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.
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"
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.
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!
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 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.
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!
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.
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.
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
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.
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.
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?
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.
I was thinking - if with Lorentz Transformations we're able to measure the true length (distance) and true time (duration) then when I'm told that there is no way to define what's moving and what isn't between inertial frames of reference, it seems that if movement is simply a function of distance and duration, and true distance and true duration can be measured by using Lorentz Transformations to make the measurement at the point of reference of the object itself then we *should* be able to measure which inertial frames of reference are moving and which aren't. The mind blowing thing is that it seems to suggest that each body isn't moving - so long as there is no acceleration then each body would measure itself as having traveled 0 distance over any given amount of time which is no movement. So all these inertial observers traveling at constant velocity in any given direction relative to each other, really aren't moving at all?!! Or have I gone off the deep end?
now to figure out the movement of all bodies in space to determine how fast in one direction you'd need to go in order to "Stop" relative to the majority of space
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...
It seems like it’s just a “Lorenz transformation” to the perspective of the event in question. In which case it is relative we’re just agreeing on what space and time are relative to.
Yes. 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). 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 inertial frame of reference is any perspective from which no fictitious forces need to be introduced to account for any accelerating bodies. 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. 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. The so-called, 'Proper length' of an object is the name given to the length of the object as measured in a frame of reference in which the object is stationary. The so-called, 'Proper time' between a pair of events is the name given to the time measured between the events, in any frame of reference in which both events occur at the same location. For any pair of events that are causally connected there can be an unlimited number of such frames and the 'proper times' measured by each frame can be different. However, all inertial frames in which the events occur at the same location agree on the 'proper time' between the pair of events and this is the maximum value measured by any frame. The 'Proper distance' between a pair of events that are not causally connected is the distance measured between the events in a frame in which they occur simultaneously. This also takes a maximum value in any inertial frame in which the events occur simultaneously. In any inertial frame, the spacetime interval between any pair of events can be calculated by the formula, ds² = (dx)² - (c*dt)² or if you prefer ds² = (c*dt)² - (dx)² depending on your choice of sign convention. Here, dx is the distance measured between the events, dt is the time interval between them, c is speed of light and ds² is the spacetime interval. The spacetime interval between a pair of events is absolute. Due to the form of the formula for calculating the spacetime interval between a pair of events from measurements made in any inertial frame, there always happens to be inertial frames in which either the time interval or distance between the events is zero, depending on whether the events are causally connected. So the square of the 'Proper time' or 'Proper distance' between events in an inertial frame is the spacetime interval between those events.
i dont know why seeing something move slower even creates the idea of "time dilation". a sound wave get stretched when you move relative to its source as well, but nobody thinks time is dilated when an ambulance drives past and its siren gets deeper
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 :)
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!
i feel a stirring in my gray matter with these videos. i am forced to think in ways i haven't since physics III in undergrad. tell me - does anyone else have to pause, then go back maybe 10 seconds to hear a statement a second time (and maybe a third time, etc.)? i need to hear again, then maybe digest something before i can go on. hopefully, many others do that, too, and i'm not a moron.
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 :)
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.
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.
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.
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.
The only way to get a negative value within the square root is if v > c which is impossible. In fact, assuming that the Lorentz factor has to be a real number, it’s an alternative way showing that velocities can never exceed c. The ‘odd’ feeling you describe is a mathematical intuition for what is being explained in this series. 😊
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.
Is the universe even older and bigger from the perspective of someone on Mars? Mars is moving slowly and there's less gravity compared to Earth, so here on Earth we must experience time dilation and length contraction when compared to how someone on Mars would perceive the universe.
Compared to this relativity, mass also shifts... so how do we know that our measurement is the propper measurement? Could we not be simple already moving near the speed of light and what we measure in time , length and mass is just the contraction or dilitation in spacetime?
As a 15 year old in high school, it's really killing me that there is literally nobody that I can talk to about this sort of stuff. If I try to ask my math or science teachers about it they either have no idea what I'm talking about or don't care enough to actually have a conversation about it. And god knows none of my classmates know anything about this. Anyone got anywhere to have conversations with others about physics and high-level math? This is super interesting to me
Can anyone answer this question for me? Given that: (1) the speed of light in a vacuum is the same for all observers, (2) that precise speed is known only from direct measurement and has not been derived from basic principles, and (3) that measured speed is, as far as we know, arbitrary, how do we know that it hasn't been changing slowly (for all observers simultaneously) over the lifetime of the universe?
It is just Pythagoras backwards. If c^2 = a^2+b^2 then a^2 = c^2-b^2 and b^2 = c^2 - a^2 The difference cannot be negative if c is the hypothenusis. This is normal geometry only that in one coordinate we deal with time (which we assume orthogonal to space) and not distance.
no, this is Pythagoras for Non-eucludian geometry. a^2 - b^2 = c^2 instead of a^2+b^2 = c^2 , and c is the separation line ds. it isn't backward, it is forward in non-eucludian space.
@minhdang1775 It's because the object moving away from you contracts in simple terms when a lorentz transformation is done. So the true length will be smaller instead of larger in simple terms, which is where the negative instead of positive comes from?
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?
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.
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.
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".
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.
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.
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
"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.
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.
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
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.
I'm loving the time globe! it really helps with getting an intuitive feel of this subject
i like how this channel explains everything in such a simple and direct manner that everybody can understand ^^
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!
Watch YT videos @ 1.25: ah, perfect
Watch minutephysics @ .75: ah, perfect
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 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
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!
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.
This was such an amazing theory to learn.
Wow.
Love the way it's taught here. So easy and quick.
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
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
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
It’s amazing how many videos he can make with this tool. I’m loving it
Absolutely *mind blown*
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
Thanks to you I kinda start to get a sense for SR
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.
You have a gift for rendering the incredibly difficult into the relatively simple. Thank you!
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.
4:44
I'm not completely comfortable with "twelve hundred million" as a unit.
Sixty symbols did a show on the Muon issue - I'm going to have to watch that again.
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?
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
This actually is very practical and useful knowledge to have. Thank you for this.
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!!!
These uploads are amazing. Great work Henry.
I was thinking - if with Lorentz Transformations we're able to measure the true length (distance) and true time (duration) then when I'm told that there is no way to define what's moving and what isn't between inertial frames of reference, it seems that if movement is simply a function of distance and duration, and true distance and true duration can be measured by using Lorentz Transformations to make the measurement at the point of reference of the object itself then we *should* be able to measure which inertial frames of reference are moving and which aren't. The mind blowing thing is that it seems to suggest that each body isn't moving - so long as there is no acceleration then each body would measure itself as having traveled 0 distance over any given amount of time which is no movement.
So all these inertial observers traveling at constant velocity in any given direction relative to each other, really aren't moving at all?!! Or have I gone off the deep end?
Indeed in their own reference frames they are not moving, but they move relative to one another.
If that's what you meant.
now to figure out the movement of all bodies in space to determine how fast in one direction you'd need to go in order to "Stop" relative to the majority of space
The apparatus doe... This dude is the god of teaching
Really thanks for these series.Keep it up please!
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...
Piece of cake
moving 1/3 the speed of light to my left.
Piece of cake...
Light cake.
Its hard tho
Sorta
OMG ! U have just made another abstract concept extremely easy!!!
It seems like it’s just a “Lorenz transformation” to the perspective of the event in question. In which case it is relative we’re just agreeing on what space and time are relative to.
Yes. 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).
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 inertial frame of reference is any perspective from which no fictitious forces need to be introduced to account for any accelerating bodies.
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.
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.
The so-called, 'Proper length' of an object is the name given to the length of the object as measured in a frame of reference in which the object is stationary. The so-called, 'Proper time' between a pair of events is the name given to the time measured between the events, in any frame of reference in which both events occur at the same location. For any pair of events that are causally connected there can be an unlimited number of such frames and the 'proper times' measured by each frame can be different. However, all inertial frames in which the events occur at the same location agree on the 'proper time' between the pair of events and this is the maximum value measured by any frame. The 'Proper distance' between a pair of events that are not causally connected is the distance measured between the events in a frame in which they occur simultaneously. This also takes a maximum value in any inertial frame in which the events occur simultaneously.
In any inertial frame, the spacetime interval between any pair of events can be calculated by the formula,
ds² = (dx)² - (c*dt)² or if you prefer ds² = (c*dt)² - (dx)² depending on your choice of sign convention.
Here, dx is the distance measured between the events, dt is the time interval between them, c is speed of light and ds² is the spacetime interval. The spacetime interval between a pair of events is absolute. Due to the form of the formula for calculating the spacetime interval between a pair of events from measurements made in any inertial frame, there always happens to be inertial frames in which either the time interval or distance between the events is zero, depending on whether the events are causally connected. So the square of the 'Proper time' or 'Proper distance' between events in an inertial frame is the spacetime interval between those events.
i dont know why seeing something move slower even creates the idea of "time dilation". a sound wave get stretched when you move relative to its source as well, but nobody thinks time is dilated when an ambulance drives past and its siren gets deeper
The fact that there actually could be two boxes simutaneously combusting 1200 million meters apart.
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 :)
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!
Where do I get one of these space/time mechanical contraptions and how much would it cost?
Absolutely love your videos, and these videos are probably, in my experience, the best explanations for relativity out there
This chapter I actually managed to comprehend somewhat more relative to the other chapters
Hey minutephysics, I hope you one day touch upon proper velocities as well!
i feel a stirring in my gray matter with these videos. i am forced to think in ways i haven't since physics III in undergrad.
tell me - does anyone else have to pause, then go back maybe 10 seconds to hear a statement a second time (and maybe a third time, etc.)? i need to hear again, then maybe digest something before i can go on. hopefully, many others do that, too, and i'm not a moron.
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 :)
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.
That actually makes sense. For the first time in my life, I actually understand it, or at least that part of it.
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.
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.
Loving this series! It makes so much sense.
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.
Using the square root feels odd because it makes it seem weird if someone gets a negative value within the square root.
The only way to get a negative value within the square root is if v > c which is impossible. In fact, assuming that the Lorentz factor has to be a real number, it’s an alternative way showing that velocities can never exceed c. The ‘odd’ feeling you describe is a mathematical intuition for what is being explained in this series. 😊
What about I move in a different way from left and right?
Knowledge expansion, loveitt.
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.
*only in a non-varying gravitational field
A very awesome series indeed!
Is the universe even older and bigger from the perspective of someone on Mars?
Mars is moving slowly and there's less gravity compared to Earth, so here on Earth we must experience time dilation and length contraction when compared to how someone on Mars would perceive the universe.
Minkowski would be proud after ur simple and elegant explanation!
Haha that was great, thank you! I was indeed thinking 'hang on one minute - you switched the order without mentioning it!'
The whole video i was just sitting with childish amusement watching that magic board with relative axis. Boy that thing is awsome!
Compared to this relativity, mass also shifts... so how do we know that our measurement is the propper measurement? Could we not be simple already moving near the speed of light and what we measure in time , length and mass is just the contraction or dilitation in spacetime?
As a 15 year old in high school, it's really killing me that there is literally nobody that I can talk to about this sort of stuff.
If I try to ask my math or science teachers about it they either have no idea what I'm talking about or don't care enough to actually have a conversation about it. And god knows none of my classmates know anything about this.
Anyone got anywhere to have conversations with others about physics and high-level math? This is super interesting to me
You are 18 now I wonder how much you have advanced 😅
I like this even though most of it was a little over my head I still learned something
Can anyone answer this question for me? Given that: (1) the speed of light in a vacuum is the same for all observers, (2) that precise speed is known only from direct measurement and has not been derived from basic principles, and (3) that measured speed is, as far as we know, arbitrary, how do we know that it hasn't been changing slowly (for all observers simultaneously) over the lifetime of the universe?
Nice work
Provably the best episode out of all of them
It is just Pythagoras backwards. If c^2 = a^2+b^2 then a^2 = c^2-b^2 and b^2 = c^2 - a^2
The difference cannot be negative if c is the hypothenusis.
This is normal geometry only that in one coordinate we deal with time (which we assume orthogonal to space) and not distance.
no, this is Pythagoras for Non-eucludian geometry.
a^2 - b^2 = c^2 instead of a^2+b^2 = c^2 , and c is the separation line ds.
it isn't backward, it is forward in non-eucludian space.
@minhdang1775 It's because the object moving away from you contracts in simple terms when a lorentz transformation is done. So the true length will be smaller instead of larger in simple terms, which is where the negative instead of positive comes from?
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?
Should use (Δx)^2 instead of Δx^2 to avoid ambiguity.
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
Please make video on how does QUANTUM PHYSICS proves the LAW OF ATTRACTION.
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.
No absolute reference frame, but rather a way to translate lengths and times from another reference frame into your own.
For most of this video, i wanted to ask "But what if my perspective is moving?"...
Yea, I did want to sleep, but thanks for uploading anyway.
I love your videos. Please don’t start with 12 seconds of complete silence, though.
Yes, I undertand some of these words.
I felt smart at the end when he called me astute
The last time my mind was blown this badly was when I realized Batman & Superman both had mothers named Martha.
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".
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 should explain acceleration with this thing. Some weird stuff has got to happen when you do that.
Nolan Palmer "special" in "special relativity" is there because there are rules applied for these theorems to hold. One of them is constant velocity
To be honest, he draws really good
very good video
Damn Thats pretty mind blowing just when I thought UA-cam had described time dialation, another video goes and fuck my whole vision of the universe up
5:53 wouldn’t be that the red dt is equal to the square root of the blue dt minus the red dx?
on my perspective i'm waiting for scientist that we are wrong about knowing the universe and started from the beginning again
Am I the only one who understand nothing of it yet still watched till the end? 🙈
Ok so if speed is distance over time and space is expanding is the speed of light really constant? What about during inflation?
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 suppose this video really gives the former ones another different .. perspective.
318Arnie
Side A:
Good one..
Side B:
Deep one...
The Lorenz time space globe is flat what if space is a circle or an oblong. How does gravity affect the measurements across great distances?