant in all frames of reference. This can really be described as the first postulate in different clothes. If the laws of physics apply equally to all frames of reference, then light (electromagnetic radiation) must travel at the same speed regardless of the frame. This is required for the laws of electrodynamics to apply equally for all frames.
This postulate is very odd if you think about it for a moment. Here is one fact you can derive from the postulate: Regardless of whether you are flying in an airplane or sitting on the couch, the speed of light would measure the same to you in both situations. The reason that is unexpected is because most physical objects that we deal with in the world add their speeds together. Consider a convertible approaching you at a speed of 50 miles/hour. The passenger pulls out a slingshot and shoots a rock 20 miles/hour at you. If you measured the speed of the rock, you would expect it to be traveling at 70 miles/hour (the speed of the car plus the speed of the rock from the slingshot). That is, in fact, what happens. If the driver measured the speed of the rock, he would only measure 20 miles/hour, since he is already moving at 50 miles/hour with the car. Now if that same car is approaching you at 50 miles/hour and the driver turns on the headlights, something different happens? Since the speed of light is known to be 669,600,000 miles/hour, common sense tells us that the car's speed plus the headlight beam speed gives a total of 669,600,
050 miles/hour (50 miles/hour + 669,600,000 miles/hour). The actual speed would measure 669,600,
000 miles/hour, exactly the speed of light. To understand why this happens, we must look at our notion of speed.
Speed is the distance traveled in a given amount of time. For example, if you travel 60 miles in one hour, your speed is 60 miles per hour. We can easily change our speed by accelerating and decelerating. In order for the speed of light to be constant, even if the light is "launched" from a moving object, only two things can be happening. Either something about our notion of distance and/or something about our notion of time must be skewed. As it turns out, both are skewed. Remember, speed is distance divided by time.
In the headlight example, the distance that you are using in your measurement is not the same as the distance that the light is using. This is a very difficult concept to grasp, but it is true. When an object (with mass) is in motion, its measured length shrinks in the direction of its motion. If the object reaches the speed of light, its measured length shrinks to nothing. Only a person that is in a different frame of reference from the object would be able to detect the shrinking - as far as the object is concerned, in its frame of reference, its size remains the same. This phenomenon is referred to as "length contraction". It means, for example, that as your car approaches the speed of light, the length of the car measured by a stationary observer would be smaller than if the car was measured as it stood still. Look at Fig 2 and Fig 3 below.
In Fig 2 the car is stopped at the stop sign. In Fig 3 the same car is moving past you. You will readily notice that the moving car in the figure is shorter than the stopped car. Note that the car would only be shorter in the direction it is traveling, its height and width are not affected - only its length. Length contraction only affects the length in the direction you are traveling. Imagine that you are running super fast toward an open door. From your perspective, the distance from the front of the door opening to the back of the door opening would decrease. From the doors perspective the width of your body - the distance from your chest to your back - would decrease.
Scientists feel that they have actually proved this notion of length contraction. Therefore, in reality, all objects are perceived to shorten in the direction they are traveling, if they are viewed by someone who is not in motion with them. If you are in a moving car and measure the length of the armrest, you will never notice the change regardless of how fast you are going, because your tape measure would also be shortened from the motion.
In our lives we do not ever perceive length contraction because we move at speeds that are very small with respect to the speed of light. The change is too small for us to notice. Remember the speed of light is 669,600,000 miles/hour or 186,400 miles/sec, so it is easy to see why our everyday speeds are negligible.
The Lorentz Transforms allow us to calculate the length contraction. How much contraction occurs is dependent on how fast an object is traveling with respect to the observer. Just to put some numbers to this, assume that a 12-inch football flies past you and it is moving at a rate of 60% the speed of light. You would measure the football to be 9.6 inches long. So at 60% the speed of light, you measure the football to be 80% of its original length (original 12 inch measurement was made at rest with respect to you). Keep in mind that all measurements are in the direction of the motion - The diameter of the ball is not changed by the ball's forward motion. Here are two points to keep in mind:
1. if you ran beside the football at the same speed, 60% the speed of light, you would always measure the length to be 12 inches. This is no different than you standing still and measuring the football while holding it.
2. if a lady running with the football measured a ruler that you are holding, she would measure you and your ruler to be length contracted as well. Remember, she has equal right to view you as being in motion with respect to her.
The Effect of Motion on TimeI mentioned that time also changes with different frames of reference (motion). This is known as "time dilation". Time actually slows with motion but it only becomes apparent at speeds close to the speed of light. Similar to length contraction, if the speed reaches that of light, time slows to a stop. Again, only an observer that is
not in motion with the time that is being measured would notice. Like the tape measure in length contraction, a clock in motion would also be affected so it would never be able to detect that time was slowing down (remember the pendulum). Since our everyday motion does not approach anything remotely close to the speed of light, the dilation is completely unnoticed by us, but it is there. In order to attempt to prove this theory of time dilation, two very accurate atomic clocks were synchronized and one was taken on a high-speed trip on an airplane. When the plane returned, the clock that took the plane ride was slower by exactly the amount Einstein's equations predicted. Thus, a moving clock runs more slowly when viewed by a frame of reference that is not in motion with it. Keep in mind that when the clock returned, it had recorded less time than the ground clock. Once re-united with the ground clock, the slow clock will again record time at the same rate as the ground clock (obviously, it will remain behind by the amount of time it slowed on the trip unless re-synchronized). It is only when the clock is in motion with respect to the other clock that the time dilation occurs. Take a look at Fig 4 and Fig 5 below.
Let's assume that the object under the sun in Fig 4 is a light clock on wheels. A light clock measures time by sending a beam of light from the bottom plate to the top plate where it is then reflected back to the bottom plate. A light clock seems to be the best measure of time since its speed remains constant regardless of motion. So in Fig 4, we walk up to the light clock and find that it takes 1 sec for the light to travel from the bottom to the top and back to the bottom again. Now look at Fig 5. In this example, the light clock is rolling to the right, but we are standing still. If we could see the light beam as the clock rolled past us, we would see the beam travel at angles to the plates. If you are confused, look at Fig 4 and you'll see that both the sent beam and received beam occur under the sun, thus the clock is not moving. Now look at fig 5, the sent beam occurs under the sun, but the reflected beam returns when the clock is under the lightning bolt, thus the clock is rolling to the right. What is this telling us? We know that the clock standing still sends and receives at 1-second intervals. We also know that the speed of light is constant. Regardless of where we are, we would measure the light beam in fig 4 and fig 5 to be the exact same speed. But Fig 5 looks like the light traveled farther because the arrows are longer. And guess what, it did. It took the light longer to make one complete send and receive cycle, but the speed of the light was unchanged. Because the light traveled farther and the speed was unchanged, this could only mean that the time it took was longer. Remember speed is distance / time, so the only way for the speed to be unchanged when the distance increases is for the time to also increase.
Using the Lorentz Transform, let's put numbers to this example. Let's say the clock in Fig 5 is moving to the right at 90% of the speed of light. You, standing still, would measure the time of that clock as it rolled by to be 2.29-seconds. It is important to note that anyone in motion with the clock in Fig 5 would only measure 1-second, because it would be no different than him standing beside the clock in Fig 4. Hence, the rider aged by 1 second but you aged by 2.29 seconds. This is a very important concept. If we look closely at the clocks, we find that they do not really measure what we think they do. Clocks record the interval between two spatial events. This interval may differ depending on what coordinate system the clock is in (ie. what frame of reference). If the speed of light is held constant (has the same measured value regardless of frame of reference), time is no longer "just" a tool to measure the procession of space. It is a property that is required for the defining and existence of the event. Remember from earlier, any occurrence is an event of space and time (hence, the Space-Time Continuum).
[Note: If the reader decides to learn more about time dilation, it is absolutely imperative that strong emphasis be put on "proper time". This concept is not discussed in this article, but "proper time" is the foundation of the frame geometry of SR. This topic is clearly derived and discussed in the book Spacetime Physics by Taylor and Wheeler.]
The Unification of Energy and Mass
Undoubtedly the most famous equation ever written is E=mc^2. This equation says that energy is equal to the rest mass of the object times the speed of light squared (c is universally accepted as the speed of light). What is this equation actually telling us? Mathematically, since the speed of light is constant, an increase or decrease in the system's rest mass is proportional to an increase or decrease in the system's energy. If this relationship is then combined with the law of conservation of energy and the law of conservation of mass, an equivalence can be formed. This equivalence results in one law for the conservation of energy and mass. Let's now take a look at a couple examples of this relationship...
You should readily understand how a system with very little mass has the potential to release a phenomenal amount of energy (in E=mc^2, c^2 is an enormous number). In nuclear fission, an atom splits to form two more atoms. At the same time, a neutron is released. The sum of the new atoms' masses and the neutron's mass are less than the mass of the initial atom. Where did the missing mass go? It was released in the form of heat - kinetic energy. This energy is exactly what Einstein's E=mc^2 predicts. Another nuclear event that corresponds with Einstein's equation is fusion. Fusion occurs when lightweight atoms are subjected to extremely high temperatures. The temperatures allow the atoms to fuse together to form a heavier atom. Hydrogen fusing into helium is a typical example. What is critical is the fact that the mass of the new atom is less than the sum of the lighter atoms' masses. As with fission, the "missing" mass is released in the form of heat - kinetic energy.
One often-misinterpreted aspect of the energy-mass unification is that a system's mass increases as the system approaches the speed of light. This is not correct. Let's assume that a rocket ship is streaking through space. The following occurs:
Energy must be added to the system to increase the ship's speed.
More of the added energy goes towards increasing the system's resistance to acceleration.
Less of the added energy goes into increasing the system's speed.
Eventually, the amount of added energy required to reach the speed of light would become infinite.
In step 2, the system's resistance to acceleration is a measurement of the system's energy and momentum. Take notice that in the above 4 steps, there is no reference to mass. Nor does there need to be.
Simultaneous Events
There is no such thing as simultaneity between two events when viewed in different frames of reference. If you understand what we have talked about so far, this concept will be a breeze. First let's clarify what this concept is stating. If Meagan sees two events happen at the same time for her frame of reference, Garret, who is moving with respect to Meagan, will not see the events occur at the same time. Let's use another example. Imagine that Meagan is standing outside and notices that there are two identical cannons 100 yards apart and facing each other. All of the sudden, both cannons fire at the same time and the cannonballs smash into each other at exactly half their distance, 50 yards. This is no surprise since, the cannons are identical and they fire cannonballs at the same speed. Now, suppose that Garret was riding his skateboard super fast towards one of the cannons, and he was directly in the line of fire for both. Also suppose he was exactly half way between the two cannons when they fired. What would happen? The cannonball that Garret was moving towards would hit him first. It had less distance to travel since he was moving towards it.
Now, let's replace the cannons with light bulbs that turn on at the same time in Meagan's frame of reference. If Garret rides his skateboard in the same fashion as he did with the cannonballs, when he reaches the halfway mark, he sees the light bulb he is moving towards turn on first and then he sees the light bulb he is moving away from turn on last. See Fig 6 below for clarification.
In Fig 6, the bulb on the right turns on first. I have shown Garret to be moving in the same direction of the distance line between the bulbs, and he is looking towards the moon. As stated earlier, when the bulbs turn on in Meagan's frame of reference, Garret will see the bulb on the right turn on before the bulb on the left does. Since he is moving toward the bulb on the right, its light has a shorter distance to travel to reach him. Garret would argue with Meagan that the bulbs did not turn on at the same time, but in Meagan's perspective they did. Hopefully, you can see how different frames of reference will not allow events to be observed as simultaneous.
Има още една точка, която ще постна по-късно, след като дискутираме тази. Night Shade, доколкото разбрах и добре с английския, така че прочети го непреведено, така дори ще го видиш в оригинал, а не както аз го препредавам. БТВ, последната(непобликуваната) точка е много трудна и изморителна за превод и е възможно нея да я оставя непреведена.
Та като понапреднеш и му разучиш "нещицата" ще ти стане по-интересно. А нещо покрай теорията ти за 4-измерния свят има ли? Нещо ново да ти е хрумнало? А допускаш ли, че всъщност света, в който живеем може да е 4-измерен, но още да не сме го разбрали? CYA!
