I love your videos! I come from an arts background (I'm a composer and pianist), but I've always been fascinated by Special and General Relativity. Unfortunately, a lot of explanations I've come across are very technical. You have managed to explain concepts as well as quite complex mathematical derivations clearly. Thank you so much.
Personally for me, this is one of the most comprehensible TH-cam video on topic of 'Spacetime', part of 'Theory of Relativity' and its sub-part 'Special Relativity'. Thank you DrPhysicsA.
The statement at 23:24 is wrong. The proper time will always be the shortest. For a person travelling only through time, their spacetime interval is purely vertical in the spacetime diagram, but this does not mean that time intervals are longer for that person. This is because spacetime distances are not measured like in euclidean geometry. In fact, for a person moving relative to the stationary observer, time intervals will be longer. From the invariance of a spacetime interval: (ct)^2 = (ct')^2 - (x')^2, where the primed frame is the moving one, and the unprimed t is the proper time, then (ct')^2 = (ct)^2 + (x')^2, and hence t' > t. By the way, thank you very much for making this videos. They are wonderful!
You sir are a genius. I've seen many videos and had hard time picturing myself even though they used graphics. your simple x,t graph made me realized that I'm traveling though with speed C in spacetime sitting i'm my chair and watching this video. Practically C being max always made sense to me as we can only see photons which we visualize as reality which is at that C.
Dr.Physics I have a question. @ 20:38 you multiply t the time taken by c in order to compare time with distance. But how can we multiply c just like that, what is the explanation behind doing so and why do you multiply it with c and not any other number. Ain't it changing the whole value of how much I have traveled in time by being stationary.
Wow this is deep.. I'll truly have to work my brain to failure in order for it grasp even the surface of these equations. The more I learn, the duller I start to feel. But in the graph there are actually places in space and time as if they're coordinates that can be pinpointed. Could this mean, that all that's past, present and future is, already there? But that we can, with our limited senses, only perceive one frame at a time. What we call the present. And that our perception of time is just a combination of memories of the past, created by observations which in turn we consider the present + expectations/estimates we create according to the previous two, and that that forms our image of moving straightforward through a set timeline, like a rollercoaster? That in reality all three are just there, in the map of space time? That we just can't see past our perception of the present? Awesome video, great explanations thanks
DrPhysicsA, How can I put this nicely, many have moved on from the Einstein space-time story. In short we want our aether back. When a stone is thrown into a pond the resulting water wave isn’t water moving from the stone to the edge of the pond. When a noise is made the air doesn’t move from the source of the sound to my ear. When light enters glass it propagates 35% slower and when leaving the glass resumes propagation +35%. The light from the source doesn’t travel it propagates just like a water wave or a sound wave. A water wave needs water, a sound wave needs atmosphere, and light needs ether, because something needs to wave for propagation to happen. Now doesn’t it make sense there is aether and perhaps matter moving through aether is physically effected and if that matter was in the form of a clock it too might be effected. A clock creates a sequence of events, even an atomic clock, a tic-toc if you like, which is in no way measuring the thing called time. This whole elaborate concoction (math included) to make sense of reality by pinning it all to the speed of light propagation is getting a bit long in the tooth.
Great Lectures , i want to ask about the last comment in the lecture , If i move at the speed of light given from the space-time chart wouldn't i experience time passing as well as space with an angle 45 , doesn't time stop if i am only moving through space ??? Thnx
Many thanks for this, I think it has cleared up a question that I had. Before I saw this I had the thought that we were all travelling through space time at a constant. I had thought something along the lines of c2=sqrt(t2+x2+y2+z2), ie pythagoras theorem, i then thought that the x2+y2+z2 distances could be extended to more dimensions. Not sure if thats right or makes sense !
You are assuming that both observers will measure the same value of t. But since one observer must traveling at a significantly different speed to the other the time measures will differ. Moving clocks run slow.
I don't really understand what "moving through spacetime" means. When we say "moving" it supposes some notion of time independent of the coordinate system in which the movement happens. So when you say "moving through spacetime" do you really mean that there is something "immutable" existing in spacetime and you are describing its properties?
In addition, the gravitational force slows down passing of time. So is the speed, because the mass increases with the speed ... So, it looks like the gravitational force is a force acting opposite to whatever is behind the passing of time.
You said we always travel at c in spacetime. The problem is, speed in spacetime doesn't quite make sense to me unless you define a new absolute time axis. This is actually what I think is going on. We can define a new absolute time axis to watch our universe. C is not going to be a constant in this new coordinate system.
Conventionally we show the speed of light at an angle of 45 degrees. If you were able to move horizontally then that would imply moving thro space but not thro time. But of course you are not allowed to do that.
Thank you very much for all of the excellent movies. As a layman I have a question. If electrons and photons move throughout space with speed c and we observe them in the double slit experiment, isn't it fair to say that in the electron's and photon's frame of reference time spent during travel is zero, in other words, all electrons pass the slits in the same time even when we fire the electrons one after the other in our frame of reference? In that case the electrons interfere with each other in their frame of reference and may cause the interference pattern. When we then observe their paths, we force nature to age a tiny bit in the other frame of reference, hence the change in fringes. So our awareness would create space and time in the reference frame of everything that moves with speed of light, which is everything we are made up of. Looking forward to your views.
The mind boggles! Does this mean intergalactic travel is possible? As my spaceship approaches the speed of light, the universe around me shrinks to a dot. An observer would see my journey taking millennia, but to me in my spaceship it takes the blink of an eye. Who needs warp drive?
Because the escape velocity of a black hole is greater than the speed of light, that is the reason why light cannot escape. Gravity cannot move faster than the speed of light.
Sorry for being stupid but what happened at minute 26:00 when your pen quickly pointed at t’ squared and your voice says into 1 and then there is a 1 where previously there wasn’t one. I got the same conclusion with several lines of algebra but you did some neat little trick and got straight there.
Sorry to point out but proper time is not the longest time. Instead it is the time measured by an observer in his own frame at the same place. It tends to be the shortest time and is typically depicted as t zero. If this proper time and its frame appears to move relative to another observer at rest then this observer at relative rest will measure the proper time as being dilated or longer.
Wonderful!! All your videos are Hats Off!. I become your Fan Sir. ... I have a question, all observers should agree on s^2=(ct)^2-(vt)^2. one observer measure speed v as C i.e v=c and other observer measure as v=c/2. For 1st observer eq => s=0 and for 2nd observer => s=1/2 (ct)^2 ?? How it is possible?
as we move in space, the rate of our body's biochemical reactions will increase compared yo when we stand still in space, so we will age at the same rate as when we stand still
+moonlight Who says you have to physically exert yourself to move? You could be flying in a plane, driving a car, on a boat, on a spaceship, on earth rotating around the sun, or a sun through a galaxy. From a reference point which sees you moving, even if you feel you are at rest, a longer time will be measured. If you measure your time through a certain space and they measure your time through that same space, their clock will have read a longer time than what yours reads.
at 23:23 you say that the proper time is the longest time .I got a little confused since I was convinced that the so called "proper time" is the time between two events measured in their rest frame and it should be, therefore, the shortest (or "quickest") time. Indeed, the time between the two events measured from any observer from a moving frame will be dilated and therefore longer. What am I missing? Thank you very much.
You have to think about it looking at the spacetime diagram. The observer at rest won't travel any distance in space, so he will "use" all his "spacetime path" to travel through the "y" axis, which is time in spacetime. In other words there won't be any "x" (space) component of his "spacetime path", so the "y" (time) will be the longest it can be.
DrPhysicsA Your method of teaching is beautiful! I have a certain question in mind. If we don't age at all when we move at the speed of light, does our body cells actually keep functioning on forever? Or do they work normally? Cells cannot get eternal energy, so how can they live? Assuming that we have enough resources to move at the speed of light for few centuries.
the flow of time cannot be perceived. you may notice someone else's time reference is different when comparing clock measurements. still, you cannot be aware of time dilation because the synapses that make up your thought processes will be slowed down, just as your metabolic rate, allowing you to live longer (but again, never noticing it)
a question. consider that earth is traveling through space. following the sun, and the motion of the milky way, etc. etc. now, if you could get off this merry go round and stop. somewhere in space you stop. would you immediately get old and die ??
Based on Einstein's equivalence principle, is the equipment they use to train astronauts, which can generate 6g, be used to test light bending. Also if you put an atomic clock in one, would time go faster?
No matter how close to the speed of light the protons travel, the speed of one seen by the other will be even closer to the speed of light but wont exceed it. See my 5 part video sequence on Special Relativity for an explanation.
If an object is at rest in a reference frame with respect to three spatial dimensions of Space, it's still in motion in Space-Time. In order to move through Space, a force is required to act upon the object. It makes me think that force is required to move an object through Space-Time as well, even if the object is at rest with respect to spatial dimensions. Actually, an object is never at rest in a Space-Time reference frame, because it always moves through time.
so if time can be swapped for speed through space or if speed through space is convertible to time then it must be that space and time are the same thing.....or else time and velocity are interchangeable and are essentially the same thing.......my question is, in the twins paradox based on travel at 3/5 c, one twin is 10 years old and the other twin is 9 years old after the 'experiment' ends and the question is "where did the lost year go?" ..... it just 'didn't happen?' ..... but something happened because both twins end up back at the same place in the same time frame so they started equal and ended equal but one twin lost a year.....where did it go?
Ok so if I get it right from what I see is that if you completely leave the milky way and travel to the centre between two galaxies and decelerate to v0 then x and p will be 0 X0 a set point with no movement p0 a set point not accelerating to any point in time absolutely zero then t will automatically be t0 and time will not exist. And Nothing will age in that space ship I'm in? Is it then that I will be stuck in that moment when everyting turns to 0 since future and past will also go to 0. Will I be suspended in animation. Just something that came to mind sorry if I'm completely wrong.
Proper Time = Local Time but it assumes all others are moving and it is stationary but what if we looked at a number of clocks in various reference frames and discovered they are all running at different rates? Wouldn't that be proof that there is a spacetime reference frame (effected by GR so it's not flat) and objective proof that this assumption (all others are moving) is wrong ? After all this Proper Time is only based on the simple assumption that the closing velocity or opening velocity is the other object's movement and not your's ? It also assumes vector velocity as objective and not subjective velocity. We know through experimental data that clocks compaired before and after acceleration are rock solid proof that time dilation is a product of velocity (with one hypothetical exception that I believe is key). Given my input the math is correct even though it gives no evidence if xt or x't' is the one experiencing dilation only assuming x't' is actually the one with vector velocity. At best we can only assume this is a differential equation but like with special relativity without outside data there is no way to tell which Reference Frame is "correct", however if in reality we could look at these clocks the one running slower is more correct, the problem with Minkowski is it's a limited model assuming one space dimension which would actually correlate to a vector speed compaired to another vector speed (if xt and x't' are both moving). Someone please tell me I'm not wasting this insight on "math majors" who lack imagination and those who are awed but don't have a clue.
Suppose 2 LHCs are kept next to eachother with protons going round at 99.9999%C in opposite directions what will be their relative velocities when they are moving away from eachother? What will one see of the other? Thank you very much..:)
i replayed this video several times. it feels like “the speed of light” equals money in the spacetime. quantizrd or something? cost? but its like a cloud in my head not obvious
While standing still, you're moving at the speed of light in time, but not moving at all in space, and vice-versa, moving at the speed of light in space means you're not moving in time at all..
Photons that travel for billions of years did so in no time according to photon's internal clock. In other words Nature sets the life time of a weightlews photon to 0 to avoid contradictions. For us photon lives, but weights more than 0.
why isn't the speed of light simply the vertical time axis like you explained at the end of the video if nothing else goes faster? 5:44 - 15:10 The S lines, isn't that a regular acceleration? So we all agree on acceleration because light doesn't accelerate. Are all of these lines experienced by both the moving object and the stationary observer then where is the relativity ? Why do you multiply t by just to measure time in distance? For example, I traveled at the speed of light from t=0 until t=5, then shouldn't my x function just be the 45 diagonal line? Then my time is 5, not c * 5 I watched the video 3 times I still don't understand the basics of how to read a minkowski-space coordinates .
for a frame moving a velocity v w.r.t a stationary frame, why does the Minkowski diagram has even x` axis inclined at an angle say alpha to the x axis? what is the physical interpretation of all this
An “observer” has absolutely NO affect on the one being observed time, distance or speed. if an observer did ones distance-per-time can NEVER be determined. Does y axis represent one’s location, or speed, or speed and distance traveled?
If it is not possible to travel greater then the c of light, then why is it that not even light can escape the gravitational collapse of a black hole. Gravity can move faster then the c of light, and that would cause a length contraction of matter to be synchronized at the same dimension that matter exist in the past. If it is not possible for matter to go to the past then why then is matter able to move to the future due to time dilation?
23:24 why always the longest time? Twins paradox says shorter, if its proper time for someone eg flying from earth to mars at .8c then back again - that proper time is shorter.
So spacetime diagram can be an analogy but we should not take it literally because this is not our real life date time. I wonder how we are made block minded not to think differently and not to see loopholes in it. But I feel there are loopholes in this spacetime diagram analogy and I will try to find it. 1. Perspective can not be physics. We can use Panama view camara for an event and transmit to all observers in real time. 2. Time of Spacetime seems emergent from a fundamental Time. 3. Objects can move through space but not through Time rather Time moves through objects. The space time diagram might be wrong representation. May be Time axis is S'/S, the rate of passage of time.
i believe that traveling at the speed of light you would continue to age and grow old. compared to other people you might be eternal, but you do get old.
Does this mean I will age less if I move around more? Also, does the fact that we are moving through Space-Time at the speed of light shut the door to time travel?
You will age in exactly the same way whatever you do. A 30 minute TV show will take 30 minutes whatever you do. But if you move around you will age less than someone moving slower. Moving around on earth makes an infinitesimally small difference.
+Diego Silva If one axis where speed and the other time than how would you set a limitation? Would the graph just be scribbled out at 3*10^8 m/s? This doesn't simplify limitations. Secondly, once another frame of reference is accounted for than you wouldn't be able to justify the different points in time & position. If you drew separate axes for other reference time and position... Imagine 2 more lines that have like 70 degrees between them reaching out from the origin in the same general directions as the axes, but obviously they are getting farther away from the axes as you reach out.. Now take these 2 axes and try to draw a line in time in the reference graph that does not change position (aka it was at 0 speed and just moved along its time axis). This line from our reference point wouldn't just be moving, as is in the range of possibility, but it is ACCELERATING. The object could never be still in our reference frame, even if that other frame is moving at a constant speed. The only way the speed could be constant is if the object was decelerating. That is just wild to think about. Objects can only be still if they are decelerating?? Or possibly the graph you are thinking of is a position versus time graph. Which would just be another example of how any value of speed is obtainable. Now what is impossible mathematically is a position versus speed graph. Remember position and speed are derivatives of each other. Imagine trying to evaluate your acceleration if you are given only a single variable for velocity. Would your acceleration exist? Even if you chose a velocity point and a different velocity point at a different point in acceleration than the graph could only exist as single points. If you drew a horizontal line from one point to another, then your acceleration would increase while velocity stays the same. Or if you drew a vertical line from one point to another than your velocity would increase without your acceleration. Note: Once you understand in this graph how to draw reference lines and other world lines from different perspectives, you will see why this space time graph is better. It really does show how time dilation and length contraction exist and what they look like from each reference including the speed of light, which is actually just a line that is showing what the asymptote of any function you write will never intersect. Once you get into general relativity, things get significantly more confusing. For now, accept that these other scientists, who have spent many years and calculations on developing a method to make things more visual and easier to comprehend, are possibly smarter than your idea. Try to understand something, before you start trying to come up with your own way to understand it. If you ever do that, you will see how idiotic you sounded.
I am a Cosmic Traveller, have to have moving through Time & Space on the path of Galaxies to my destination of my very own Sagittarius purvasara , my sweet home
At 20:36, why can you multiply by c? Is this not implying that the object is moving at the speed of light through space? Could you please clarify? Thanks in advance!
How about for the point view of photon it self. Length become zero because of length contraction. This is redicilious, we know photon need time to travel long distance, like from sun to earth they need 8 minute.
Or put in words, photons move at C through space, therefore they cannot move through time at all. That is, all of the motion is taken up by moving though space so there is 0 left for movement through time. So from the photon's reference 0 time has passed. In fact, from the photons reference the entire universe is a single point which it can traverse instantly since the photon does not travel through time. Boggles the mind.
So, hypothetically, if we're talking about time freezing, does that mean we should be travelling at twice the speed of light? (if speed of light makes a 45 degree angle with the horizontal, twice the speed of light would make a parallel line with the horizontal and so that would mean moving in space while time is stopped, right?)
Nope. The angle is given by the expression arctan(t/x). If you travelled at twice the speed of light, it would mean that in 1 year you travelled 2 light years, so the angle of the line would be arctan(1/2) ≈ 27º. To freeze time you need an angle of 0º, so arctan(t/x) must be 0º. There's only one value that can fulfill the equation arctan(a) = 0, and it's a = 0. So, to freeze time t/x must be 0, and to accomplish that either t has to be 0 (no time and no movement) or x has to be infinity (which is impossible).
No. If you sat on a photon time would pass at the usual rate. But if you sit on a photon your clock will appear to stop when observed by someone else. The 45 degree angle is the speed of light.
DrPhysicsA But, if you are moving at the speed of light, you are not moving through the time dimension, but only the spatial ones. So, why would you still experience time?
+DrPhysicsA NOTE: A lot of what I'm writing will not make sense, try to hold through 'till the end, hopefully things will start to click as you reach vicinity of my overall point. This is true. But I think the miscommunication here is what our frame of space is. If we sat on a photon, yes our perspective of the world would be moving at the normal rate. This perspective is not actually of our own. This perspective is what the world views our time span as, due to what time they measured us to go through to cover a certain length. So they could say we went 1 light year in a year, thus we saw this area within some perspective of time assumed to be shorter. The problem here is, when you are going at the speed of light, you don't view these points as happening before one another. This is a part of time dilation. Because you are traveling at a speed which cannot be surpassed by any object, then you are actually unable to see anything else moving. All objects in the world, whatever speed they are moving, count the speed of light to be the same value. So if you are moving at the speed of light, than any object in the universe whether or not it is moving, is also moving at the speed of light. Thus nothing you ever see can be viewed as normal. Even light traveling in the opposite direction would still only be moving at the speed of light. If we measure both rays of light, we could measure the distance they covered in opposite directions and that their speeds are both the speed of light. But since they only saw each other moving at a speed they are moving to a single reference frame then there is an indication that in any reference frame light will travel the same speed. Whether or not the other ray is moving away or still, they are moving at the same speed. Since no object can change this parameter, than no object can actually exist in one space and another in any reference to what we viewed. What I'm trying to state here, is that we saw that object moving at the same constant speed even though it was moving an "added or subtracted" speed, in its own reference. Thus did we perceive the object as not moving at all?? If the object was not moving in our reference (because our speed was always constant to it), then the object could be perceived as being in the same spot. If the object is not moving, but in its reference it was, we could assume that we were able to stop time. We stopped time when we were moving because the properties of the object did not change over our start and end point, besides the constant speed of course. Thus as long as we are moving at the speed of light, we can assume that the world is motionless, that nothing is happening, that we are at a single point in space and everything is moving at the speed of light around us. THERE IS NO CHANGE, every point in the world is moving at exactly the same speed. Ultimately, if there was no change, would time change? We know that time would change, in our reference frame. But the light moving, does not see any differences, nor will it ever see a difference until it either views an object moving faster than it, or that it stops. When it stops, the world must catch up all the changes INSTANTLY. Imagine you are traveling, nothing is changing, you stop, and suddenly there is a huge gap in time that was just lost. From an observer's perspective of our perspective, light had found a way to instantaneously change positions. If light were to move, experience no change, and stop. The world would then move vast quantities of time and space to catch up with its new halted position and time. Ask yourself would light then be changing positions? Light moving, sees time stopped. Light stopped, sees time moving. If an object is moving, and time is not changing, then it is simultaneously in both positions at the same time.
what happen to the object/person/anything else if can travel faster than speed of light, not in case by effort but by unknown intervention. is that would make it more sense to travel faster than speed of light?. i made this question for connecting physics to the story of prophet Muhammad called "Isra Mi'raj"
I have a little bit of problem with the 45 degree line, because it gives massless things like photons which travel with c through space an amount of time which is greater than 0.
RagHelen The 45 degree line represents the speed of light. So anything moving at an angle of less that 45 degrees would be exceeding the speed of light.
DrPhysicsA Thanks for your quick reply, Doc. The 45 degree angle is based on observing light moving through space (sic) with the finite speed of c, then? My question arose from the perspective of light in spacetime (sic) itself: When c is the sum of possible movements in spacetime and light already reaches the maximum value on the x-axis (maximum speed in speed), t would have to be 0, which led me to a ninety degree angle parallel to the x-axis. But my conundrum remains: At 1:10 the backwards arrow depicts going back in (space)time, in 3:20 the past lies elsewhere in the triangle ∠ C -C. Moreover, when I got right that x > c means going back in time, there would be a third area of the past, namely the lower triangle in the upper left quadrant (∠ XC).
+RagHelen Light doesnt travel through time from the perspective of light. If we view the light from the sun hitting the earth with a delay of x lightyears, then from the perspective of light, it would measure that the sun and the earth are in the same spot. Since light doesn't travel through time, it can't go back or forward in time. From our perspective we can see lights movement, but thats only because we arent traveling at the same speed. In order to go backwards you would have to change the definition of time. In our reference time always moves forward. In light's it does not change forwards or backwards. For now, anything in the 2nd and 3rd quadrant labels where you were, the origin being where you are, and the past being where you will be. I'm not sure what your question is. The 45 degree angle that light world-line has is just a statement that c*t [or y] = x, and connect that point with a line from the origin. Since the x and y lengths of the triangle are equal, they form 45 degree angles with the hypotenuse. For now we cannot get x>ct (and connect that point with the origin). This would state that from now to the future you will move in more space than time will. Remember, light doesn't know what time is. For you to start with light and reach a point before it, you would have to view both start and end points as being more closely than being at exactly the same spot. Does that help?
I've tried applying the constancy of S^2 to your previous example of the twins --one travels 3 ly at 0.6c and back again , and the other stays at home -- but it never works out for me . I guess I'm using the wrong T' and x',s -- (anyone) care to show answer?
+il2xbox That is if you will stay in the car all of your life, live in it, drive it 24/7 at the fastest speed then MAYBE you will live 1 second more than your average life
Yes. But also travelling the "maximum distance" in a given amount of time. If moving, you would travel lesser distance in time. In other words, from a stationary perspective, time would pass slowly for you, i.e. you take MORE time in getting from point a to point b from the perspective of the standing observer. You are correct. Those are different things. Time dilation and duration contraction.
@Devashish Dey: I can try to explain. The Y axis is not actually an independent "time" quantity T . . . because X and Y aren't ultimately different -- both are just "spacetime" quantities. So it's more accurate/usual to label Y as CT -- time viewed in terms of the distance that light travels. That way, the X and Y axes are the same type of quantity and can be seen to be related to one another. This also reflects, for example, the fact that the distance that light travels per unit of "time" is always the same: 1 unit of CT time = 1 unit of distance, 2 units of CT time = 2 units of distance, etc. The line connecting (1,1), (2,2), etc . . .) is therefore 45 degrees. It's a way to represent the path that light travels through spacetime . . . compared to other objects that can be plotted on the diagram.
+Sapiens Sapiens -- It means that you are always on the move within space-time, and that you do so always at the speed of light. Thus if you stop, meaning to stop as far a motion across space is concerned, you are still in motion, but now in motion across the dimension of time only. If you take this into account and create a simple space-time diagram which is composed of both motion vectors and length scalars stacked on top of each other, you can quickly create all of the SR equations, including the Lorentz transformation equations. Click on NEWKNOWLEDGE to gain access to my videos which show this method.
By far the greatest explanation I have had on this matter... thank you!
The "moving at the speed of light while immobile in space" blew my mind
THANK YOU for explaining special relativity in 26 minutes. It took me 18 years to understand this concept.
I trying, wactch more and more this vedio.
I love your videos! I come from an arts background (I'm a composer and pianist), but I've always been fascinated by Special and General Relativity. Unfortunately, a lot of explanations I've come across are very technical. You have managed to explain concepts as well as quite complex mathematical derivations clearly. Thank you so much.
You just solved every single one of my life problems in 26 minutes
if any author should have 10 million subscribers it is DrPhysicsA!!
Personally for me, this is one of the most comprehensible TH-cam video on topic of 'Spacetime', part of 'Theory of Relativity' and its sub-part 'Special Relativity'.
Thank you DrPhysicsA.
Those last 2 minutes blew my mind. That's so cool.
The statement at 23:24 is wrong. The proper time will always be the shortest. For a person travelling only through time, their spacetime interval is purely vertical in the spacetime diagram, but this does not mean that time intervals are longer for that person. This is because spacetime distances are not measured like in euclidean geometry. In fact, for a person moving relative to the stationary observer, time intervals will be longer. From the invariance of a spacetime interval: (ct)^2 = (ct')^2 - (x')^2, where the primed frame is the moving one, and the unprimed t is the proper time, then (ct')^2 = (ct)^2 + (x')^2, and hence t' > t. By the way, thank you very much for making this videos. They are wonderful!
@TheMaxman22 Thanks. I was a professional scientist and gave lectures.
Wonderful. Greatest lectures ever. Difficult subject like physics made so easy
You sir are a genius. I've seen many videos and had hard time picturing myself even though they used graphics. your simple x,t graph made me realized that I'm traveling though with speed C in spacetime sitting i'm my chair and watching this video. Practically C being max always made sense to me as we can only see photons which we visualize as reality which is at that C.
This video pretty much just changed my life. Kind of on a knowledge high right now. Thank you so much
23:40 Everyone travels through spacetime at the speed of light ... let that sink in for a minute
This is far more enjoyable than watching a movie.
Wow I got some concept on spacetime . Thank you so much sir
The author is so talented in teaching, clear! profound! fun!
Thank you, thank you, thank you. this was exactly the explanation I've been looking for and it was awesome.
Best vid about spacetime I ever saw. Thanks for that.
What a great explanation of the spacetime interval invariant linked to time dilation. Thank you!
I have to agree this is one of the best playlists on relativity around
Brilliant! Once again crystal clear. Keep up the good work.
i like you videos, thanks for effort and sharing.
Dr.Physics I have a question. @ 20:38 you multiply t the time taken by c in order to compare time with distance. But how can we multiply c just like that, what is the explanation behind doing so and why do you multiply it with c and not any other number. Ain't it changing the whole value of how much I have traveled in time by being stationary.
Wow this is deep.. I'll truly have to work my brain to failure in order for it grasp even the surface of these equations. The more I learn, the duller I start to feel. But in the graph there are actually places in space and time as if they're coordinates that can be pinpointed. Could this mean, that all that's past, present and future is, already there? But that we can, with our limited senses, only perceive one frame at a time. What we call the present. And that our perception of time is just a combination of memories of the past, created by observations which in turn we consider the present + expectations/estimates we create according to the previous two, and that that forms our image of moving straightforward through a set timeline, like a rollercoaster? That in reality all three are just there, in the map of space time? That we just can't see past our perception of the present? Awesome video, great explanations thanks
DrPhysicsA, How can I put this nicely, many have moved on from the Einstein space-time story. In short we want our aether back. When a stone is thrown into a pond the resulting water wave isn’t water moving from the stone to the edge of the pond. When a noise is made the air doesn’t move from the source of the sound to my ear. When light enters glass it propagates 35% slower and when leaving the glass resumes propagation +35%. The light from the source doesn’t travel it propagates just like a water wave or a sound wave. A water wave needs water, a sound wave needs atmosphere, and light needs ether, because something needs to wave for propagation to happen.
Now doesn’t it make sense there is aether and perhaps matter moving through aether is physically effected and if that matter was in the form of a clock it too might be effected. A clock creates a sequence of events, even an atomic clock, a tic-toc if you like, which is in no way measuring the thing called time. This whole elaborate concoction (math included) to make sense of reality by pinning it all to the speed of light propagation is getting a bit long in the tooth.
Great Lectures , i want to ask about the last comment in the lecture ,
If i move at the speed of light given from the space-time chart wouldn't i experience time passing as well as space with an angle 45 , doesn't time stop if i am only moving through space ??? Thnx
Many thanks for this, I think it has cleared up a question that I had.
Before I saw this I had the thought that we were all travelling through space time at a constant.
I had thought something along the lines of c2=sqrt(t2+x2+y2+z2), ie pythagoras theorem, i then thought that the x2+y2+z2 distances could be extended to more dimensions.
Not sure if thats right or makes sense !
just realised that i put c2, should have just put c
You are assuming that both observers will measure the same value of t. But since one observer must traveling at a significantly different speed to the other the time measures will differ. Moving clocks run slow.
I don't really understand what "moving through spacetime" means. When we say "moving" it supposes some notion of time independent of the coordinate system in which the movement happens. So when you say "moving through spacetime" do you really mean that there is something "immutable" existing in spacetime and you are describing its properties?
excellent explained
I love you. Ty ty ty ty!
In addition, the gravitational force slows down passing of time. So is the speed, because the mass increases with the speed ... So, it looks like the gravitational force is a force acting opposite to whatever is behind the passing of time.
These vids are great... I can totally see this channel becoming quite popular in the foreseeable future.
You said we always travel at c in spacetime. The problem is, speed in spacetime doesn't quite make sense to me unless you define a new absolute time axis. This is actually what I think is going on. We can define a new absolute time axis to watch our universe. C is not going to be a constant in this new coordinate system.
Conventionally we show the speed of light at an angle of 45 degrees. If you were able to move horizontally then that would imply moving thro space but not thro time. But of course you are not allowed to do that.
U are great!
Thank you very much for all of the excellent movies. As a layman I have a question. If electrons and photons move throughout space with speed c and we observe them in the double slit experiment, isn't it fair to say that in the electron's and photon's frame of reference time spent during travel is zero, in other words, all electrons pass the slits in the same time even when we fire the electrons one after the other in our frame of reference? In that case the electrons interfere with each other in their frame of reference and may cause the interference pattern. When we then observe their paths, we force nature to age a tiny bit in the other frame of reference, hence the change in fringes. So our awareness would create space and time in the reference frame of everything that moves with speed of light, which is everything we are made up of. Looking forward to your views.
The mind boggles! Does this mean intergalactic travel is possible? As my spaceship approaches the speed of light, the universe around me shrinks to a dot. An observer would see my journey taking millennia, but to me in my spaceship it takes the blink of an eye. Who needs warp drive?
Great!!
Very clear. Congratulations for your excellent explanation. Thank you very much.
Because the escape velocity of a black hole is greater than the speed of light, that is the reason why light cannot escape. Gravity cannot move faster than the speed of light.
Sorry for being stupid but what happened at minute 26:00 when your pen quickly pointed at t’ squared and your voice says into 1 and then there is a 1 where previously there wasn’t one. I got the same conclusion with several lines of algebra but you did some neat little trick and got straight there.
Sorry to point out but proper time is not the longest time. Instead it is the time measured by an observer in his own frame at the same place. It tends to be the shortest time
and is typically depicted as t zero.
If this proper time and its frame appears to move relative to another observer at rest then this observer at relative rest will measure the proper time as being dilated or longer.
Wonderful!! All your videos are Hats Off!. I become your Fan Sir.
... I have a question, all observers should agree on s^2=(ct)^2-(vt)^2. one observer measure speed v as C i.e v=c and other observer measure as v=c/2. For 1st observer eq => s=0 and for 2nd observer => s=1/2 (ct)^2 ?? How it is possible?
how did u got the the first two equations in thhe begining of the video....the delta x' and delta t'
as we move in space, the rate of our body's biochemical reactions will increase compared yo when we stand still in space, so we will age at the same rate as when we stand still
+moonlight Who says you have to physically exert yourself to move?
You could be flying in a plane, driving a car, on a boat, on a spaceship, on earth rotating around the sun, or a sun through a galaxy.
From a reference point which sees you moving, even if you feel you are at rest, a longer time will be measured. If you measure your time through a certain space and they measure your time through that same space, their clock will have read a longer time than what yours reads.
at 23:23 you say that the proper time is the longest time .I got a little confused since I was convinced that the so called "proper time" is the time between two events measured in their rest frame and it should be, therefore, the shortest (or "quickest") time. Indeed, the time between the two events measured from any observer from a moving frame will be dilated and therefore longer. What am I missing? Thank you very much.
You have to think about it looking at the spacetime diagram. The observer at rest won't travel any distance in space, so he will "use" all his "spacetime path" to travel through the "y" axis, which is time in spacetime. In other words there won't be any "x" (space) component of his "spacetime path", so the "y" (time) will be the longest it can be.
DrPhysicsA Your method of teaching is beautiful! I have a certain question in mind. If we don't age at all when we move at the speed of light, does our body cells actually keep functioning on forever? Or do they work normally? Cells cannot get eternal energy, so how can they live? Assuming that we have enough resources to move at the speed of light for few centuries.
the flow of time cannot be perceived. you may notice someone else's time reference is different when comparing clock measurements. still, you cannot be aware of time dilation because the synapses that make up your thought processes will be slowed down, just as your metabolic rate, allowing you to live longer (but again, never noticing it)
a question.
consider that earth is traveling through space. following the sun, and the motion of the milky way, etc. etc.
now, if you could get off this merry go round and stop. somewhere in space you stop. would you immediately get old and die ??
Based on Einstein's equivalence principle, is the equipment they use to train astronauts, which can generate 6g, be used to test light bending. Also if you put an atomic clock in one, would time go faster?
please upload more videos about relativity and space-time geometry.....
This made me soo happy!! Thank you!!
No matter how close to the speed of light the protons travel, the speed of one seen by the other will be even closer to the speed of light but wont exceed it. See my 5 part video sequence on Special Relativity for an explanation.
A GOOD WORK, THANK YOU!
Excellent Explanation (Y)
If an object is at rest in a reference frame with respect to three spatial dimensions of Space, it's still in motion in Space-Time. In order to move through Space, a force is required to act upon the object. It makes me think that force is required to move an object through Space-Time as well, even if the object is at rest with respect to spatial dimensions. Actually, an object is never at rest in a Space-Time reference frame, because it always moves through time.
At 13:20 doesn't the c² Δt² - Δx² has to be in brackets?
+Tach' auch Yes, that should be in brackets. :)
Yes because (1-v^2/c^2) is taken as a factor out of both the terms from the previous equation.
so if time can be swapped for speed through space or if speed through space is convertible to time then it must be that space and time are the same thing.....or else time and velocity are interchangeable and are essentially the same thing.......my question is, in the twins paradox based on travel at 3/5 c, one twin is 10 years old and the other twin is 9 years old after the 'experiment' ends and the question is "where did the lost year go?" ..... it just 'didn't happen?' ..... but something happened because both twins end up back at the same place in the same time frame so they started equal and ended equal but one twin lost a year.....where did it go?
Ok so if I get it right from what I see is that if you completely leave the milky way and travel to the centre between two galaxies and decelerate to v0 then x and p will be 0 X0 a set point with no movement p0 a set point not accelerating to any point in time absolutely zero then t will automatically be t0 and time will not exist. And Nothing will age in that space ship I'm in? Is it then that I will be stuck in that moment when everyting turns to 0 since future and past will also go to 0. Will I be suspended in animation. Just something that came to mind sorry if I'm completely wrong.
Proper Time = Local Time but it assumes all others are moving and it is stationary but what if we looked at a number of clocks in various reference frames and discovered they are all running at different rates? Wouldn't that be proof that there is a spacetime reference frame (effected by GR so it's not flat) and objective proof that this assumption (all others are moving) is wrong ? After all this Proper Time is only based on the simple assumption that the closing velocity or opening velocity is the other object's movement and not your's ? It also assumes vector velocity as objective and not subjective velocity. We know through experimental data that clocks compaired before and after acceleration are rock solid proof that time dilation is a product of velocity (with one hypothetical exception that I believe is key). Given my input the math is correct even though it gives no evidence if xt or x't' is the one experiencing dilation only assuming x't' is actually the one with vector velocity. At best we can only assume this is a differential equation but like with special relativity without outside data there is no way to tell which Reference Frame is "correct", however if in reality we could look at these clocks the one running slower is more correct, the problem with Minkowski is it's a limited model assuming one space dimension which would actually correlate to a vector speed compaired to another vector speed (if xt and x't' are both moving). Someone please tell me I'm not wasting this insight on "math majors" who lack imagination and those who are awed but don't have a clue.
Suppose 2 LHCs are kept next to eachother with protons going round at 99.9999%C in opposite directions what will be their relative velocities when they are moving away from eachother?
What will one see of the other? Thank you very much..:)
i replayed this video several times. it feels like “the speed of light” equals money in the spacetime. quantizrd or something? cost?
but its like a cloud in my head not obvious
nice, but you failed to explained LORENTZ TRANSFORMATION! People may get confused what is prime and where you got 1/(v^2-c^2). Thank you for the rest!
Outstanding lecture! Appreciate the effort.
So traveling at the speed of light changes us physiologically so that we do not age.
I do not see how this can be true.
But since "moving" is relativistic, aren't we all *not* moving at the speed of light in spacetime?
of course we are not moving at the speed of light
But the reason is not that "moving" is relativistic
While standing still, you're moving at the speed of light in time, but not moving at all in space, and vice-versa, moving at the speed of light in space means you're not moving in time at all..
Photons that travel for billions of years did so in no time according to photon's internal clock.
In other words Nature sets the life time of a weightlews photon to 0 to avoid contradictions. For us photon lives, but weights more than 0.
why isn't the speed of light simply the vertical time axis like you explained at the end of the video if nothing else goes faster? 5:44 - 15:10 The S lines, isn't that a regular acceleration? So we all agree on acceleration because light doesn't accelerate. Are all of these lines experienced by both the moving object and the stationary observer then where is the relativity ? Why do you multiply t by just to measure time in distance? For example, I traveled at the speed of light from t=0 until t=5, then shouldn't my x function just be the 45 diagonal line? Then my time is 5, not c * 5
I watched the video 3 times I still don't understand the basics of how to read a minkowski-space coordinates .
This guy is kind of a champ
for a frame moving a velocity v w.r.t a stationary frame, why does the Minkowski diagram has even x` axis inclined at an angle say alpha to the x axis? what is the physical interpretation of all this
An “observer” has absolutely NO affect on the one being observed time, distance or speed. if an observer did ones distance-per-time can NEVER be determined.
Does y axis represent one’s location, or speed, or speed and distance traveled?
Why is the speed of light invariable and not relative?
you are wrong the fastest anything can go is information in quantum entanglement
He left a major hole in his theory
If it is not possible to travel greater then the c of light, then why is it that not even light can escape the gravitational collapse of a black hole. Gravity can move faster then the c of light, and that would cause a length contraction of matter to be synchronized at the same dimension that matter exist in the past. If it is not possible for matter to go to the past then why then is matter able to move to the future due to time dilation?
23:24 why always the longest time? Twins paradox says shorter, if its proper time for someone eg flying from earth to mars at .8c then back again - that proper time is shorter.
wonderful explanation
So spacetime diagram can be an analogy but we should not take it literally because this is not our real life date time. I wonder how we are made block minded not to think differently and not to see loopholes in it. But I feel there are loopholes in this spacetime diagram analogy and I will try to find it.
1. Perspective can not be physics. We can use Panama view camara for an event and transmit to all observers in real time.
2. Time of Spacetime seems emergent from a fundamental Time.
3. Objects can move through space but not through Time rather Time moves through objects. The space time diagram might be wrong representation. May be Time axis is S'/S, the rate of passage of time.
how can i plot both of them in the same graph when they are at different tym frame
i believe that traveling at the speed of light you would continue to age and grow old. compared to other people you might be eternal, but you do get old.
Does this mean I will age less if I move around more?
Also, does the fact that we are moving through Space-Time at the speed of light shut the door to time travel?
You will age in exactly the same way whatever you do. A 30 minute TV show will take 30 minutes whatever you do. But if you move around you will age less than someone moving slower. Moving around on earth makes an infinitesimally small difference.
DrPhysicsA but it's still a difference. Fitbit should use this in their marketing campaign lol
Thanks for the reply
thnx 4 sharing
What reference frames are these Spacetime diagrams relative to?
Wouldn't it make more sense if the speed of light were the x axis? Since faster you travel in space, slower you travel in time...
+Diego Silva If one axis where speed and the other time than how would you set a limitation? Would the graph just be scribbled out at 3*10^8 m/s?
This doesn't simplify limitations. Secondly, once another frame of reference is accounted for than you wouldn't be able to justify the different points in time & position. If you drew separate axes for other reference time and position... Imagine 2 more lines that have like 70 degrees between them reaching out from the origin in the same general directions as the axes, but obviously they are getting farther away from the axes as you reach out.. Now take these 2 axes and try to draw a line in time in the reference graph that does not change position (aka it was at 0 speed and just moved along its time axis). This line from our reference point wouldn't just be moving, as is in the range of possibility, but it is ACCELERATING. The object could never be still in our reference frame, even if that other frame is moving at a constant speed. The only way the speed could be constant is if the object was decelerating.
That is just wild to think about. Objects can only be still if they are decelerating??
Or possibly the graph you are thinking of is a position versus time graph. Which would just be another example of how any value of speed is obtainable.
Now what is impossible mathematically is a position versus speed graph.
Remember position and speed are derivatives of each other.
Imagine trying to evaluate your acceleration if you are given only a single variable for velocity. Would your acceleration exist?
Even if you chose a velocity point and a different velocity point at a different point in acceleration than the graph could only exist as single points. If you drew a horizontal line from one point to another, then your acceleration would increase while velocity stays the same. Or if you drew a vertical line from one point to another than your velocity would increase without your acceleration.
Note: Once you understand in this graph how to draw reference lines and other world lines from different perspectives, you will see why this space time graph is better. It really does show how time dilation and length contraction exist and what they look like from each reference including the speed of light, which is actually just a line that is showing what the asymptote of any function you write will never intersect.
Once you get into general relativity, things get significantly more confusing. For now, accept that these other scientists, who have spent many years and calculations on developing a method to make things more visual and easier to comprehend, are possibly smarter than your idea.
Try to understand something, before you start trying to come up with your own way to understand it. If you ever do that, you will see how idiotic you sounded.
I am a Cosmic Traveller, have to have moving through Time & Space on the path of Galaxies to my destination of my very own Sagittarius purvasara , my sweet home
At 20:36, why can you multiply by c? Is this not implying that the object is moving at the speed of light through space? Could you please clarify?
Thanks in advance!
+Ellie Ong. Multiplying the vertical axis by c does not imply anything physical. c is a constant so we are simply changing the dimensions of the axis.
13:17 to 13:30: A bracket is missing, should be γ^2*[(c^2*Δt^2-Δx^2)*(1-v^2/c^2)]
The further steps are right, but the missing brackets are confusing
thank you I got really lost until you pointed this out
How about for the point view of photon it self. Length become zero because of length contraction. This is redicilious, we know photon need time to travel long distance, like from sun to earth they need 8 minute.
Or put in words, photons move at C through space, therefore they cannot move through time at all. That is, all of the motion is taken up by moving though space so there is 0 left for movement through time. So from the photon's reference 0 time has passed. In fact, from the photons reference the entire universe is a single point which it can traverse instantly since the photon does not travel through time. Boggles the mind.
So, hypothetically, if we're talking about time freezing, does that mean we should be travelling at twice the speed of light? (if speed of light makes a 45 degree angle with the horizontal, twice the speed of light would make a parallel line with the horizontal and so that would mean moving in space while time is stopped, right?)
Nope. The angle is given by the expression arctan(t/x).
If you travelled at twice the speed of light, it would mean that in 1 year you travelled 2 light years, so the angle of the line would be arctan(1/2) ≈ 27º.
To freeze time you need an angle of 0º, so arctan(t/x) must be 0º. There's only one value that can fulfill the equation arctan(a) = 0, and it's a = 0.
So, to freeze time t/x must be 0, and to accomplish that either t has to be 0 (no time and no movement) or x has to be infinity (which is impossible).
***** Alright that makes a lot of sense actually! Thanks for the clarification!!
No because to us, we aren't moving but when people see us we are travelling at the speed of light.
Shouldnt the time stop when I move at the speed of light? But 45 degrees imply that time in fact does not stop? shouldnt it be 0 degrees?
No. If you sat on a photon time would pass at the usual rate. But if you sit on a photon your clock will appear to stop when observed by someone else. The 45 degree angle is the speed of light.
DrPhysicsA
But, if you are moving at the speed of light, you are not moving through the time dimension, but only the spatial ones. So, why would you still experience time?
+DrPhysicsA
NOTE: A lot of what I'm writing will not make sense, try to hold through 'till the end, hopefully things will start to click as you reach vicinity of my overall point.
This is true. But I think the miscommunication here is what our frame of space is. If we sat on a photon, yes our perspective of the world would be moving at the normal rate. This perspective is not actually of our own. This perspective is what the world views our time span as, due to what time they measured us to go through to cover a certain length.
So they could say we went 1 light year in a year, thus we saw this area within some perspective of time assumed to be shorter.
The problem here is, when you are going at the speed of light, you don't view these points as happening before one another.
This is a part of time dilation. Because you are traveling at a speed which cannot be surpassed by any object, then you are actually unable to see anything else moving.
All objects in the world, whatever speed they are moving, count the speed of light to be the same value.
So if you are moving at the speed of light, than any object in the universe whether or not it is moving, is also moving at the speed of light.
Thus nothing you ever see can be viewed as normal. Even light traveling in the opposite direction would still only be moving at the speed of light.
If we measure both rays of light, we could measure the distance they covered in opposite directions and that their speeds are both the speed of light. But since they only saw each other moving at a speed they are moving to a single reference frame then there is an indication that in any reference frame light will travel the same speed.
Whether or not the other ray is moving away or still, they are moving at the same speed.
Since no object can change this parameter, than no object can actually exist in one space and another in any reference to what we viewed.
What I'm trying to state here, is that we saw that object moving at the same constant speed even though it was moving an "added or subtracted" speed, in its own reference.
Thus did we perceive the object as not moving at all??
If the object was not moving in our reference (because our speed was always constant to it), then the object could be perceived as being in the same spot.
If the object is not moving, but in its reference it was, we could assume that we were able to stop time.
We stopped time when we were moving because the properties of the object did not change over our start and end point, besides the constant speed of course.
Thus as long as we are moving at the speed of light, we can assume that the world is motionless, that nothing is happening, that we are at a single point in space and everything is moving at the speed of light around us.
THERE IS NO CHANGE, every point in the world is moving at exactly the same speed.
Ultimately, if there was no change, would time change?
We know that time would change, in our reference frame.
But the light moving, does not see any differences, nor will it ever see a difference until it either views an object moving faster than it, or that it stops.
When it stops, the world must catch up all the changes INSTANTLY.
Imagine you are traveling, nothing is changing, you stop, and suddenly there is a huge gap in time that was just lost.
From an observer's perspective of our perspective, light had found a way to instantaneously change positions.
If light were to move, experience no change, and stop. The world would then move vast quantities of time and space to catch up with its new halted position and time. Ask yourself would light then be changing positions?
Light moving, sees time stopped. Light stopped, sees time moving.
If an object is moving, and time is not changing, then it is simultaneously in both positions at the same time.
what happen to the object/person/anything else if can travel faster than speed of light, not in case by effort but by unknown intervention. is that would make it more sense to travel faster than speed of light?. i made this question for connecting physics to the story of prophet Muhammad called "Isra Mi'raj"
I suggest you to learn more about the speed of light. The speed of light cant be faster because you would need infinite energy.
I have a little bit of problem with the 45 degree line, because it gives massless things like photons which travel with c through space an amount of time which is greater than 0.
RagHelen The 45 degree line represents the speed of light. So anything moving at an angle of less that 45 degrees would be exceeding the speed of light.
DrPhysicsA Thanks for your quick reply, Doc. The 45 degree angle is based on observing light moving through space (sic) with the finite speed of c, then? My question arose from the perspective of light in spacetime (sic) itself: When c is the sum of possible movements in spacetime and light already reaches the maximum value on the x-axis (maximum speed in speed), t would have to be 0, which led me to a ninety degree angle parallel to the x-axis.
But my conundrum remains: At 1:10 the backwards arrow depicts going back in (space)time, in 3:20 the past lies elsewhere in the triangle ∠ C -C. Moreover, when I got right that x > c means going back in time, there would be a third area of the past, namely the lower triangle in the upper left quadrant (∠ XC).
+RagHelen you think light travels from a to b in no time??
+RagHelen Light doesnt travel through time from the perspective of light. If we view the light from the sun hitting the earth with a delay of x lightyears, then from the perspective of light, it would measure that the sun and the earth are in the same spot. Since light doesn't travel through time, it can't go back or forward in time. From our perspective we can see lights movement, but thats only because we arent traveling at the same speed.
In order to go backwards you would have to change the definition of time. In our reference time always moves forward.
In light's it does not change forwards or backwards.
For now, anything in the 2nd and 3rd quadrant labels where you were, the origin being where you are, and the past being where you will be.
I'm not sure what your question is. The 45 degree angle that light world-line has is just a statement that c*t [or y] = x, and connect that point with a line from the origin. Since the x and y lengths of the triangle are equal, they form 45 degree angles with the hypotenuse. For now we cannot get x>ct (and connect that point with the origin).
This would state that from now to the future you will move in more space than time will. Remember, light doesn't know what time is. For you to start with light and reach a point before it, you would have to view both start and end points as being more closely than being at exactly the same spot. Does that help?
Thanks for your comments. I see what my problem was.
Thankyou
I've tried applying the constancy of S^2 to your previous example of the twins --one travels 3 ly at 0.6c and back again , and the other stays at home -- but it never works out for me .
I guess I'm using the wrong T' and x',s -- (anyone) care to show answer?
at 14.00 (approx) is that your wife in the background doing dishes? btw awesome vid!
So if I want to convince my parents to buy me a fast sports car I should tell them I'll live longer because moving fast slows down aging?
+il2xbox That is if you will stay in the car all of your life, live in it, drive it 24/7 at the fastest speed then MAYBE you will live 1 second more than your average life
What's that equation the first box ??
Do you mean proper time being the shortest possible time interval?
Yes. But also travelling the "maximum distance" in a given amount of time. If moving, you would travel lesser distance in time. In other words, from a stationary perspective, time would pass slowly for you, i.e. you take MORE time in getting from point a to point b from the perspective of the standing observer. You are correct. Those are different things. Time dilation and duration contraction.
Thanks dr.physicsA
Why is the 45 degree line the speed of light (c) and not any other angle is not clear?
@Devashish Dey: I can try to explain. The Y axis is not actually an independent "time" quantity T . . . because X and Y aren't ultimately different -- both are just "spacetime" quantities. So it's more accurate/usual to label Y as CT -- time viewed in terms of the distance that light travels. That way, the X and Y axes are the same type of quantity and can be seen to be related to one another. This also reflects, for example, the fact that the distance that light travels per unit of "time" is always the same: 1 unit of CT time = 1 unit of distance, 2 units of CT time = 2 units of distance, etc. The line connecting (1,1), (2,2), etc . . .) is therefore 45 degrees. It's a way to represent the path that light travels through spacetime . . . compared to other objects that can be plotted on the diagram.
What does it mean that even if you stop, you travel through spacetime at the speed of light??
+Sapiens Sapiens -- It means that you are always on the move within space-time, and that you do so always at the speed of light. Thus if you stop, meaning to stop as far a motion across space is concerned, you are still in motion, but now in motion across the dimension of time only. If you take this into account and create a simple space-time diagram which is composed of both motion vectors and length scalars stacked on top of each other, you can quickly create all of the SR equations, including the Lorentz transformation equations. Click on NEWKNOWLEDGE to gain access to my videos which show this method.
+NEWKNOWLEDGE Thanks, at an opportune time i am going to watch all of your videos.