We All Move At The Speed Of Light… Kind Of.
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- čas přidán 3. 05. 2024
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The speed you know is only your spatial speed, but you also have a speed through time. The two together make something called a 4-velocity and its size is always the speed of light.
Nick Lucid - Host, Writer, Editor, Animator
Em Lucid - Producer
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TIME CODES
00:00 Cold Open
00:37 Introduction
00:48 3D Velocity
01:31 What is a Tangent?
02:12 What is Speed?
02:46 Coordinate System
03:47 4D Spacetime
04:18 4-Velocity is just like 3-Velocity
04:57 Mathematical Definition
05:43 The 2 Points of View
06:23 Intuition
07:24 What about Photons?
08:08 Summary
08:26 Sponsor Message
09:48 Outro
09:54 Featured Comment
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Thanks! I'd like to take some credit for suggesting this. It's one of my favorite concepts.
But Shirley, this doesn't fit in with the Block Universe? One doesn't normally think of anything moving within the Block Universe.
Also we all move faster than the speed of the light depending on the relativity! So why didnt go with this better video? 🤔
Βro, the Greek τ is pronounced "taff" in Greek. That "tau" thing has a "u" that is not pronounced as "oo". It is a myth that it sounds like taoo. In reality it is pronounced like taf or tough...
@Seventh7Art Let's ask 10 physicists...
@@numbersix8919 Physicists are not linguists. I am sure you know the difference. The same applies to the Greek letter π which is pronounced like a pie, when in reality it is like pee but with a short vowel sound. Greek letters can only be pronounced correctly, when you use the original Greek pronunciation. Anything else is a corrupted version. Δ which is known as Delta, in reality it is "Τhelta" where th does not sound like in "thesis" but like "they".
I feel so lucky to live in a time period where I can learn relativity from someone for free! You assume the watcher knows little but can explain it in such simple terms. I love your content so much, you are a gem to have on youtube.
Advice I received: "Don't underestimate your audience's intelligence, just their vocabulary." and I try to live by that as much as possible.
@@ScienceAsylum That's great advice for anyone.
It's okay to be a little gem 😂
One of the reasons I like this channel so much is the fact that complex ideas are explained in a simple way so you don't need much math or physics background to understand them.
dont forget the the friendly animations they the best to follow along
I'm in agreement with you! Math is a more precise way to express generalizations. Accuracy comes from how we define things, which can also be improved with math. I hope one day math can provide you with as much satisfaction as friendly explanations :)
I’ve been arguing this for years. Now I can just point people to this video instead of explaining it poorly myself 🙏
You could also point people to a FermiLab youtube video posted about 6 years ago, titled "Why Can't You Go Faster Than Light?" And I think the PBS Space Time channel posted a video about this about a year or two ago.
I'm going to post a comment soon that you might want to read.
Yes.. I called "c", the "c" magnitude of motion, rather than speed of motion. Many many years ago, I mentioned how even a high school dropout who knows nothing about physics, can still derive the Special Relativity(SR) equations if just able to recall a bit of math and a bit geometry, and taking this constant "c" magnitude into account. Nobody believed me. So about 10 years ago I jumped onto YT to prove my point.
Yep same, when I first read about light speed years ago, this was also my understanding on what was happening, it is easier to imagine it as changing a ratio.
I had a thought about this recently. I tried to imagine what it would look like if something stopped moving through time. Let's say we have a box at rest. Even if it looks motionless, it's still moving through time because at one instant, it's there and at another instant, it's still there. But let's say it stopped moving through time. What would happen? One instant, it's there. The next, it isn't. And it's not like the box went somewhere else because that too would require motion through time. No, in this case, the box just up and disappears. It's literally erased from the universe, violating conservation of mass and energy, which isn't possible. Which is why everything must always be traveling through time, because otherwise conservation of mass/energy wouldn't be valid.
It's also interesting how this line of thinking hints at the underlying connection between time and mass/energy conservation. Of course, we know it's really energy conservation that stems from time symmetry so it's kind of easy when we already know what to look for 😀
And it shouldn't be that surprising that energy is the time component of the 4-momentum 👍
I thought an object that isn’t moving in time is moving at the speed of light? Can’t move faster but if none of your energy is in the time direction then it’s all in spatial. All C of it!
@@richardwallis9374 Interesting point. I hadn't thought of that 😄
7:03
Note that when he said "a loss in temporal speed," what he meant is that as the rock moves faster, the proper time of the rock (𝜏) passes more slowly. However, since we defined the temporal speed as dt/d𝜏, the denominator of the derivative becomes smaller as the rock moves faster. This implies that both dx/d𝜏 and dt/d𝜏 approach infinity as proper time passes more slowly.
What he intended to convey is that more time passes for us than for the rock.
As the rock approaches the speed of light, both dt/d𝜏 and dx/d𝜏 approach infinity. This also means that you cannot use the Pythagorean theorem to add velocities. In spacetime, you have to use the Minkowski metric, which is:
ds² = c² d𝜏² = c² dt² - dx²
it means the total velocity is
c² = c² dt²/d𝜏² - dx² /d𝜏² = c² (Uᵗ)² - (Uˣ)²
if you define the temporal velocity in spatial unit
then c² = (Uᵗ)² - (Uˣ)²
Thanks for the info! Gonna return to your comment a bit later when I have the chance to compare what you're saying to the visuals of equations in the video.
I heard about this idea a few months back and, while I’m sure I don’t fully grasp all the subtleties, it’s the first picture of the universe that makes me *believe* nothing can go faster than the speed of light. I accepted it before but always with a “…but what if…” tacked on. But if the speed of light is the speed everything is going in 4-space, then nothing can go faster than C in 3-space because there’s no place for that extra velocity to come from.
*"Nothing can go faster than C in 3-space because there’s no place for that extra velocity to come from."*
Exactly! 🤓
My son, 9, is gonna be so stoked there’s a new video! We watch these in bed at night before sleeping. Keep up the good work. (I’m excited too).
That's wonderful. Thanks for sharing!
Always learn something worthwhile from your videos no matter how much advance knowledge I already had! This one had a slight vibe of your older videos in pacing which seems to blend nicely with your currently more visual content. Will re-watch one or two more times, as it went really deep. Love it!
This is the video i was looking for! I dont think ive seen anyone else explain this. I believe you mentioned it was coming soon. Thanks for the many explanations, one of my favorite science channels.
Everything comes back to circles and trig. There's no escaping it.
Speaking of getting different sources of information, I have heard about this stuff about moving at the speed of light before, but it was great to finally hear your take on it as well.
Thats 'cause you live inside world managed by a self concious computer/entity. Kind of. can't better describe it. All energy and thus everything which comes from it, is alive. Yes even smallest particles are self aware and can think for themselfves. You just can not proove it yet. You can think of the world as like a holodeck from StarTrek, you just do not know the pass to open doors to the main world. 😁
Yep, the simple math is always there. People often ask me what equation I use the most expecting me to say "E=mc²" or something. The answer is always "the quadratic formula" 😆
Sometimes they don't come back to circles. Sometimes they come down to hyperbolas! (Though it's still trig, just hyperbolic trig instead of spherical trig.)
When I saw the title, I thought it was about us moving at the speed of light relative to an observer on the cosmological horizon.
Is that like the unruh effect?
Everything moves with the speed of light. We gain massful particles, by enclosing a massless particle, which is moving with the speed of light, into a confined space, like a quark or an electron. These particles act like a clock, where every so called “oscillation” of that massless particle is a “tick”. If we move the massful particle in space, the massless particle in it needs to move along, and less of its speed is spent on “ticking”. Therefore time slows down.
And since all of the particles in our body is built like that, including our brain, everything slows down.
Aren't we traveling faster than the speed of light?
From a distant galaxys perspective - we are at the edge of their visible universe - and as such, we are moving away from them faster than the speed of light. The space surrounding us is expanding and we are being carried along with it, faster than light speed.
A friend told me about this and I've been waiting eagerly for a great explanation from yours truly
A new perspective on understanding the speed of light
always happy to see a good video on relativity posted
Yep. Matt on Spacetime taught me that as matter I’m traveling through time at the speed of light.
Thank you Nick Lucid!🌈
Another great video...I'll have to watch it again to really grasp it crazy for life!
I liked this explanation a lot. I learned a lot of this through the in-variance of the interval concept. That and c = 1. But this gives a good perspective where it clears up who's time is it anyway.
So essentially, everything always moves at the speed of causality through space-time, and if you want to move faster through the spatial dimensions, that necessarily means you move slower through time, otherwise causality would be violated.
Good to see you in motion!
On another tangent… you mentioned your book. I need a copy, preferably signed! Thanks for continuing to make interesting content that expands our crazy minds!
I absolutely LOVE this relativity stuff, especially when we go TO THE TIMELINE!! Seriously, relativity does interest me the most...even if I am a geologist.
Hey... what do you think of this obsidian knife i'm holding on my left hand?
I love the relativity stuff too.
@@ScienceAsylumMy dream is you making a video when you focus on the timeline; what exactly led to the discovery of relativity. Lorenz, Minkowski, who helped Einstein with maths on GR? To the timeline!
@@GraveUypo Is that your LEFT HAND? or are you just looking at it from a different perspective?
@@GraveUypooh shit -- OP, run and don't get obsessed over obsidian!
This is such a good explanation. I wish my undergraduate classes had shared this, and 4-d thinking had been introduced earlier. The explanations of spacetime diagrams were more confusing that enlightening, and these were foundational to understanding later work.
The traditional method of teaching relativity is to start with algebra, but I've noticed that seem to ingrain misconceptions in people's heads. Starting with diagrams is the best method. There's a lot less room for preconceived notions to sneak in.
That was one hell of a smooth transition
Maybe a pov thing.
Consider the twin paradox. Earl stays on earth, while his twin Rocky takes off in a rocket close to speed of light. They meet up in 10 years earth time. Earl has aged 10 years, but Rocky has only aged 5 years due to time dilation. So Rocky has traveled 10 years in only 5 years. He clearly was moving faster through time. He was also moving faster through space. They could not both have been moving at the same speed. Therefore they were not both moving at C.
Incredible video as always!
Thanks!
Great explanations as usual!
Thanks! Glad you appreciate them. I put a lot of thought into these.
Great video! Also, Ground News is amazing, thank you!
Oh good! I've always been nervous to take a news sponsor, but they seem like they have a good mission.
Yes! I have thought about it!
Love the Eye of Sauron shout out...
I always get excited every time you upload a new video...
I'm glad you enjoy them.
Nice breakdown , seen the circle explanation on scienclic and you defo warm us up to that from a more beginner level .
Awesome job on a really complex subject that is just there to shoot people down . I found it tricky to follow first time when I wasn’t watching the screen but your graphics really helped .
Have a wonderful Xmas to you , the clones and your amazing wife 👨🔬👩🔬
I keep hearing a lot of people listen, but don't watch 🤔. Makes me wonder if, maybe, I should only put a graphic on the screen when it _really_ matters.
@@ScienceAsylum for instance it’s great to put you on while I’m driving , or cooking . Great to listen to and then review a second time in the evening when I can concentrate more . Defo no harm in the graphics though although it does mean less screen time for you 🙌
@@ScienceAsylum I always find the graphics to be essential but I have aphantasia.
I picked this up in The Elegant Universe but Nick always has a great way of teaching
I see the edges of it, but I think I'm missing a few connections. Maybe the cake just needs to bake a little longer. These videos have opened my eyes. Thx!
But spacetime is hyperbolic!
(4 velocity)² = (temporal velocity)² - (spatial velocity)² = c²
The magnitude of this 4 velocity is always c (using the (+,-,-,-) metric)
So the faster you move through space, the faster you move through time.
Faster... slower...
Amazing as always!! I’ve always thought about what it would be like him. We had two or three temporal dimensions and what that would potentially cause we’re how it would make our physics equations and things completely different, as well as real world, stuff and technology.. very very neat stuff!!
Videos about light are my FAVORITE 🎉 it can be so trippy and exciting!!!
I don't think time without motion is even possible. Time is a measure or description of motion. Also, in terms of our physical brains time is a sensory and conscious perception that can only exist as a result of molecular motion.
The reason this video has lower engagement is not the thumbnail...it's the clickbait ass title. I love all your videos, the title is just a bit off putting tbh. We respect you for your knowledge, we'll watch you even without all the hype
The speed of light is really only limited by the speed of causality for which everything (seemingly?) happens instantly. But 'particles' that interact with mass (such as us) travel much slower than the speed of causality and therefore experience time.
I tend to think of our current experienced reality as existing in slow motion relative to the actual 'speed of time' (speed of causality/light).
Loved this on Nebula ❤
6:51 "In relativity, the faster we see something moving, the slower we see its personal time pass"
Here's what I don't understand. If you're the astronaut, then in your view, the rock's time is moving slowly. So one second for the rock is equal to several seconds for the astronaut. That means from the rock's perspective, the astronaut's time is moving really fast (many seconds pass for the astronaut while only 1 second passes for the rock). BUT that doesn't make sense, because from the rock's perspective, the astronaut is moving really fast and thus the astronaut's time should be moving slower.
*"If you're the astronaut, then in your view, the rock's time is moving slowly. So one second for the rock is equal to several seconds for the astronaut."*
Correct.
*"That means from the rock's perspective, the astronaut's time is moving really fast."*
Incorrect.
*"From the rock's perspective, the astronaut is moving really fast and thus the astronaut's time should be moving slower."*
Yes, exactly this. They each see each other's time pass slower. The reason that works is because two observers traveling at constant velocity in a straight line never have more than one event in common. That means they can only ever agree on when to start their watches _OR_ stop their watches, but never both.
@@ScienceAsylum Thank you. Intuitively it still feels like a contradiction. Can you entertain this thought experiment for me?
Thought experiment: Let's replace the astronaut and rock with two pieces of cheese. Let's say that cheese starts with 0% mold and gets more moldy over time. Let's say the moving cheese goes out for 1 hour, changes direction 180 degrees suddenly, and then comes right back. At the point where it passes the fixed cheese, which piece of cheese is more moldy?
From the perspective of the fixed cheese, the moving cheese will grow mold more slowly, so when they pass, the fixed cheese will have MORE mold than the moving cheese. BUT the moving cheese could say the same thing about the fixed cheese. So which cheese will have more mold? (Does the change in direction mess up the experiment somehow?)
@@mariusfacktor3597 The cheese who went there and back will be less moldy when they meet. It's the famous twins paradox. I find these 2 short videos explaining it best: czcams.com/video/Bg9MVRQYmBQ/video.html
I've been trying to tell people this for years, usually they just stare at me blankly, but now I can show them this video instead!
I've always thought of it as you travel the speed of light through time and space. The slower you move through one the faster you move through the other.
Although it's common to use the Special Relativistic equation that's in hyperbolic form
c²t² - x² = c²τ²
which leads to the imaginary coefficient i when you take the square root of the negative term, as Nick did, I think that's a mistake in this context. It makes more sense to subtract the negative term from both sides of that equation to arrive at the Pythagorean form of the equation:
c²t² = c²τ² + x²
Next, divide both sides by t² to get
c² = c²τ²/t² + x²/t²
That's more relevant in the context of the "speed" through 4-dimensional spacetime, because τ/t is the traveler's rate of aging from the perspective of the stationary observer (the floating astronaut), and x/t is the traveler's speed through 3-dimensional space from the perspective of the stationary observer. Together those two terms provide the traveler's "speed" through 4-dimensionsal Minkowski spacetime, from the perspective of the stationary observer. The c² coefficient in the c²τ²/t² term is just the conversion factor between the arbitrary units of time & length, and is equal to 1 if the units are chosen appropriately:
c² = τ²/t² + x²/t²
Note that it's a Pythagorean equation, where the square of a right triangle's hypotenuse equals the sum of the squares of the triangle's other two sides. The hypotenuse is the "speed" of the traveler through 4-dimensional Minkowski spacetime (which has the time dimension orthogonal to each spatial dimension, which means the triangle is a right triangle). So the square root of the left side is the traveler's "speed" through Minkowski spacetime... it equals c, the same as the speed of light through 3-dimensional space (and it equals 1 in the appropriate units of time & length). This equation works for any kind of traveler, including light.
And it does NOT have the imaginary coefficient i that Nick mentioned, assuming the travel through 3-d space isn't faster than light.
The equation also tells us the rate of aging of a traveler that's moving through 3-d space faster than light. It's not negative... it's the square root of a negative number, so it's imaginary. But it's unclear whether aging at an imaginary rate has any physical meaning, so it might be impossible to travel faster than light (in Minkowski 3-d space).
I was confused by the thought I should be traveling at the speed of light from the perspective of a photon, but since photons don’t experience time or space, such perspective shouldn’t exist.
Fun fact: Rail Track Engineers refer to straight sections of track as ‘tangent track’!
Interesting!
Going into this blind I’m guessing some percent of our total speed is invested in movement through time.
Edit: friggin called it.
Yep. I learned this on another channel a couple of years ago. Came to see if he adds anything new to what I've already learned.
99.9% or so.
gj
Yup. Nice! Tho it might be more intuitive (or not) to just think of it in reverse, so...
*"The faster you move through space, the slower you move through time".* 👻
Well done!
you explain nicely.
Thanks!
That 4-V is an important clue in how gravity works. Give light a reason to slow and Time has to change with it, which changes the accelerations in all the subatomics in every bit of normal matter.
8:59 .... DAYYYYYUM. He's not wrong, though.
I used this explanation once during a bar argument. I was too many beers in to go into the Lorentz transformation, length contraction, infinite energy, etc, etc. I feel vindicated! Although I don't actually remember whether I won or lost the argument, or why we even got into the discussion in the first place. 😅
So if we stop moving, we get to experience more time?
Time to go lay down on the couch! 😁
The sloth knows better.
Hi. You are a genius. ❤the most complex stuff made simple. Never banal… ❤❤❤❤
Brilliant 🤩
That's a great way of thinking about spacetime. So much simpler than a ball bouncing as a train goes by 😉 Thanks for sharing 👍
but the ball gave us dt/dtau
@scienceasylum I don't know the numbers, but it seems like cosmic inflation could be explained by spacetime slowing down. Therefore everything gets farther from one another.
Photons are identical to what they've always been, but spacetime itself is slowing down so interactions occur less frequently.
Anyhoo, just a thought. Would love to see that video 😁 I've been talking about it for years with little traction.
Note also that this would imply that everything is shrinking (I think anyways).
Science is Bonkers, thanks for all your great shows, Have a wonderful Christmas and New year. PEACE AND LOVE TO EVERYONE ❤❤.
You have a good holiday time with your family also 🙂
Best segway to the sponsor's message yet.
I do not (yet) have an opinion on the content. I think three or four views will be needed before I "get" it. And reference to my copy of your book.
It’s actually way more trivial. Speed (or frequency) is whatever you’re counting (milles, meters, ticks, seconds, etc) divided by a standard time unit, eg seconds. All matter travels through time at a speed of one second per second. If you measure your own speed through time, you’re actually measuring your own clock’s rate, which is always a trivial 1 (s/s). This is also the constant speed of the 4-velocity.
Saying that the 4-velocity speed is ic, is technically the same, based on the idea that a time unit is an imaginary distance, like one second equals i lightseconds. It’s just a more complicated way of saying it.
Personally, I prefer to think of it the other way around: time is real and spatial distance is imaginary time, so a lightsecond is an imaginary second and c = i.
Actually the faster an object moves through space the faster it also moves through time as spacetime is anti euclidean, meaning that the square of the spacetime distance is equal to the square of the distance through time minus the square of the distance through space. When an object moves faster through space it actually has to also move faster through time in order to maintain the same speed through spacetime, in contrast to what one would expect from normal euclidean geometry.
I think it depends on whose coordinates you use to measure the passage of time.
Love it when you show anti-intuitive concepts. Because all matter has to experience time, it can't ever put all it's velocity into space. Because light has to always travel at c, it can't ever experience time.
Someone asked me what speed do time travelers move at and I was thinking about this idea of change in time being inversely related to speed to some extent.
Sorta made sense for me intuitively, but makes it concrete
This is very interesting.
Right before this video, I read an alternative theory about the expansion of the universe.
He explains that the universe has an expansion rate of the speed of light. But then only in the 4th dimension.
Thus the space we see is 3d, but as a surface on a 4d sphere.
Not does not explain the expansion rate we have found in the 3 space dimensions.
But if we use that 73 km/s per Mpc, we can use it to calculate the age of the universe.
Which then ends up roughly the same as what scientists have discovered so far.
Maybe this "out of the box" theory, if correct, can be linked to what you explained in this video.
"Because of a weird quirk of reality," is gonna be my new favorite answer I give to questions about basically anything.
"Weird Quirk of Reality" would also make a good album name.
Who can't love this guy?
Now all we need is a case for or against the video topic with regards to space-time expansion.
The accurate use of the verbal metaphor is much closer to the literal than you think, being a comment which begins from a single point of connection with the initial subject in a direction which will never again return to intersect the initial subject however far you follow it forwards or backwards
This is why we always measure light in a vacuum at the same speed. If we move faster through space in spacetime then we will move slower in the time dimension. More correctly, we're always traveling through time as fast as physically possible dependant on our velocity through spacetime.
The whole, "generalize things to death" joke is _awesome!_
😁
You don't know how right you are. We are moving with the speed of light and light moves with a speed ... zero.
True
Thank you for addressing this. Too often I see people asserting that lightspeed is a barrier that can be crossed, and that time travel exists on the other side of that line, because they have this fundamental misunderstanding of the nature of C. They don't conceptualize space-time as a singular structure and still try to talk about space, time, and speed/velocity as though they're all separate things. And these aren't just simple members of the science laity. These are actual science communicators and otherwise well educated people who should know better. There is only one other science channel I've seen address this concept, and I share their vid every time I see someone make the flawed claim that C is some kind of barrier that can be crossed if you just have enough kinetic energy.
only seen 30 seconds and i already love this video!
A force applied at 90 degrees to motion doesn't change speed, it changes the direction of the motion. If time is simultaneously 90 degrees to x, y, and z, like z is simultaneously 90 degrees to x and y, then any force we apply in our three dimensions can't change time axis speed, it would change time's direction and it's projection into our beloved three dimensions.
That makes sense to me. I do not have the education to know if there is anything to it or not, so please don't carve my face on Mount Dunning-Kruger. I just like to daydream.
As a physicist, I'm qualified to supersize your order of fries. Past that, not so much.
Oh my goodness, time speed and space speed are traded for each other,
oh my goodness the relationship is quadratic-hyperbolic, thats why things at the 100% speed of light do not really experience time, theyre like, at the limit
*"That's why things at the 100% speed of light do not really experience time, they're like, at the limit."*
Exactly!
And when you combine this fact with "now slices" that span the Universe and change what is happening "right now" in other parts of the Universe depending upon which speed you're moving...it's hard not to think of the Universe as one big pre-recorded event. Yes, I'm saying the future is pre-determined. It almost certainly has to be if someone on the other side of the Universe can see my future just by traveling at a different speed.
We live in a pre-recorded simulation that is stuck playing on loop.
I go to the other extreme and think of the universe as one giant collection of _local_ "heres and nows."
8:20 "If a factoid sounds simple, it's probably at least a little wrong."
Occam's lesser-known electric razor.
Hey, maybe the Science Asylum can market Occam's After-Shave. Which of course would be unscented.
I enjoy looking at this as an intuitive explanation of how falling objects get their speed from gravity. A falling object looks like it accelerates for no "good" reason-- nothing is pushing on it; where is the energy for movement coming from?
When we think of gravity as representing the curvature of spacetime, and conceptualize all massive objects as moving through spacetime at c, it becomes apparent that a falling object isn't getting its acceleration from "nothing"-- it's just changing the direction of its 4-velocity, from entirely through time to mostly through time and a little bit through space.
Not even that. It's just moving in a straight line. It's just that space is warped. There are no forces in gravity. (A good analogy is 2 person some distance apart on the equator on earth walking straight north at constant velocity. The distance between them will get smaller until they meet at the North pole. But theres no force acting on them that results in moving closer. It's just that ther straight parallel paths cross each other)
@@Fluxikator Another good way of looking at it! What I mean in terms of your North Pole analogy is that the 2 people don't need a reason to start "walking" through bent space-- rather, they are always walking, just through the dimension of time, which through gravity has detoured slightly into that bent space.
If you go faster than the speed of light, you’d go back in time.
If you wish to exit a black hole, you’d need to go faster than light to escape. If you went faster than light to leave a black hole, your present state was in the black hole, you’d be going back in time which was before you went into the black hole.
Potentially if a black hole has so much mass that exceed the speed of light, it’s not where the matter is that went into he black hole, it’s when.
And perhaps that’s the entire cyclic nature of the universe, black holes send matter back in time to which the matters future will eventually be… to return to the black hole.
All I know is that objects with mass make time run slower to the observer, even though their proper time is unaffected.
Being a bit weighty, that explains why I always seem to be late, even though I could swear that my watch is keeping the correct time.
Another plat that might be useful is to plot an objects total distance traveled a vs time. Total distance (D) traveled would be like what an audiometer measures in one's car and thus only monotonically increases and never decreases (that is never legally).
Thus one can have two graphs for any object , one that is 2D, time vs total distance traveled and a 3D plot, x, y, z where t is a parametric variable (i.e. would be seen as tic marks on the paths of the x, y, z traces.
This approach might be a bit easier to visualize than say a 4D plot but has all the info for all four dimensions.
And for that 2D plot (T, D) one might add a 3rd axis that stands for S, that defines what is simultaneous, that is two objects with the same s cannot effect each other unless they occupy the exact same x, y ,z coordinates. This then could be see as a stack of 2D planes where each plane is a unique value of S.
This too can define an extrinsic coordinate system where Einstein's equations could be written as such vs using intrinsic coordinates as Einstein chose to formulate them. This too might be easier to visualize vs curved space time and the Christoffel coefficients also are simpler than when using intrinsic coordinates.
Also, one could model the expansion of space by having a scale factor vs s between the T, D, S plot and the X, Y, Z plot. Thus D is scaled by lambda and is mapped to each corresponding point in x, y, z space.
Note if this is done right it should give the same results (for all invariant quantities) but it might be a bit easier to visualize as such.
I prefer just to think of velocity as the angle between two lines on a spacetime diagram (or rapidity as the hyperbolic angle).
Rapidity is the superior way to look at speed.
This is true and matter doesn't move through space. What we call time is just displacement in 4D spacetime. This is why everything shares the same spacetime interval. So the speed of light is like a projector speed. It gives you a limit to how fast displacement occurs in spacetime. So it's frame by frame by frame and the speed of light is how fast these frames can be projected. At the speed of light there's no frames or time. How can anything actually move through space when nothing can reduce the space time interval?
Whoa dude this is deep
Another way to think of this is that you don’t feel velocity, but rather, you feel acceleration - changes in direction. The quicker that change in direction, the more force you feel.
Think about it. When you’re sitting in an airplane flying above the earth at 500mph, you don’t feel like you’re moving, except moments of turbulence, and when the plane turns. Same in a car. You only feel anything when you speed up or slow down or turn, or hit a bump.
Bizarre, huh?
There is a philosophical question for me...
So as I understand it it doesn't matter if a car is going forward or backward, time dilation is always the same when I look at it from my frame of reference (small, but still present). I use the car analogy here because a car has a defined "front" and "back", I could also say "rocket is going to the left / to the right from my POV", of course.
On the other hand, time has a clear direction from my POV.
So at least there is one really significant difference between space dimensions and the time dimension. Space: direction doesn't matter, time: direction is very important.
Yep, exactly. That's why I said "not exactly the same, but similar." 👍
Man, Ground News are sponsoring every video in my timeline this month
They're really pushing their holiday sale.
Since the magnitude of this four-velocity vector is always C (representing the speed of light in the three spacial dimensions and "normal" passage of time in the temporal dimension), we can take something's observed speed and derive the observed speed of its clock by treating those two values as two legs of a right triangle whose hypotenuse has a length of C. In other words, there is a tight mathematical relationship between the Lorentz factor and the Pythagorean theorem. And if you look at the Lorentz formula, you can see how an observed speed of C gives you division by zero, which is bad for it. Similarly, if one side of a right triangle has the same length as the hypotenuse, the other side has to have a length of zero and... you don't really have a triangle anymore. Not a very good one anyway.
If your feeling bored, maybe you can share your thoughts on a hypothesis I've been playing with... I'm sure you get these all the time, but I find this concept intriguing and It seems to me that it could answer a lot of seeming paradoxes that we see under the current models. It's nothing too crazy, and really it's just subtly different from current QFT models, but I feel it could have some merit...
This hypothesis maintains the core principles of QFT, particularly the existence of fields that underlie all particles. However, it deviates from QFT in its interpretation of how these fields manifest as particles. In traditional QFT, particles are continuously existing excitations of these fields; in this revised model, the particle like excitation with defined properties only exists during an interaction, Kind of like the initial spike when a stone is thrown in water, but unless there is continuous interactions between fields, like a standing wave pattern, such as is seen with orbitals, the propagating excitations are not particles themselves but are pulses that carry the potential for particle-like interactions, not all that unlike the ripples that propagate out across the water after the stone is thrown in. An important note is that the energy from the interaction become diffused across the probability wave, which if spreading out spherically, decreases at the square of the distance. So the probability wave and the "potential wave" are one in the same.
The core concept hinges on the idea of "field renormalization" in which the fundamental fields only communicate locally, but will renormalize/harmonize after an excitation, which only occurs during "measurement"/exchange of force carriers, giving the appearance of nonlocality, or even retro causality... I'll explain.
In this revised framework, fundamental particles such as photons, electrons, and quarks are not considered as discrete, continuously-existing entities. Instead, they are manifestations of pulse-like waves of field potential within their respective quantum fields. These pulses are akin to fluctuations in voltage or pressure waves, carrying the necessary information to exhibit inherent particle-like properties during interactions, but are too diffuse to be considered as particles themselves.
In this model, quantum fields are constantly fluctuating, not unlike the classical fields in electromagnetism. These fluctuations are not particles themselves but are more akin to wave packets or pulses of increased field potential. These pulses carry the quantum information (like spin, charge, mass) typically associated with particles. When these pulses interact with other fields or particles, the quantum information carried by them manifests as what we observe as particles. This interaction is the point at which properties like position and momentum become defined, in line with the principles of quantum mechanics.
Where this all becomes relevant, and potentially testable, is in the concept of wavefunction collapse and it's reinterpretation in this model. Instead of an instantaneous collapse, the field potential undergoes a non-instantaneous adjustment as it 'borrows' energy from its local surroundings. This process results in the appearance of an instantaneous wavefunction collapse from an external observer's perspective, but is in fact a more gradual process within the field itself which propagates at the speed of light.
This is the process of "renormalization" I mentioned earlier. Backpropagation of this field collapse will "rewrite" a new coherent field state across the field as it settles into a lower energy state (or a higher energy state if it is the receiving field). This may include the "erasure" of prior information when forming this new mathematically consistent state.
For example. for entangled particles, this would mean that each value is chosen locally, so a quantum pair may initially both be spin up, but once the effect of the collapse at the two points in the corresponding field reach each other, the field values are forced to renormalize to reflect the combined entangled value, with one being spin up, and the other spin down. This effectively re-writes the past with the new coherent narrative in the present.
Key to this is the fact that all we ever know about the past is the information about it stored in the experience of the present, so when we are looking at the data from an experiment, we are looking at the data from a prior interaction, we don't observe these interactions in real time. We only ever know that a pair of entangled particles remained correlated once the information regarding the state of one arrives at the other, which in this model, could actually change the result.
This would explain a host of quantum paradoxes such as the delayed choice quantum eraser "paradox". It could also imply that although the exchange of virtual particles occurs in quanta, the fields themselves may actually be continuous, in line with the predictions of relativity. Relativity deals with the geometries of the fields, quantum mechanics deals with energy interaction within and between fields. So it's not a question of one or the other, but rather they are discrete aspects of a greater whole, kind of like the story about blind men trying to identify an elephant.
This is barely a hypothesis at this point, more like an idea, but an intriguing one all the same. It has some interesting ramifications if true though. It takes a hard stance on now being the only thing that's real, and it would mean that each point experiences its own reality, but as realities collide, entirely new realities emerge. This opens up a host of mind boggling possibilities.
Anyway.. just some interesting thoughts that I thought I'd share... I'd be happy to hear your thoughts if you'd care to comment... or not.. that's ok too... lol.
"How can you move at the speed of light??"
Me: 'Cause it's the only speed there is, baby.
Yep...
I always try to explain this to my collegeas.
But they look like they see a burning bush.
New Asylum dropped?!?! Im here for it.
I am experiencing my reality at the speed of light.
Interestingly, you'll get very similar stuff if you switch to Planck's scale and assume the world works as in some kind simulation with pixels and clock ticks, where in each tick of a 'proper clock' you can move either by one pixel or one tick of local time.
Hard to imagine a world without the Cartesian coordinate system.
How did I not discover this channel sooner
Glad you found it now 🙂
What happened to your channel? You are one of my favorite science education CZcamsrs. You inspired me to start making pop-sci videos. But why is your channel now receiving fewer views, and I haven't seen your videos recommended by CZcams for almost half a year?
I have no idea. I've been struggling since September 2022. That's how this business goes. There are a lot of variables, most of which you can't control.
@@ScienceAsylum did youtube give you enough impressions?
@@ssrphysics Getting the algorithm to show the video to people is usually the first obstacle. It's hard to know how it judges what is good and what isn't.
I know plenty of people who spend the majority of their 4-velocity temporally.