Help Understanding Special Relativity

[Infinitatis]

I've always loved the elegance of physics, but, as I have had no professional instruction in the field, there are many questions that I find difficult to grasp.

Currently, I am having difficulties with understanding special relativity. More specifically, I am having difficulties with understanding how no object, massive or massless, can exceed c, 299792458 m/s. What is so special about this number? Can it be calculated (or have we calculated) it theoretically and not just experimentally?

Another question that I've struggled with involve the idea that time is relative. I understand the concept in general but not with much rigor. I've devised a few thought problems that have helped me understand this partially, but I would like to hear if they are correct, and/or if better thought problems exist:

Let's say that you are watching a baseball game from up above. If you begin moving upward at the speed of light, the baseball game will appear to halt. This occurs because any light that is being reflected off of the players, ball, bat, etc. toward you is no longer fast enough to reach you. You are stuck seeing the light (or frame) that had reflected off of them at the point in time in which you had begun moving at the speed of light because that light is moving as fast as you are. If you moved close to the speed of light, but not at it, the game will appear in slow-motion, because it takes significantly longer for the light (or frames) to reach you. If you were to, hypothetically, travel faster than the speed of light, like a tachyon, the game would appear to "rewind" as you surpass "frames" that had already passed you.

Is this reasoning correct?

What would happen if you were to move at the speed of light toward the baseball field from above? For the very short amount of time that you're traveling, I would imagine that the game would appear to be slightly faster (not noticeably) than it would if you were stationary, since you are seeing "frames" before you would if you were stationary.

Is this reasoning correct? The reason for which I suspect it not to be is that time is supposed to stop if you move at the speed of light, but my reasoning tells me that:

-time stops as you move away from something at the speed of light
-time speeds up very slightly as you move toward something at the speed of light

Furthermore, let's say you have object A traveling at the speed of light in one direction, and object B traveling at the speed of light in the other direction. From the point of view of object A, object B would appear to be stopped, because object A is moving as fast as the light reflecting off of object B. The reverse would appear true for object B.

Is this reasoning correct?

What I don't really understand is how the two object's speeds relative to one another is c, and not 2c. I know that there is the formula for combined velocities (see below), but that doesn't really help me understand the idea conceptually.

Thanks to anyone who is willing to help me understand this.

 

[headspace]

Can it be calculated (or have we calculated) it theoretically and not just experimentally?

Interestingly,

I think the meter is actually defined by the speed of light.
And the second is defined by radioactive decay of a Cesium atom.

I think.

That's about all I can do for you right now until I finish reading your post.

 

[Infinitatis]

I think the meter is actually defined by the speed of light.
And the second is defined by radioactive decay of a Cesium atom.

After a quick Google, I have found that originally, the meter was defined relative to Earth's circumference, but later it was defined by how far light travels in 1/c seconds. That's somewhat helpful, but I have a feeling that they just decided to find how long it would have to take for light to travel the approximate distance of the then-current meter and found it to be 1/c seconds. I guess what I mean to say is: why is the speed, c, so important? – not so much the number and unit.

As for the measurement of a second, I would imagine that the situation is similar.

Thanks

 

[Infinitatis]

Any more help I can get from someone?

 

[Ex-User (9086)]

Here are a few video explanations that most people would find digestible:

Spoiler

https://www.youtube.com/watch?v=msVuCEs8Ydo
I recommend the whole relativity playlist, it gives a gist of what's going on at relativistic physics and allows you to know where to look for more detailed information.
Relativity - YouTube

There are good reading resources that explain the same in detail if you prefer to devote more time and attention to it. At this moment I can only offer some wiki links which are often of questionable quality but are, nonetheless, a good place to start in absence of anything better.

If you like maths then learning about Lorentz transformation and the preliminary theories can give you a lot more insight into the mechanics of space. Here's how there are multiple ways from which a similar constant causality speed can be derived.

I don't have the time to answer the rest of your post, but if you search the forum for similar threads I'm certain similar problems have been solved by others. Your last question can be easily googled and understood, it is a pretty common problem with relativity.

 

[Reluctantly]

I'm not sure if I can help, but I've come to understand relativity as meaning that objects distort space, depending on their motion. As an object begins to move very fast, it compresses the space in front of it (along with the object) and decompresses the space behind it. Light fills space and will compress and decompress with it.

So basically, if you are an object moving towards another object, classically you'd imagine that we'd measure light as moving slower behind us and faster in front of us. However, we measure light as the same speed in front of us and behind of us because in front of us, the light has been squashed so that it slows down, while behind us the light has been expanded so that it doesn't slow down.

Naturally, light would have to be both a particle (occupy space) and a wave (compressible/decompressible) for this to be true, but in relativity particles also become squashed or expanded as their speeds change (length dilution), so I suppose everything becomes both a wave and particle to certain extents.

The interesting question for me is why light appears to move at the limit of c to us and not any faster. But maybe that's because we haven't figured out a way to manipulate light particles. We only interact with them. They exist seemingly separate from our control.

 

[Infinitatis]

Spoiler

Here are a few video explanations that most people would find digestible:

Spoiler

https://www.youtube.com/watch?v=msVuCEs8Ydo
I recommend the whole relativity playlist, it gives a gist of what's going on at relativistic physics and allows you to know where to look for more detailed information.
Relativity - YouTube

There are good reading resources that explain the same in detail if you prefer to devote more time and attention to it. At this moment I can only offer some wiki links which are often of questionable quality but are, nonetheless, a good place to start in absence of anything better.

If you like maths then learning about Lorentz transformation and the preliminary theories can give you a lot more insight into the mechanics of space. Here's how there are multiple ways from which a similar constant causality speed can be derived.

I don't have the time to answer the rest of your post, but if you search the forum for similar threads I'm certain similar problems have been solved by others. Your last question can be easily googled and understood, it is a pretty common problem with relativity.

Thanks, that was actually really helpful. "The speed of causality" is a much more logical way of thinking about c. It's also kind of exciting to find that I have reached some similar conclusions with my theories regarding determinism. I'm going to try to work my way through the Lorentz transformation sometime soon.

 

[Pedro]

I think that the main problem in grasping the idea of the value of c is not contained in relativity, but in electromagnetism.

Electromagnetism is a theory that manages to formulate the effects of charged particles in reality. Its description precedes and create a motivation for relativity as a substitute of the newtonian physics, and introduce the idea of eletric and magnetic fields as a real phenomenon (more or less like gravity).

So, the thing about newtonian physics is that the forces in nature are instant transmitted (or "the speed of causality is infinite" - don't really know if this is right, but sure is food for thought ) and electromagnetism by the maxwell's equations predicts that there is a equation, called wave equation, for the propagation of eletric and magnetic fields. The interesting caracteristic of a wave equation is that we can actually know the speed of this waves , and it turns out that it is exactly c, as measured for the speed of light rays in the vaccum in previous experiments. So the conclusion is, light is a wave, and the forces caused in an object by electromagnetic effects are not instantly transmitted.
Now, relativity was born in the idea that the laws of physics are the same in all universe (the basis of physics as a science) and on this idea that light propagates at the speed c for all observers (https://en.wikipedia.org/wiki/Observer_(special_relativity)).

After the formulation of special relativity, physicist concluded that the flow of time depends on your velocity relative to another observer, and that the energy required for movement increases to infinite as you aproach c. That is why it is impossible for massive bodies to reach c, and establishes the speed of light as the "speed of causality" (https://en.wikipedia.org/wiki/Light_cone).

The effects of moving closer to c can be seen in this very cool game by MIT gamelab https://www.youtube.com/watch?v=TCz7oIzcpBE.

 

[Architect]

I am having difficulties with understanding how no object, massive or massless, can exceed c, 299792458 m/s. What is so special about this number?

Because it is. Maybe if we knew why c was special, we'd know more than what we know today. But then, that would just lead to another bit of knowledge that "just is", because this isn't religion, there's always some fundamental things you just have to accept. This is one of them.

 

[Pizzabeak]

Photons can go faster than the speed of light (just like how they can go slower) but not for that long.