He did a high-level overview of the topic in 7 minutes. He does answer the most common question of all, tho, "but what does this _really_ mean?" which is often glossed over in those complex lectures.
@@kindlin "High level overviews" are still incredibly important and difficult to execute effectively. One can't appreciate what something "really means" unless one understands the premise of the question in the first place.
@@sasca854 Very true. And understanding the way a topic works with or is played off of other disciplines can be extremely helpful, and typically requires a more high-level, holistic view.
The debate over which signature to use for the Minkowski metric: (+---) or (-+++). They are qualitatively identical, but we have to make a choice, just like we did when we decided to call the charge of protons positive and electrons negative instead of the other way around. The signature of the metric determines the signs of the space and time components in the calculation of the spacetime interval, which is also called the Minkowski metric. Essentially, in the Euclidean space of Newtonian mechanics, distances are always positive, but in the Minkowski space of special relativity, spacetime intervals can be either positive or negative depending on whether the separation between two events in time is greater than in space. Depending on the convention, timelike separations are positive while spacelike ones are negative or vice-versa. The metric (spacetime interval) between event A with spacetime coordinates (ctₒ, xₒ, yₒ, zₒ) and event B with coordinates (ct, x, y, z) is given by: d(A,B)² = (ct-ctₒ)²-(x-xₒ)²-(y-yₒ)²-(z-zₒ)² , if the signature is (+---) d(A,B)² = -(ct-ctₒ)²+(x-xₒ)²+(y-yₒ)²+(z-zₒ)² , if the signature is (-+++) There is no reason a scientific convention couldn't be established for one or the other, but it hasn't been, and it's of little consequence.
Well let's first imagine that we had one big ABSOLUTE 4D environment, call it Space-Time, and that all objects within this environment are constantly on the move, and that they do so with an equal magnitude of motion which is of an ABSOLUTE measure, (Perhaps caused by a big bang or something.). What would be the outcome of such a setting ? The outcome is the Special Relativity phenomena. Thus we have an absolute foundation creating a relativistic outcome.
As a supplement to actually reading a physics textbook and attending university lectures, this series is pretty cool for being able to make me view this in a completely different way I never had before. The textbook is great and I really love the math it goes through, but I also really enjoyed the different way of looking at these things with the spacetime globe of yours. Thanks a lot.
hyperbolic things incoming! x^2-t^2=spacetime interval. Iff you are past high school, a hyperbola on a graph is defined by x^2-y^2=r, so the Spacetime graph is hyperbolic(if you plot the spacetime intervals on the spacetime graph regardless of what position you are in).
Raymond Hu Yes! And if you look carefully at the device he uses in the video (the one designed by Mark Rober), you'll notice that there is a family of hyperbolic curves/slots that constrain the movement of the pieces on the device.
Yes! Minkowski space is hyperbolic! One of the many consequences of this is that, while velocity isn't additive in special relativity, rapidity (the inverse hyperbolic tangent of the velocity), which is a hyperbolic angle, is additive! This means that if you deal in rapidities instead of velocities, you can boost into any frame you want just by adding the appropriate rapidities between the frames.
The Nefarious Nerd Absolutely! There is some pretty cool stuff out there on the web about deriving the velocity addition and Lorentz transformation from hyperbolic trig functions.
I finally caught up to this series, and it still just kind of blows me away. This is the kind of stuff that brought me to this channel way back when (I want to say close to 10 years ago). I realize that a lot of my disinterest in some of the videos that you were putting out about a year or two ago is because I already knew about a lot of what you made videos on, but this is just _so cool_ to watch and have that spacetime globe to have everything make immediate sense as you're describing it.
Yup although rotations in space are generatlly referred to as "rotation" and rotation in space-time, aka making something change velocity, is called a "boost"
As other say, quantum mechanics (including Planck distance) and relativity (the ongoing series) have in common about as much as acoustics and electricity. So, basically nothing in common.
Wonderful series about relativity! Two questions and three comments: Comment 1: I prefer a time-like metric (+---) in special relativity. In general relativity space-like has an advantage (comment 3) and a disadvantage (comment 2). In this case I can't decide which is better. And this is why: Comment 2: Given a world line. Then the proper time between two points makes sense (integral of proper time of the derivative). This is the time which was measured by an observer following the world line. Space-like world lines represent tachyons, which travel faster then light and they are physically irrelevant. Hence the time-like version has more physical meaning for world lines. Comment 3: In general relativity world lines are "free falling" if they are geodesic (local metric minimizers) in the space-like metric. This is analogous to the Riemann manifold version of geodesics. Hence "free falling" means longest local proper time. One last remark about this: This is in harmony with time dilation. Time travel to future is easy. But no one can travel slower in time or even travel back in time locally with respect to a free falling observer. To do this one has to take a GLOBAL shortcut. Question 1: Given two points on two different world lines. Is there always a nice interpretation of the relativistic metric difference like this (some kind of proper length)? The example in the video features world lines which are not moving relative to one another and points which are simultaneous for a stationary observer. Question 2: Are there any advantages or disadvantages for time-like metrics you are aware of and which are not mentioned in comments 2 and 3?
I think the word “invariant” better describes the concept of “proper” or “true”, it implies that it doesn’t change between frame changes. “proper” or “true” seem to imply that certain frames are preferred, when there is no such thing and the fact that the invariant spacetime interval and the “proper” time/length, that is time/length measured in the events’ own perspective coincides does not imply that the proper frame is preferred in anyway.
For your last note while it’s true that the signature of the metric matters, it is true in all metric sign conventions that the proper length and proper times have reversed signs under the square root. The idea is that for time like (more time change than space change) intervals, we can define proper time and not proper length, while for space like intervals (more space change than time change), we can define proper length and not proper time. These are two fundamentally different classes of interval so the constant quantity we are interested in changes it’s sign. The crossing point between these intervals is the light like interval. I’m sure you will cover this all later but just be careful with that signature of the metric remark - it’s over complicating an issue which doesn’t actually exist
I'm starting to feel like you could lead half of an entire grad-level relativistic physics course on just this series. Which I love, they're great videos, and that tool is super handy for visualizations, this series is so much fun!
Wow. Okay. Thank you for bringing this one around and making it make sense. I almost moved on to another video about a minute in, but stuck through because I love your content. By the end, I could actually conceptualize what you were doing because of how you explained it. It clicked. I don't know that I have the acumen to complete some of these equations myself, but I at least have an understanding of the underlying mechanics, and completely agree that "Spacetime Inversion" is a boring name and add that it sounds like something the crew of the USS Voyager would have to deal with.
Fun fact: just add a positive factor per spatial dimension and a negative factor per temporal dimension and the Pythagorean theorem works out intervals in any spacetime with any number of dimensions! For instance, sqrt(w^2+x^2+y^2+z^2) describes a spacetime with 4 only spatial dimensions and sqrt(w^2+x^2-y^2-z^2) describes a spacetime with 2 spatial dimensions and 2 temporal dimensions.
Obviously. Btw, it's called a 'term' not 'factor'. Also the spacetime interval is the square of what you are calling the interval. No need to square-root it. And the spatial and temporal terms just needs to have opposite signs compared to each other. Which is positive is a matter of convention.
This is my favorite video you’ve made in a long time! It’s elucidated the reason for wanting to define the interval in terms of the metric tensor for me, as I can see now that it lets us find the invariant interval regardless of the curvature we ourselves are surrounded by. Awesome!
It's actually amazing how even though everything else in 4D spacetime is non-Euclidean, this one property stays the same between the two metrics. Does this mean that the Pythagoras theorem is a fundamental property of all metrics?
Actually, it is. Because every spacetime dimention is orthogonal to others. So, you used Pythagoras theorem to calculate hypotenuse in spacetime triangle.
That's just how a metric works, just its definition. When the metric is identity matrix, you've got Euclidean space where well known Pythagoras formula works. When the metric is different, the formula gains more coefficients and terms, you get to non-Euclidean geometry.
No, it isn't. For example, there's the taxicab metric (also known as the Manhattan metric) where distance = dx + dy (+dz +dt), or the Chebyshev distance (also known as the maximum metric) where distance = max(dx, dy), or arbitrarily many weird metrics.
hahaha.. I literally just wrote a comment on an earlier video talking about "proper time".. how things DO happen simultaneously, even though it may look like the things happen at different times depending on your relative speed. And then I watched this video which explained exactly what I were feeling to be true. Thank you so much to post these videos.
No. Events which are simultaneous for one observer occur at different times for observers who are moving with respect to that observer. They do not "look like" the things happen at different times. The theory of Relativity is about how the quantities that are measured by one observer (Alice) relate to corresponding quantities that are measured by another observer (Bob) who are moving with respect to (wrt) each other. The value of some quantities change depending on your perspective; such as the velocity of an object, the time interval/the distance that is measured between a pair of events, the energy/momentum associated with a physical system, the frequency/wavelength of light, etc. Transformation laws describe how the values change from the perspective of one observer (Alice) to another (Bob) depending on how the first observer (Alice) is moving wrt the second (Bob). The equations involving the time interval/the distance that is measured between a pair of events wrt one observer (Alice) and the velocity of that observer (Alice) wrt a second observer (Bob) is just another example of a transformation law that allows the time interval/the distance that is measured between the same pair of events wrt the second observer (Bob) to be computed. So in this case, it's a transformation law for the time interval/the distance that is measured between a pair of events. There is a transformation law for every quantity that is relative (i.e changes depending on your perspective). These transformation laws can be deduced from two experimentally verifiable starting points: a) The laws of physics have the same mathematical form in all inertial frames of reference. b) The speed of light in a vacuum is measured to be the same by all observers. The laws of physics describes the patterns among the quantities that can be measured by any observer in a particular frame of reference. Transformation laws describe how those quantities change from the perspectives of observers in different frames of reference. An event is something that can be ascribed a particular set of space and time coordinates wrt some coordinate system associated with an observer. The space and time coordinates of an event are determined by measuring the distance and time intervals between the event in question and some reference event which has been chosen as the origin for the spacetime coordinates. Events which have the same time coordinate are said to be simultaneous wrt that observer. Events which have the same space coordinates are said to occur at the same location wrt that observer. Transformation laws allow spacetime coordinates of events measured by one observer to be transformed into the coordinates that would be measured by another observer for the same events. The time interval between a pair of events (A,B) that occur at the same location wrt one observer will be measured to be longer by another observer who is moving relative to the first observer. The two events (A,B) will also occur at different space coordinates wrt the second observer. The time interval between another pair of events (C,D) that occur at the same location wrt the second observer will also be measured to be longer by the first observer who is moving relative to the second observer. This is time dilation. The distance between a pair of events (E,F) that occur at the same time wrt one observer will be measured to be longer by another observer who is moving relative to the first observer. The two events (E,F) will also occur at different time coordinates wrt the second observer. The distance between another pair of events (G,H) that occur at the same time wrt the second observer will also be measured to be longer by the first observer. This is distance dilation. We define the length of a moving object based on the positions of the end points of the object as they are measured to be at the same time coordinate. Simultaneous events (I,J) such as the end points of the object at a particular time coordinate, wrt an observer for whom the object is stationary, occur at different time coordinates for an observer for whom the object is moving. So by comparing the distance between the end points at the same time wrt one observer (I,J) with the distance between the end points at the same time wrt the other observer (I,K); we are no longer comparing distances between the same pair of events. This results in the length of moving objects being measured to be shorter along the direction in which it is moving. The same applies to the separation between bodies which are both moving at the same velocity. This is length contraction. The density of an object and any other quantity that depends on the density will also be measured to be different depending on whether the object is moving or stationary wrt the observer. This is just an extension of the idea that the angular size of an object depends on how far it is measured to be from the observer. There is a simple transformation law to calculate the angular size of an object wrt one observer to another depending on the ratio of their respective distances from the object. Measurements made by each observer are equally valid. There's no such thing as the "true" distance or time interval between a pair of events or the "true" length of an object. They are relative quantities just like the angular size of an object. Each measurement of these quantities in any inertial reference frame is as equally valid as any other. However, everybody can calculate what the length of an object would be in a frame of reference in which the object is stationary. This is called the object's "proper length". It's just a name based on an agreed upon standard, just like how everybody can calculate and agree on the angular size of any object from some standard distance away from the object. Nonetheless, there is no such thing as the "true" angular size of an object because it depends how far the object is from the observer.
or "Relativity isn't what a lot people think it is". A lot of people assume that because something is relative, it is somehow not "true" or set in stone. While there is so much truth in consistently getting the same values from the same perspective.
I just realized this provides an alternate explanation for why redshift occurs. Conservation of energy. The lightbulb has a fixed power output. If we disagreed about how long the bulb was turned on, we would be disagreeing about how much energy it put out, which would be nonsensical. The solution is that the light the moving observer sees is redshifted, so that there is less energy per photon emitted over a longer time. Now I don't even know how to do the math on this without looking it up, but I'd bet those two differences cancel exactly, and we could compute the amount of redshift with the math given in this video.
Now imagine the light source is moving towards you. In this case light will be blue-shifted by Doppler effect, not red-shifted, even though its clocks tick slower in your frame of reference.
thedeemon oops. Good point. The extra energy seems to come from kinetic energy of the observers (some people online are explaining the conservation that way).
The theory of Relativity is about how the quantities that are measured by one observer (Alice) relate to corresponding quantities that are measured by another observer (Bob) who are moving with respect to each other. The value of some quantities change depending on your perspective; such as the velocity of an object, the time interval/the distance that is measured between a pair of events, the energy/momentum associated with a physical system, frequency of light emitted by a body, etc. Transformation laws describe how the values change from the perspective of one observer (Alice) to another (Bob) depending on how the first observer (Alice) is moving with respect to the second (Bob). There is an equation involving the Energy of a physical system with respect to one observer (Alice) and the velocity of that observer (Alice) with respect to a second observer (Bob) which is just another example of a transformation law that allows the Energy of the physical system with respect to the second observer (Bob) to be computed. So in this case, it's a transformation law for the Energy of a physical system. There is a transformation law for every quantity that is relative (i.e changes depending on your perspective). These transformation laws can be deduced from two experimentally verifiable starting points: a) The laws of physics have the same mathematical form in all inertial frames of reference. b) The speed of light in a vacuum is measured to be the same by all observers. The laws of physics describes the patterns among the quantities that can be measured by any observer in a particular frame of reference. Transformation laws describe how those quantities change from the perspectives of observers in different frames of reference. This is a sort of extension of the idea that the angular size of an object depends on how far it is measured to be from the observer. There is a simple transformation law to calculate the angular size of an object with respect to one observer to another depending on the ratio of their respective distances from the object.
THATS SOO COOL Thank you so much for making this channel, half the time I have no clue what just happened and the other half I'm blown away and it clicks!!! This is so awesome :D
In the video you said that you need to know your speed if you're moving to calculate real space and time intervals, but if you are moving at a constant speed ¿how can you know that you are the one that is moving?
From your perspective, you aren't moving. The object you are measuring is. So from the perspective of the object, you are moving at the same speed and in the opposite direction as the object you measure. For the sake of math, you can view it from either perspective.
LocalToast The “observer“ in this context is just any object in spacetime. That could be a scientist, a radiation detector, or just a lone proton. When we say “observer“, we really mean a certain perspective to look at something, certainly not a conscious mind. It's a common misconception about quantum physics (Keyword Heisenberg) as well. Hope that helped :)
As usual with your videos, mind ... BLOWN (and this is writing this only half way through the video and having scraped brains off the walls TWICE already.) GREAT stuff.
I think this is the first episode where I 100% learned something. Can't believe this wasn't covered in my college class on special relativity (even if it was a pretty short one). But hey, awesome video!
As someone who was very interested in physics but was not able to pursue it, this series is amazingly interesting and very well explained! Thank you very much :)
But wouldn't the sign of the metric be a consequence of the special case for Gᵐᵑ = (8πG/c⁴)Tᵐᵑ when the metric is describing a flat geometry? I would love to see you discussing GR, btw... Just saying...
Super cool! You explained this really well, though I can tell that it's a super complicated topic. Having the space-time globe that mark made you is such a great prop for helping us wrap our heads around this otherwise very abstract concept. This whole series is so well done!
PLEASE CAN YOU DO VIDEOS ON-1.WHY INTERNAL CONSTITUENTS OF A SYSTEM CANT AFFECT IT EXTERNALLY?( ie a person inside a box cant cause the box to move by hitting against the wall of the box from inside...I think this is also reason why we doubt emdrive cant work)2.WHY WE NEED FORCE CARRIER PARTICLES TO DESCRIBE FORCE?3.CAN WE EVER CHANGE THE LAWS OF PHYSICS INTO WHAT WE LIKE?
We can measure time intervals between events in metres or distances between events in seconds. It's optional. Both just needs to be in the same units. The SI unit of time is the second.
Thanks. My point was the spelling in the video. An extremely rare and very minor mistake by Henry (and team) I think. Really I should be thanking him/them for doing what they do, but at the same time I think it helps if this stuff does get tidied up.
At 5:05, won't the time difference be more than 1.41 seconds as the objects get further apart? So is it 1.41 seconds only at a particular distance or am I getting this whole thing wrong?
I had a good physics professor in college so I have a decent understanding of these concepts but I am here to say that your mechanical apparatus is as confusing as hell, for me it distracts more than it helps. For what it is worth.
Vulpine Deity We used to think that way for a lot of things. A negative number in mathematics was illogical, an imaginary number was illogical, a changing mass was illogical. But now the former two are widely used in practice and the latter is accepted as fact. You still need to justify exactly why you say it's illogical - just saying "it's illogical" doesn't mean much.
A remark and questions about "quantum" or planck time and length: It seems so intuitive to have something that can be shorter than a given length or time (either measured in distance or measured in duration) If everything, on the scale of subatomic particles, is considered to be like discrete little packages and time is also quantized then what lies between two planck times or between two planck lengths ? It really is fascinating that there is really an absolute minimum lenght or minimum time, even when considering that planck time and planck length is really really small. If I'm correct about that there is an absolute minimum size or time. But how does the structure look like? I mean would you have a planck length of something and then a planck length of nothing and then something again ? Meaning that there is really absolute nothing in between two planck lengths? Or is a planck length of nothing non-existant, meaning that it really really is nothing? I mean no quantum fluctuations, no foam, absolute truly nothing? I hope I make some sense, but the fact that something can be quantized or is quantum does fascinate me. The very fact that something exists in seperate units must mean that there IS something in between, even if that something is absolutely nothing. Or would they seemingly be joined together but still behave as seperate? The more I think about it, the more complicated it seems to get. ehm I try again with different wording: If planck time is considered to be a 'thing' that is truly the smallest 'thing' that can exist, then how are two planck times separated from eachother? Is there truly nothing between two planck times or is there 'something' ? (planck time - nothing - plancktime - nothing - plancktime) ? I'm hoping I'm making some sense. Sorry if this is impossible to answer, but it still very very interesting to think about.
Kyle Sandeman there's always a way to present information in an interesting way to educate though. I'm long finished school and college so I don't know if it's changed much nowadays, but when I was in school everything was a wall of text. My whole governmental educational experience was essentially a memory excercize rather than actual learning. I've learned far more from the internet than I did in school. Now of course with internet you need to learn to differentiate the fluff and actual fact, but that's neither here nor there.
+Olterior That's simply not true. A lot of information simply cannot be presented in a superficially interesting way, especially abstract content like higher level math & physics. MinutePhysics only scratches the surface, and that's good for videos series intended for laymen. But as you go deeper, there's less and less visual you can rely on, and have to resort to abstract concepts and more formal (and boring) language for precision and efficiency.
One thing I haven't underem stood completely. dx e dt are based on two different units to misure them, so how are you able to make r?them interact together? Cause their are still differences of their repsective measures.
great but what is so, well, special about me observing objects at my position that i can claim i am seeing their true length or true duration? i assume the implication is that unless there is exactly zero distance between me and an object i cannot observe any true properties of that object
What matters isn't that you're at the object's position, but that you're in its native reference frame, i.e. moving with the same velocity as it (in the case of true time--I'll get to true length in a moment). Let's take the example of the lightbulb turning on, then turning off after time Δt. You are holding the lightbulb, so it doesn't move from your perspective. (Note that this would also be true if you were standing 100 meters from the lightbulb, or if you were on separate train cars.) This means that Δx=0, which simplifies the calculation of the spacetime interval to sqrt(Δt^2), which of course =Δt. This means that the spacetime interval between the lightbulb turning on and the lightbulb turning off is exactly the time that elapses in the reference frame where *the events happen in the same place*. So if any other observer calculates the spacetime interval, they'll get the same thing. The term "true time" reflects the idea that your measurement of the time is unaffected by time dilation, since there is no relative motion. The case of true length is completely analogous. You measure two events--say, the combustion of two boxes--in a reference frame where *the events happen at the same time*. This means that Δt=0, so the spacetime interval is sqrt(Δx^2)=Δx. The distance between the boxes, as measured by you, is exactly the spacetime interval. Your measurement is unaffected by distance dilation or length contraction, hence the term "true length".
Which grade do they teach you Quantum Physics and Relativity in school? I’m relying on UA-cam and books to learn physics, and would want to know which grade they will start teaching it in schools.
to get that 4.24 seconds did you take into account the time the last photons from the light have to travel to catch up with the person moving away? in 4 seconds the person should have moved 1.3333 light seconds away from you so it should be atleast 5.3333 seconds even without time dialition taken into account AND the person will get even further away in that 1.3333 seconds.
sugibudder No, we do not consider light bringing us information of events far away. Or, we have already taken that into account. Or whichever way is more correct to say it. At which time coordinate in our reference frame something happened, and at what time we get the information that that thing happened, are two different things in special relativity, as you rightly point out. We can, in practice, measure the latter. But in calculations we use the former, and everything in this video is the former.
Unless otherwise specified, descriptions of observations in scenarios in relativity are understood to have the travel time of light accounted for and factored out.
Is there proper distance or duration though? and if so does that mean that you can determine if two things, moving at the same speed, happen simultaneously from a true perspective? I don't expect to get an answer considering how late I am to the vid, but if you know and happen to see this please answer.
Please consider a new frame of referrence to calculate spacetime intervals. A geodesic sphere made up of 20 equalateral triangles (the minimum number required to close a perfect sphere). Add to that three interior lines connectting opposite points of the sphere and you will have all of the triangular elements required to accurately calculate spacetime. BTW, the three interior lines serve as an axis about any one of which the sphere is free to rotate.
Very cool. I somehow suspect Pythagoras would be pleased that the math named after him still works on even the most extreme of scales, if with some fairly minor modifications.
Both. They each calculate the proper length and proper time using their own measurements, and would come to the exact same conclusion. That's the point of proper length and proper time.
you mis understand me, proper time and proper space is calculated to be what length/duration it is for the thing being measured. So the reference frame of that object. But the 2 objects moving relative to each other don't have a shared static reference frame. In the reference frame of the first object the second object is moving, while in the reference frame of the second object the first one is moving.
But we don't need a shared rest frame for this to work. Say, A & B are moving relative to each other. Whatever A measures about themselves is automatically "proper", whatever B measures about A can be converted to "proper" by using the formula, and the two results would agree. Whatever B measures about themselves are automatically "proper", and whatever A measure about B can be converted to "proper" by using the formula, and the two results would agree.
Dont forget that special relativity always assumes that something with a speed v will and always has been moving with a speed v, or at the start of the observation the moving object will instantly move at speed v. Of course, the object has speed v in your frame of reference.
If an observer was moving >0.5c would there also be a redshift or blueshift (depending on what direction of the observer and what's the observed are) WITH the change in time/length perspective?
This video was relatively good, at least in my frame of reference.
I don't think it was just relatively good, I think it was relativity special
Lex
From my perspective it was so-so, but then again, I moved away from you 12*(10^8) meters in that time so who's to say?
This deserves a like.
This video is not relative it is absolute.
So you just went through 4 hours worth of complex lectures in an advance physics program in about 7 minutes, and I got it. brilliant.
He did a high-level overview of the topic in 7 minutes. He does answer the most common question of all, tho, "but what does this _really_ mean?" which is often glossed over in those complex lectures.
@@kindlin "High level overviews" are still incredibly important and difficult to execute effectively. One can't appreciate what something "really means" unless one understands the premise of the question in the first place.
@@sasca854
Very true. And understanding the way a topic works with or is played off of other disciplines can be extremely helpful, and typically requires a more high-level, holistic view.
You could watch Arindam Kumar Chaterjee’s Stanford lectures but this simplifies.
6:40 Age old debate? From what perspective?
From the perspective of the debate. Didn't you watch the video?
The debate over which signature to use for the Minkowski metric: (+---) or (-+++). They are qualitatively identical, but we have to make a choice, just like we did when we decided to call the charge of protons positive and electrons negative instead of the other way around.
The signature of the metric determines the signs of the space and time components in the calculation of the spacetime interval, which is also called the Minkowski metric. Essentially, in the Euclidean space of Newtonian mechanics, distances are always positive, but in the Minkowski space of special relativity, spacetime intervals can be either positive or negative depending on whether the separation between two events in time is greater than in space. Depending on the convention, timelike separations are positive while spacelike ones are negative or vice-versa.
The metric (spacetime interval) between event A with spacetime coordinates (ctₒ, xₒ, yₒ, zₒ) and event B with coordinates (ct, x, y, z) is given by:
d(A,B)² = (ct-ctₒ)²-(x-xₒ)²-(y-yₒ)²-(z-zₒ)² , if the signature is (+---)
d(A,B)² = -(ct-ctₒ)²+(x-xₒ)²+(y-yₒ)²+(z-zₒ)² , if the signature is (-+++)
There is no reason a scientific convention couldn't be established for one or the other, but it hasn't been, and it's of little consequence.
I know, I was just making a relatively bad joke.
I say it's (+---). Time is real, and the three space dimensions are imaginary, making a quaternion.
To my understanding, in astrophysics (-+++) is more common, whereas in quantum field theory (+---) is used more.
"not everything is relative" well, that's just like your opinion man.
everything is an opinion bro, truth is only a rhetorical stratagem
^What yo said is an opinion,theres no truth into it,just a rhetorical stratagem
Tomer Wolberg That quote really tied the room together.
Well let's first imagine that we had one big ABSOLUTE 4D environment, call it Space-Time, and that all objects within this environment are constantly on the move, and that they do so with an equal magnitude of motion which is of an ABSOLUTE measure, (Perhaps caused by a big bang or something.). What would be the outcome of such a setting ? The outcome is the Special Relativity phenomena. Thus we have an absolute foundation creating a relativistic outcome.
Things being constant is a lot more weird than things changing.
Einstein once said that he should have called relativity theory "invariance theory".
Now that I saw this yes it is
As a supplement to actually reading a physics textbook and attending university lectures, this series is pretty cool for being able to make me view this in a completely different way I never had before. The textbook is great and I really love the math it goes through, but I also really enjoyed the different way of looking at these things with the spacetime globe of yours. Thanks a lot.
hyperbolic things incoming! x^2-t^2=spacetime interval.
Iff you are past high school, a hyperbola on a graph is defined by x^2-y^2=r, so the Spacetime graph is hyperbolic(if you plot the spacetime intervals on the spacetime graph regardless of what position you are in).
Raymond Hu Yes! And if you look carefully at the device he uses in the video (the one designed by Mark Rober), you'll notice that there is a family of hyperbolic curves/slots that constrain the movement of the pieces on the device.
Yes! Minkowski space is hyperbolic! One of the many consequences of this is that, while velocity isn't additive in special relativity, rapidity (the inverse hyperbolic tangent of the velocity), which is a hyperbolic angle, is additive! This means that if you deal in rapidities instead of velocities, you can boost into any frame you want just by adding the appropriate rapidities between the frames.
The Nefarious Nerd Absolutely! There is some pretty cool stuff out there on the web about deriving the velocity addition and Lorentz transformation from hyperbolic trig functions.
Hyperbolic functions have the same role in Lorentz boosts that trigonometric functions have in spatial rotations.
I finally caught up to this series, and it still just kind of blows me away. This is the kind of stuff that brought me to this channel way back when (I want to say close to 10 years ago). I realize that a lot of my disinterest in some of the videos that you were putting out about a year or two ago is because I already knew about a lot of what you made videos on, but this is just _so cool_ to watch and have that spacetime globe to have everything make immediate sense as you're describing it.
There is something else truly awesome about relativity. Lorentz transformation is a rotastion matrix, not a trygonometric rotation but hyperbolic one.
Yup although rotations in space are generatlly referred to as "rotation" and rotation in space-time, aka making something change velocity, is called a "boost"
He missed a good opportunity to introduce rapidity and hyperbolic trigonometry - makes it all much easier, IMO
Wtf are u guys talking abt?
I lost u at lorentz tramsformation
Relatively cool! I’ll leave now...
At near the speed of light.
Now that just makes you look short
John of Us lol
John of Us #nerdjokes
John of Us Steht da einer auf Marc-Uwe Kling? :D
The Science Biome C you later.
I'm loving the time globe! it really helps with getting an intuitive feel of this subject
Could you maybe do a video on planck time/length?
That's a whole different topic. I'd love to see it, too, though!
Planck's Constant and The Origin of Quantum Mechanics | Space Time | PBS Digital Studios
minutephysics The Origin of Quantum Mechanics (feat. Neil Turok)
As other say, quantum mechanics (including Planck distance) and relativity (the ongoing series) have in common about as much as acoustics and electricity. So, basically nothing in common.
Science Asylum
Wonderful series about relativity!
Two questions and three comments:
Comment 1: I prefer a time-like metric (+---) in special relativity. In general relativity space-like has an advantage (comment 3) and a disadvantage (comment 2). In this case I can't decide which is better. And this is why:
Comment 2: Given a world line. Then the proper time between two points makes sense (integral of proper time of the derivative). This is the time which was measured by an observer following the world line. Space-like world lines represent tachyons, which travel faster then light and they are physically irrelevant. Hence the time-like version has more physical meaning for world lines.
Comment 3: In general relativity world lines are "free falling" if they are geodesic (local metric minimizers) in the space-like metric. This is analogous to the Riemann manifold version of geodesics. Hence "free falling" means longest local proper time. One last remark about this: This is in harmony with time dilation. Time travel to future is easy. But no one can travel slower in time or even travel back in time locally with respect to a free falling observer. To do this one has to take a GLOBAL shortcut.
Question 1: Given two points on two different world lines. Is there always a nice interpretation of the relativistic metric difference like this (some kind of proper length)? The example in the video features world lines which are not moving relative to one another and points which are simultaneous for a stationary observer.
Question 2: Are there any advantages or disadvantages for time-like metrics you are aware of and which are not mentioned in comments 2 and 3?
The way he says while “plugging and chugging” to get the interval sounds so poetic 😊😊
4:44
I'm not completely comfortable with "twelve hundred million" as a unit.
I think the word “invariant” better describes the concept of “proper” or “true”, it implies that it doesn’t change between frame changes. “proper” or “true” seem to imply that certain frames are preferred, when there is no such thing and the fact that the invariant spacetime interval and the “proper” time/length, that is time/length measured in the events’ own perspective coincides does not imply that the proper frame is preferred in anyway.
I agree, this is important. I think it's very misleading to the fundamental message of relativity to use the word "true" here
For your last note while it’s true that the signature of the metric matters, it is true in all metric sign conventions that the proper length and proper times have reversed signs under the square root. The idea is that for time like (more time change than space change) intervals, we can define proper time and not proper length, while for space like intervals (more space change than time change), we can define proper length and not proper time. These are two fundamentally different classes of interval so the constant quantity we are interested in changes it’s sign. The crossing point between these intervals is the light like interval.
I’m sure you will cover this all later but just be careful with that signature of the metric remark - it’s over complicating an issue which doesn’t actually exist
I'm starting to feel like you could lead half of an entire grad-level relativistic physics course on just this series.
Which I love, they're great videos, and that tool is super handy for visualizations, this series is so much fun!
Wow. Okay. Thank you for bringing this one around and making it make sense. I almost moved on to another video about a minute in, but stuck through because I love your content. By the end, I could actually conceptualize what you were doing because of how you explained it. It clicked. I don't know that I have the acumen to complete some of these equations myself, but I at least have an understanding of the underlying mechanics, and completely agree that "Spacetime Inversion" is a boring name and add that it sounds like something the crew of the USS Voyager would have to deal with.
i like how this channel explains everything in such a simple and direct manner that everybody can understand ^^
the way you changed the color of the stikman that represents you to blue and the color of your friend to orange blow my mind at the beginning
Watch YT videos @ 1.25: ah, perfect
Watch minutephysics @ .75: ah, perfect
Fun fact: just add a positive factor per spatial dimension and a negative factor per temporal dimension and the Pythagorean theorem works out intervals in any spacetime with any number of dimensions! For instance, sqrt(w^2+x^2+y^2+z^2) describes a spacetime with 4 only spatial dimensions and sqrt(w^2+x^2-y^2-z^2) describes a spacetime with 2 spatial dimensions and 2 temporal dimensions.
Obviously. Btw, it's called a 'term' not 'factor'. Also the spacetime interval is the square of what you are calling the interval. No need to square-root it. And the spatial and temporal terms just needs to have opposite signs compared to each other. Which is positive is a matter of convention.
Could you plz make a video on Unruh effect. (Ur videos are astounding)
This is my favorite video you’ve made in a long time! It’s elucidated the reason for wanting to define the interval in terms of the metric tensor for me, as I can see now that it lets us find the invariant interval regardless of the curvature we ourselves are surrounded by. Awesome!
the best series in yt...
Absolutely *mind blown*
This was such an amazing theory to learn.
Wow.
Love the way it's taught here. So easy and quick.
It's actually amazing how even though everything else in 4D spacetime is non-Euclidean, this one property stays the same between the two metrics. Does this mean that the Pythagoras theorem is a fundamental property of all metrics?
Actually, it is. Because every spacetime dimention is orthogonal to others.
So, you used Pythagoras theorem to calculate hypotenuse in spacetime triangle.
That's just how a metric works, just its definition. When the metric is identity matrix, you've got Euclidean space where well known Pythagoras formula works. When the metric is different, the formula gains more coefficients and terms, you get to non-Euclidean geometry.
Feynstein 100 The generalised Pythagorean theorem works in any number of spatial and temporal dimensions, which is cool!
No, it isn't.
For example, there's the taxicab metric (also known as the Manhattan metric) where distance = dx + dy (+dz +dt), or the Chebyshev distance (also known as the maximum metric) where distance = max(dx, dy), or arbitrarily many weird metrics.
rmsgrey GOD DAMN TAXI CABS
hahaha.. I literally just wrote a comment on an earlier video talking about "proper time".. how things DO happen simultaneously, even though it may look like the things happen at different times depending on your relative speed.
And then I watched this video which explained exactly what I were feeling to be true. Thank you so much to post these videos.
No. Events which are simultaneous for one observer occur at different times for observers who are moving with respect to that observer. They do not "look like" the things happen at different times.
The theory of Relativity is about how the quantities that are measured by one observer (Alice) relate to corresponding quantities that are measured by another observer (Bob) who are moving with respect to (wrt) each other. The value of some quantities change depending on your perspective; such as the velocity of an object, the time interval/the distance that is measured between a pair of events, the energy/momentum associated with a physical system, the frequency/wavelength of light, etc. Transformation laws describe how the values change from the perspective of one observer (Alice) to another (Bob) depending on how the first observer (Alice) is moving wrt the second (Bob). The equations involving the time interval/the distance that is measured between a pair of events wrt one observer (Alice) and the velocity of that observer (Alice) wrt a second observer (Bob) is just another example of a transformation law that allows the time interval/the distance that is measured between the same pair of events wrt the second observer (Bob) to be computed. So in this case, it's a transformation law for the time interval/the distance that is measured between a pair of events.
There is a transformation law for every quantity that is relative (i.e changes depending on your perspective). These transformation laws can be deduced from two experimentally verifiable starting points:
a) The laws of physics have the same mathematical form in all inertial frames of reference.
b) The speed of light in a vacuum is measured to be the same by all observers.
The laws of physics describes the patterns among the quantities that can be measured by any observer in a particular frame of reference. Transformation laws describe how those quantities change from the perspectives of observers in different frames of reference.
An event is something that can be ascribed a particular set of space and time coordinates wrt some coordinate system associated with an observer. The space and time coordinates of an event are determined by measuring the distance and time intervals between the event in question and some reference event which has been chosen as the origin for the spacetime coordinates. Events which have the same time coordinate are said to be simultaneous wrt that observer. Events which have the same space coordinates are said to occur at the same location wrt that observer. Transformation laws allow spacetime coordinates of events measured by one observer to be transformed into the coordinates that would be measured by another observer for the same events.
The time interval between a pair of events (A,B) that occur at the same location wrt one observer will be measured to be longer by another observer who is moving relative to the first observer. The two events (A,B) will also occur at different space coordinates wrt the second observer. The time interval between another pair of events (C,D) that occur at the same location wrt the second observer will also be measured to be longer by the first observer who is moving relative to the second observer. This is time dilation.
The distance between a pair of events (E,F) that occur at the same time wrt one observer will be measured to be longer by another observer who is moving relative to the first observer. The two events (E,F) will also occur at different time coordinates wrt the second observer. The distance between another pair of events (G,H) that occur at the same time wrt the second observer will also be measured to be longer by the first observer. This is distance dilation.
We define the length of a moving object based on the positions of the end points of the object as they are measured to be at the same time coordinate. Simultaneous events (I,J) such as the end points of the object at a particular time coordinate, wrt an observer for whom the object is stationary, occur at different time coordinates for an observer for whom the object is moving. So by comparing the distance between the end points at the same time wrt one observer (I,J) with the distance between the end points at the same time wrt the other observer (I,K); we are no longer comparing distances between the same pair of events. This results in the length of moving objects being measured to be shorter along the direction in which it is moving. The same applies to the separation between bodies which are both moving at the same velocity. This is length contraction.
The density of an object and any other quantity that depends on the density will also be measured to be different depending on whether the object is moving or stationary wrt the observer. This is just an extension of the idea that the angular size of an object depends on how far it is measured to be from the observer. There is a simple transformation law to calculate the angular size of an object wrt one observer to another depending on the ratio of their respective distances from the object. Measurements made by each observer are equally valid.
There's no such thing as the "true" distance or time interval between a pair of events or the "true" length of an object. They are relative quantities just like the angular size of an object. Each measurement of these quantities in any inertial reference frame is as equally valid as any other. However, everybody can calculate what the length of an object would be in a frame of reference in which the object is stationary. This is called the object's "proper length". It's just a name based on an agreed upon standard, just like how everybody can calculate and agree on the angular size of any object from some standard distance away from the object. Nonetheless, there is no such thing as the "true" angular size of an object because it depends how far the object is from the observer.
Where do I get one of these space/time mechanical contraptions and how much would it cost?
It’s amazing how many videos he can make with this tool. I’m loving it
or "Relativity isn't what a lot people think it is". A lot of people assume that because something is relative, it is somehow not "true" or set in stone. While there is so much truth in consistently getting the same values from the same perspective.
I just realized this provides an alternate explanation for why redshift occurs. Conservation of energy. The lightbulb has a fixed power output. If we disagreed about how long the bulb was turned on, we would be disagreeing about how much energy it put out, which would be nonsensical. The solution is that the light the moving observer sees is redshifted, so that there is less energy per photon emitted over a longer time. Now I don't even know how to do the math on this without looking it up, but I'd bet those two differences cancel exactly, and we could compute the amount of redshift with the math given in this video.
Now imagine the light source is moving towards you. In this case light will be blue-shifted by Doppler effect, not red-shifted, even though its clocks tick slower in your frame of reference.
thedeemon oops. Good point. The extra energy seems to come from kinetic energy of the observers (some people online are explaining the conservation that way).
The theory of Relativity is about how the quantities that are measured by one observer (Alice) relate to corresponding quantities that are measured by another observer (Bob) who are moving with respect to each other. The value of some quantities change depending on your perspective; such as the velocity of an object, the time interval/the distance that is measured between a pair of events, the energy/momentum associated with a physical system, frequency of light emitted by a body, etc. Transformation laws describe how the values change from the perspective of one observer (Alice) to another (Bob) depending on how the first observer (Alice) is moving with respect to the second (Bob). There is an equation involving the Energy of a physical system with respect to one observer (Alice) and the velocity of that observer (Alice) with respect to a second observer (Bob) which is just another example of a transformation law that allows the Energy of the physical system with respect to the second observer (Bob) to be computed. So in this case, it's a transformation law for the Energy of a physical system. There is a transformation law for every quantity that is relative (i.e changes depending on your perspective). These transformation laws can be deduced from two experimentally verifiable starting points:
a) The laws of physics have the same mathematical form in all inertial frames of reference.
b) The speed of light in a vacuum is measured to be the same by all observers.
The laws of physics describes the patterns among the quantities that can be measured by any observer in a particular frame of reference. Transformation laws describe how those quantities change from the perspectives of observers in different frames of reference.
This is a sort of extension of the idea that the angular size of an object depends on how far it is measured to be from the observer. There is a simple transformation law to calculate the angular size of an object with respect to one observer to another depending on the ratio of their respective distances from the object.
Great to see minute physics covering much more advanced topics!!!
You have a gift for rendering the incredibly difficult into the relatively simple. Thank you!
These uploads are amazing. Great work Henry.
THATS SOO COOL
Thank you so much for making this channel, half the time I have no clue what just happened and the other half I'm blown away and it clicks!!! This is so awesome :D
You deserve so many more subs and views XD
In the video you said that you need to know your speed if you're moving to calculate real space and time intervals, but if you are moving at a constant speed ¿how can you know that you are the one that is moving?
ciencia con vtorres awesome question!
The "speed" used here is the relative speed between two objects.
From your perspective, you aren't moving. The object you are measuring is. So from the perspective of the object, you are moving at the same speed and in the opposite direction as the object you measure. For the sake of math, you can view it from either perspective.
Everything in the universe is constantly moving, you still have to take in account relativity.
LocalToast
The “observer“ in this context is just any object in spacetime. That could be a scientist, a radiation detector, or just a lone proton. When we say “observer“, we really mean a certain perspective to look at something, certainly not a conscious mind. It's a common misconception about quantum physics (Keyword Heisenberg) as well. Hope that helped :)
謝謝！
Piece of cake
moving 1/3 the speed of light to my left.
Piece of cake...
Light cake.
Its hard tho
Sorta
As usual with your videos, mind ... BLOWN
(and this is writing this only half way through the video and having scraped brains off the walls TWICE already.)
GREAT stuff.
I think this is the first episode where I 100% learned something. Can't believe this wasn't covered in my college class on special relativity (even if it was a pretty short one). But hey, awesome video!
Really thanks for these series.Keep it up please!
The apparatus doe... This dude is the god of teaching
As someone who was very interested in physics but was not able to pursue it, this series is amazingly interesting and very well explained! Thank you very much :)
The 'space-time' device is a genius work!
I love this machine and want one though I am not sure why. mechanical minkowski diagram
You can play with a digital one here ibises.org.uk/Minkowski.html
OMG ! U have just made another abstract concept extremely easy!!!
This actually is very practical and useful knowledge to have. Thank you for this.
But wouldn't the sign of the metric be a consequence of the special case for Gᵐᵑ = (8πG/c⁴)Tᵐᵑ when the metric is describing a flat geometry?
I would love to see you discussing GR, btw...
Just saying...
Super cool! You explained this really well, though I can tell that it's a super complicated topic. Having the space-time globe that mark made you is such a great prop for helping us wrap our heads around this otherwise very abstract concept. This whole series is so well done!
How do you do this for more spacial dimensions? Linear transformation maybe? idk
Yes, see here: en.wikipedia.org/wiki/Lorentz_transformation#Mathematical_formulation
Loving this series! It makes so much sense.
Absolutely love your videos, and these videos are probably, in my experience, the best explanations for relativity out there
Been waiting for a while.
PLEASE CAN YOU DO VIDEOS ON-1.WHY INTERNAL CONSTITUENTS OF A SYSTEM CANT AFFECT IT EXTERNALLY?( ie a person inside a box cant cause the box to move by hitting against the wall of the box from inside...I think this is also reason why we doubt emdrive cant work)2.WHY WE NEED FORCE CARRIER PARTICLES TO DESCRIBE FORCE?3.CAN WE EVER CHANGE THE LAWS OF PHYSICS INTO WHAT WE LIKE?
Thanks to you I kinda start to get a sense for SR
3:10 Should be *metres* because it's the SI unit?
We can measure time intervals between events in metres or distances between events in seconds. It's optional. Both just needs to be in the same units. The SI unit of time is the second.
Thanks. My point was the spelling in the video. An extremely rare and very minor mistake by Henry (and team) I think. Really I should be thanking him/them for doing what they do, but at the same time I think it helps if this stuff does get tidied up.
No, it should be *meters* cuz Britney Eng sucks XD
I love this series. Please keep it up!
That actually makes sense. For the first time in my life, I actually understand it, or at least that part of it.
Best video in physics thank you
A very awesome series indeed!
Sixty symbols did a show on the Muon issue - I'm going to have to watch that again.
At 5:05, won't the time difference be more than 1.41 seconds as the objects get further apart? So is it 1.41 seconds only at a particular distance or am I getting this whole thing wrong?
Knowledge expansion, loveitt.
I had a good physics professor in college so I have a decent understanding of these concepts but I am here to say that your mechanical apparatus is as confusing as hell, for me it distracts more than it helps. For what it is worth.
Ok...I’m sorry but my brain 🧠 hurts now! ☹️
5:34
I kinda felt weird hearing your voice without that music in the background until then. I've just gotten so used to them being paired together.
You'll know they're the wrong way round if you get a negative value.
And that’s how you almost run out of time in your exam.
That's how a student thinks. A scientist, in the other hand, has to justify why a negative value is wrong.
Isn't it obvious? Because a value within the universe being negative is illogical.
Vulpine Deity We used to think that way for a lot of things. A negative number in mathematics was illogical, an imaginary number was illogical, a changing mass was illogical. But now the former two are widely used in practice and the latter is accepted as fact. You still need to justify exactly why you say it's illogical - just saying "it's illogical" doesn't mean much.
How can a quantity of distance be negative? A value can be negative, but a distance is a gap between two values. So...
This chapter I actually managed to comprehend somewhat more relative to the other chapters
A remark and questions about "quantum" or planck time and length:
It seems so intuitive to have something that can be shorter than a given length or time (either measured in distance or measured in duration)
If everything, on the scale of subatomic particles, is considered to be like discrete little packages and time is also quantized then what lies between two planck times or between two planck lengths ?
It really is fascinating that there is really an absolute minimum lenght or minimum time, even when considering that planck time and planck length is really really small.
If I'm correct about that there is an absolute minimum size or time.
But how does the structure look like? I mean would you have a planck length of something and then a planck length of nothing and then something again ?
Meaning that there is really absolute nothing in between two planck lengths? Or is a planck length of nothing non-existant, meaning that it really really is nothing? I mean no quantum fluctuations, no foam, absolute truly nothing?
I hope I make some sense, but the fact that something can be quantized or is quantum does fascinate me. The very fact that something exists in seperate units must mean that there IS something in between, even if that something is absolutely nothing.
Or would they seemingly be joined together but still behave as seperate?
The more I think about it, the more complicated it seems to get.
ehm I try again with different wording:
If planck time is considered to be a 'thing' that is truly the smallest 'thing' that can exist, then how are two planck times separated from eachother?
Is there truly nothing between two planck times or is there 'something' ? (planck time - nothing - plancktime - nothing - plancktime) ?
I'm hoping I'm making some sense. Sorry if this is impossible to answer, but it still very very interesting to think about.
Yes physics!!!!
I "think" I understood 50% of this video, I "know" that my mind is 100% blown! :)
To be honest, he draws really good
5:53 wouldn’t be that the red dt is equal to the square root of the blue dt minus the red dx?
A long series on general relativity plz
This is the future. Not the boring school book stuff. This would've captivated me as a kid a lot more than a wall of text we get nowadays.
Olterior minute physics is showing the interesting part though. Go pick up a textbook and it's mostly wall of text like you'd expect
Kyle Sandeman there's always a way to present information in an interesting way to educate though. I'm long finished school and college so I don't know if it's changed much nowadays, but when I was in school everything was a wall of text. My whole governmental educational experience was essentially a memory excercize rather than actual learning. I've learned far more from the internet than I did in school. Now of course with internet you need to learn to differentiate the fluff and actual fact, but that's neither here nor there.
+Olterior That's simply not true. A lot of information simply cannot be presented in a superficially interesting way, especially abstract content like higher level math & physics. MinutePhysics only scratches the surface, and that's good for videos series intended for laymen. But as you go deeper, there's less and less visual you can rely on, and have to resort to abstract concepts and more formal (and boring) language for precision and efficiency.
as Chenfeng Bao said, but no, information cannot always be made interesting.
Prime example would be general relativity's tensor stuff
What about I move in a different way from left and right?
One thing I haven't underem stood completely. dx e dt are based on two different units to misure them, so how are you able to make r?them interact together? Cause their are still differences of their repsective measures.
great but what is so, well, special about me observing objects at my position that i can claim i am seeing their true length or true duration? i assume the implication is that unless there is exactly zero distance between me and an object i cannot observe any true properties of that object
What matters isn't that you're at the object's position, but that you're in its native reference frame, i.e. moving with the same velocity as it (in the case of true time--I'll get to true length in a moment).
Let's take the example of the lightbulb turning on, then turning off after time Δt. You are holding the lightbulb, so it doesn't move from your perspective. (Note that this would also be true if you were standing 100 meters from the lightbulb, or if you were on separate train cars.) This means that Δx=0, which simplifies the calculation of the spacetime interval to sqrt(Δt^2), which of course =Δt.
This means that the spacetime interval between the lightbulb turning on and the lightbulb turning off is exactly the time that elapses in the reference frame where *the events happen in the same place*. So if any other observer calculates the spacetime interval, they'll get the same thing. The term "true time" reflects the idea that your measurement of the time is unaffected by time dilation, since there is no relative motion.
The case of true length is completely analogous. You measure two events--say, the combustion of two boxes--in a reference frame where *the events happen at the same time*. This means that Δt=0, so the spacetime interval is sqrt(Δx^2)=Δx. The distance between the boxes, as measured by you, is exactly the spacetime interval. Your measurement is unaffected by distance dilation or length contraction, hence the term "true length".
Which grade do they teach you Quantum Physics and Relativity in school? I’m relying on UA-cam and books to learn physics, and would want to know which grade they will start teaching it in schools.
Great series.
to get that 4.24 seconds did you take into account the time the last photons from the light have to travel to catch up with the person moving away? in 4 seconds the person should have moved 1.3333 light seconds away from you so it should be atleast 5.3333 seconds even without time dialition taken into account AND the person will get even further away in that 1.3333 seconds.
sugibudder No, we do not consider light bringing us information of events far away. Or, we have already taken that into account. Or whichever way is more correct to say it.
At which time coordinate in our reference frame something happened, and at what time we get the information that that thing happened, are two different things in special relativity, as you rightly point out. We can, in practice, measure the latter. But in calculations we use the former, and everything in this video is the former.
Unless otherwise specified, descriptions of observations in scenarios in relativity are understood to have the travel time of light accounted for and factored out.
I love your videos. Please don’t start with 12 seconds of complete silence, though.
I like this even though most of it was a little over my head I still learned something
You are doing gods work man :D
Hey minutephysics, I hope you one day touch upon proper velocities as well!
Haha that was great, thank you! I was indeed thinking 'hang on one minute - you switched the order without mentioning it!'
Brilliant! I love your new toy.
Is there proper distance or duration though? and if so does that mean that you can determine if two things, moving at the same speed, happen simultaneously from a true perspective? I don't expect to get an answer considering how late I am to the vid, but if you know and happen to see this please answer.
Please do more series!
Thus series is amazing
Science Envisions yeah man!
Please consider a new frame of referrence to calculate spacetime intervals. A geodesic sphere made up of 20 equalateral triangles (the minimum number required to close a perfect sphere). Add to that three interior lines connectting opposite points of the sphere and you will have all of the triangular elements required to accurately calculate spacetime. BTW, the three interior lines serve as an axis about any one of which the sphere is free to rotate.
From where can I get this equipment which you r using in this video? Request help
Very cool. I somehow suspect Pythagoras would be pleased that the math named after him still works on even the most extreme of scales, if with some fairly minor modifications.
Provably the best episode out of all of them
4:45 but what if the boxes were moving relative to each other. Which box gives the proper true distance?
Both. They each calculate the proper length and proper time using their own measurements, and would come to the exact same conclusion. That's the point of proper length and proper time.
you mis understand me, proper time and proper space is calculated to be what length/duration it is for the thing being measured. So the reference frame of that object. But the 2 objects moving relative to each other don't have a shared static reference frame. In the reference frame of the first object the second object is moving, while in the reference frame of the second object the first one is moving.
But we don't need a shared rest frame for this to work.
Say, A & B are moving relative to each other. Whatever A measures about themselves is automatically "proper", whatever B measures about A can be converted to "proper" by using the formula, and the two results would agree. Whatever B measures about themselves are automatically "proper", and whatever A measure about B can be converted to "proper" by using the formula, and the two results would agree.
Dont forget that special relativity always assumes that something with a speed v will and always has been moving with a speed v, or at the start of the observation the moving object will instantly move at speed v. Of course, the object has speed v in your frame of reference.
If an observer was moving >0.5c would there also be a redshift or blueshift (depending on what direction of the observer and what's the observed are) WITH the change in time/length perspective?