Submitted by -cool--beans- t3_10q3k9c in explainlikeimfive
Thank you so much for all the answers, they have all be so helpful. :)
Comments
NIRPL t1_j6nodax wrote
What does axiom mean?
DoctorKokktor t1_j6np6h4 wrote
Good question, sorry for not clarifying in my original post. An axiom is a statement that we take to be self-evident. I.e. it's a statement that we don't need to prove because we just ASSUME that it's true. Then, based on that assumption (i.e. axiom), we try to deduce certain conclusions.
This is also how we do things in geometry (and indeed every single branch of math)! You may have heard of Euclid's five postulates (another word for axiom). All of Euclidean geometry can be derived by using the five axioms that Euclid laid out some 2000 years ago.
However, it turns out that if you refuse to accept the fifth axiom of Euclid, then you can deduce/derive other kinds of geometries. These are called non-euclidean geometries.
NIRPL t1_j6nxhmx wrote
Thank you for explaining!
Regarding the non-euclidean geometries link, the images describing elliptical Euclidean and hyperbolic lines, why is the identified 90° angle significant? Or is that the point? Regardless of bend, we can assume a 90° angle will exist?
If I'm completely off-base with my question and wasting your time, feel free to say so lol
DoctorKokktor t1_j6nynl9 wrote
Another good question :)
So basically, Euclidean geometry is founded on five posulates, the last of which is called the "parallel postulate". It turns out that the statement that describes this parallel postulate is ambiguous, and so you can have multiple descriptions/variations of this postulate (you can even omit the 5th postulate altogether!), all of which allow you to derive entirely new geometries.
Those 90 degree angles in different shapes are a consequence of the different statements of the parallel postulate. Those figures shown in the article are all examples of parallel lines, which at first seem preposterous but are a natural consequence of accepting a different version of Euclid's parallel postulate.
NIRPL t1_j6oe0q2 wrote
I sincerely hope you are an educator. You have a talent for explanations. Thank you for taking the time to respond and teach me something new today.
DoctorKokktor t1_j6om43l wrote
Thank you for your kind words :)
Incidentally, Einstein's theory of special and general relativity are also a different kind of geometry! Just like how Euclidean geometry takes place in Euclidean space, special relativity takes place on what's known as "Minkowski" space or spacetime, whereas general relativity takes place on what's known as a pseudo-Riemannian manifold.
These words sound complex but just remember that they are merely names for some kind of foreign geometry that are derived from a completely different set of axioms than the normal Euclidean geometry that we studied in high school. This article is very nice at introducing the history and context behind non-euclidean geometries!
But you don't even have to think about something as abstract as relativity to realize that non-euclidean geometries are everywhere. Even the surface of the earth has a non-euclidean geometry (the geometry that takes place on the surface of the earth is called "spherical geometry"). In this sort of geometry, you can have triangles which can have two right angles!
The reason I am introducing all these different types of geometries is because in the end, relativity theory is a geometric theory of spacetime. If you can understand the context behind some of the different kinds of geometries, then you can understand the context behind relativity theory as well! In this way, relativity won't seem as mysterious anymore. It's still very counter-intuitive, but at least you can understand that relativity is just a consequence of choosing some set of axioms, and drawing conclusions from there, just like any other sort of non-euclidean geometry.
Sorry for all these other links haha. This topic is extremely interesting to me and I wanted to share some resources to hopefully get you excited about it too! :)
segelnhoch3 t1_j6nq4q1 wrote
Its a statement that is so basic, you cannot prove it. Because it is (together with other axioms) the basis for every proof.
These are the "assumptions" we make in order to get startet with proving stuff. For example, in math there is an axiom "there exists (the concept of) infinity" You cannot really prove this without using other statements like it that can't be proven.
breckenridgeback t1_j6o6fyq wrote
In this case, "axiom" is a bit misleading. It's an assumption, but not an axiom.
Relativity arose out of the observation that the speed of light was the same for all observers, which had become clear by the time relativity was developed. What relativity does is goes back and says "okay, what assumptions about physics are wrong in order for that to be possible?"
It turns out the wrong assumption was the idea that all observers, regardless of position or movement, agree on lengths in space and time.
-cool--beans- OP t1_j6nvj08 wrote
thank you so so so much. this clarified a lot. :)
DoctorKokktor t1_j6nvlwp wrote
No problem! :)
TwentyTwoTwelve t1_j6oxmkw wrote
Does the contraction only happen within the vector of travel or from all directions?
DoctorKokktor t1_j6pi9e3 wrote
It should only occur in the direction of travel of the object.
EDIT: Actually, length contraction occurs in a direction parallel to the direction of motion, not just the direction of motion. In other words, even if the object was going the exact opposite way as its original direction of motion, a stationary observer would still see the spaceship as being contracted. The only difference between moving toward a stationary observer and moving away from a stationary observer is that when moving toward the observer, the spaceship would be blue shifted and when moving away, the spaceship would be red shifted (relativistic doppler effect).
[deleted] t1_j6pi8qk wrote
[deleted]
n_o__o_n_e t1_j6ntu6k wrote
You have to think about us (and all other matter) as not moving separately through space and through time, but rather moving through spacetime.
On a ferris wheel, you are always moving at the same speed, right? However, the faster you are moving in the vertical direction, the slower you are moving in the horizontal direction, and vice versa. Your speed, the magnitude of your velocity, remains constant, rather it is the weighting of the horizontal and vertical components that make up that speed that changes with time.
Spacetime works the same way: Imagine a 4 dimensional analogue of velocity that tracks how "quickly" you move through spacetime. This quantity (rather unimaginatively named "4-velocity") is constant for all matter. In the same way as the ferris wheel, that means the faster you move through space, the slower you move through time. The magnitude of your 4-velocity remains fixed; it is only the weighting of the spatial components vs the time component that changes.
Humans are, relative to each other, effectively stationary: Nearly all of our motion through spacetime is, from any of our reference frames, through time. This is why we can, in daily life, treat space and time as unrelated quantities. u/DoctorKokktor's answer is a great example of how that breaks down in more extreme environments. If you ask why the universe behaves this way, we could point to the fundamental fact that the speed of light appears to be the same in every frame of reference, from which all the rest of this is derived. As for why that's the case, in physics the answer to "why" questions is always eventually "that's just how the universe seems to work".
One thing physics teaches you is that our brains evolved over millions of years to keep us alive on a cold, fairly small, low energy rock where nothing is moving very fast. The universe in more extreme environments is under no obligation to make sense to our extremely limited intuition
Biokabe t1_j6nx1g9 wrote
This is a tricky one, but I'll try to keep it simpler. I'm not certain that what I'm about to say is 100% consistent with the math of relativity, but it's reasonably close enought to at least understand why time dilation occurs.
With that out of the way:
First, the speed of light is not really about light. The fact that light travels at that speed is a consequence of the nature of photons. The speed of light is the ultimate speed limit of the universe - you could call it the speed of causality more accurately. In fact, in a sense everything travels at the speed of light - that might not seem accurate, but I'll explain more in a little bit.
Second, what is speed? It's how fast something is moving in a particular direction. All movement is directional - you don't just arbitrarily go fast. You travel along a path. Typically, we think of this path as three-dimensional. If you're flying in an airplane, for example, then relative to a stationary object, you're moving upwards at a certain speed, to the left or right at a certain speed, and forward at a certain speed. Add those together according to some relatively basic math, and you have your overall speed and direction of travel.
Third - what I just explained isn't actually correct, because it ignores something rather huge that all of us take for granted - time. You see, we don't travel a three-dimensional path. We travel a four-dimensional path. And that fourth dimension is time. For most objects traveling at the speeds most humans deal with, time is actually the largest part of our velocity. That's why time seems to pass at the same rate at the scales that you're used to dealing with - the differences between your time velocity and something traveling at 60 mph is so miniscule that it's impossible for a human to notice it.
Fourth - remember how I said everything travels at the speed of light? Well, that's why time dilation is a thing. Your total velocity through four dimensions must remain constant. So if you are traveling through space faster, then the only way for you to do that is to travel through time slower. So as you speed up, your experience of time slows down. However, because you have mass, you can never actually reach the speed of light. What happens instead is that as you get faster, the extra energy actually makes you more massive.
Incidentally, because photons travel at the speed of light, they don't experience the flow of time. From the point of view of the photon, its entire lifespan (from the moment it's emitted until it's absorbed by another particle) passes instantaneously and simultaneously. This happens because photons don't have mass, and so their velocity in the "time" dimension is 0.
LongAssNaps t1_j6nn790 wrote
If you stand still on earth and 1 second = 1 second, is there any significant difference in time dilation relative to an astronaut floating in space who is completely still? (ie, not pulled in any direction due to orbits of any kind? Is there any frame of reference in the universe that would allow an object floating in space to be completely at rest? (factoring in planetary, stellar, galactical orbits and the expansion of the universe?)
h4x_x_x0r t1_j6nqynq wrote
So if you stood completely still in space, let's say ignoring any gravitational pull, your relativistic subjective time would pass faster than anything else's in the universe that's moving, which is pretty much everything since gravitational pull affects everything eventually even by the tiniest bit. However these differences are marginal until you hit speeds in the c-percentages so most objects wouldn't get to those speeds by accident, in comparison, the ISS travels at 8000m/s (or roughly 0.000027% of c) and has in its lifetime experienced roughly 1/10s in time dilation. So a human spending their entire life in a comparable orbit would get ~1s more subjective lifetime, compared to earth, accounting for all the bad stuff space does to your body, probably not worth it.
However the dilation is measurable and has to be accounted for e.g. by satellites because for electronics, these "rounding errors" can add up and cause problems.
Bensemus t1_j6nsni2 wrote
The largest reference frame is the CMB. There is no absolute reference frame which is a fundamental part of general and special relativity.
[deleted] t1_j6o4d8q wrote
[deleted]
confuseray t1_j6omglg wrote
As if you're 5??
Ok I'll try. All of us are always moving, even if we think we are standing still. You see, even if you stand as still as you can, time still passes for you. You're still moving through time.
Scientists have determined that this stuff we move around in, this...space, this reality it's actually part of the same stuff as time. We can call it spacetime.
Now, there is a max speed you can move through spacetime. We don't really know why, it's just a rule of the universe. If you stand as still as possible, you move through time as fast as you can. 1 second a second. If you start moving though, you increase your...spacespeed. You start subtracting from your timespeed.
Now the way the conversion ratio works, if you're moving as you normally do, you don't really slow down moving through time much. You have to move really really fast, like light speed fast, to have a significant effect on your timespeed. And as you get closer and closer to lightspeed, your timespeed gets closer and closer to zero, because you're taking that travelling speed away from time and putting it into spacespeed.
CryonautX t1_j6ori4c wrote
Short answer: It had been decided that light will always move at a specific speed no matter who or what observes light and even time itself would bend to make that be always true.
Long answer: Let's start with understand a bit about relativity. Let's say you're on a train with a friend and your friend gets up and walks towards the bathroom. From your perspective you see your friend moving at about walking speed towards the bathroom. It's not particularly fast. But what about someone outside the train? Let's say a man is standing a safe distance away from the train tracks and your train zooms past this man. This man sees your friend who was walking to the bathroom. From his perspective, she is going really fast and is zooming past the man. Now your friend has 2 speeds. One really fast speed from the perspective of the man outside the train and a slow speed from your perspective. Both speeds are correct and it all depends on what the speed of the observer is. Everyone will have many different speeds just like your friend and that is what relativity is.
But here's the thing. Light is special because it will always have 1 speed: c! No matter who the observer is and how fast the observer moves, light will always move at the same speed(in vacuum) which is a specific number that is roughly about 300 million meters a second. Now obviously this would seem to contradict the earlier point about relativity but here's the magical thing that lets light move at c. The observers looking at light will either have their time sped up or slowed down to make it such that light is moving at c. So if you try to run really really fast to try and catch up to light, light won't appear to have a lower speed, it would still be moving at c by magic because time slows down for you and light will appear to go faster to make it so it moves at c.
Salindurthas t1_j6p8zn2 wrote
Space and time are related. We call them together 'spacetime'.
You have a limited and fixed speed through spacetime.
If you are statioanry, then all your speed goes into time. You get to go the maximum rate through time. We'll call it aging 1 second per second.
If you move, then you have to split your speed between time and space. If you move slowly through space, then you might age 0.999999 seconds per second, which is hardly a ntoicible difference. If you move very fast through space, then you might age 0.10 seconds per second, which is a very noticible.
Some objects move just fast enough, and need precision timing enough, that we notice it. Like software that works with GPS satellites needs to account for the tiny time dilation between them, because that tiny difference would make a difference in where the GPS believes you are.
fiendishrabbit t1_j6pcg2u wrote
I kind of imagine this as a ping-pong ball going up and down. The ping-pong ball always travels at the speed of light.
Now ping-pong ball is put on a ship, and that ship starts travelling. The ping-pong ball is still moving at the speed of light, but as the ship travels faster and faster the ping-pong ball is moving sideways. From inside the ship the ping-pong ball is going up and down (and time stays normal, but only from the perspective of the observer that's travelling with the ping-pong ball). From an outsiders perspective the ping-pong ball is going to move in a zig-zag movement. As the ship goes faster the zig and zags will be longer and longer, and so (since the ball always travels at the speed of light) it's going to travel up and down slower.
Now. This is applied to all reactions between particles. Everything is going to move slower and slower since their movement is capped at the speed of light and more and more of their movement is taken up by keeping up with the movements in realspace. Until, when the ship travels at the speed of light, time becomes infinitely slow.
the_criminal_lawyer t1_j6pfu1p wrote
Because you're catching up to the speed of time.
A photon traveling at the speed of light is also traveling at the same speed at which time "happens." Because it's going the same speed as time, the photon doesn't experience time passing at all.
When you go faster and faster, the difference between time's speed and your speed decreases (from your perspective). Should you ever get to light speed, it would seem to you as if time had stopped.
DoctorKokktor t1_j6nm87v wrote
You're asking about relativity, which isn't exactly a subject that can easily be explained in simple terms. But I will try my best.
To understand why time slows down with increased velocity, you must first accept that the universe conspires so as to keep the speed of light the same for ALL observers, regardless of their frame of reference. This axiom of the constancy of the speed of light is directly responsible for time passing at different rates for different observers. Let's see how.
Suppose that you have a friend who is stationary (with respect to, say, the Earth). Suppose also that you're in a spaceship travelling at, say, 0.5c with respect to your friend's frame of reference. In other words, if your friend measures your speed, they will see that you're moving at 0.5c. (c = speed of light, so 0.5c means "half the speed of light").
Now, let's perform a physics experiment. Actually, let's perform two experiments -- you perform one experiment, and your friend performs the other experiment.
Inside your spaceship, you try to measure the speed of light. How do you do that? Well, c = d/t and so you measure the distance that light travels in a certain time period. Suppose that you measure how long it takes light to reach from one end of your spaceship to the other end. You know what d is because you can easily measure the length of your spaceship. It is important to note that your clock and your measuring stick retain their length. 1 meter is exactly equal to 1 meter, and 1 second is exactly equal to 1 second in your frame of reference. This sounds like a really dumb (and obvious) thing to say, but keep it in mind. So, you measure what t must be. Then, when you perform the calculations, you get that c = 299,792,458 m/s.
Likewise, your friend, who is not in your frame of reference, also performs the same experiment. He also notes that 1 meter is exactly equal to 1 meter, and that 1 second is exactly equal to 1 second in HIS frame of reference (again, a seemingly dumb observation). He measures the speed of light by measuring how long it takes light to reach from one end of your spaceship to the other end. When he does the calculations, he too gets that c = 299,792,458 m/s.
How is this possible?
It's because when your friend measures distances, he finds that your spaceship is actually SHORTER than what YOU measured. Even though 1 meter = 1 meter for him in HIS reference frame, and 1 meter = 1 meter for you in YOUR reference frame, when you compare the length of a meter from one reference frame to another, 1 meter in one frame of reference is no longer equal to 1 meter in the other frame of reference: your friend has just discovered the phenomenon of length contraction.
Now, c = d/t, and your friend measured d to be shorter than what YOU measured it to be. Yet, c must always equal 299,792,458 m/s for both you and your friend. How is this possible? Well, if d is different for your friend, then t must ALSO be different. However, the RATIO, d/t MUST equal the same: c. Hence, if d is smaller, then t must be bigger so as to keep the ratio, the speed of light, the same: your friend has just discovered time dilation.
This makes sense -- the word "contraction" in "length contraction" means to shorten. The word "dilation" in "time dilation" means to lengthen. So, if length contracts (i.e. d is shorter) then time must dilate (i.e. t is bigger) so as to exactly compensate.
Now I hope you can appreciate "relativ"ity. In your reference frame, time and space act the same -- 1 meter = 1 meter, and 1 second = 1 second. Likewise, in your friend's frame of reference, 1 meter = 1 meter and 1 second = 1 second. However, 1 meter in your friend's frame of reference, WITH RESPECT TO (i.e. RELATIVE TO) your frame of reference is no longer 1 meter. Similarly, 1 second in your friend's frame of reference RELATIVE TO your frame of reference is no longer 1 second.
Weird stuff starts happening only when we start measuring things RELATIVE TO other frames of references. Otherwise, in their own individual frames of references, everything appears to be normal.
Once you have understood the above, then the next natural question to ask is "why does the universe force the speed of light to remain constant for all observers?" And unfortunately, physics doesn't have the answer to this question. It's just how the universe seems to work. Perhaps a deeper theory will answer this question.