This week’s edition of The Biggest Ideas in the Universe completes a little trilogy, following as it does 4. Space and 5. Time. The theory of special relativity brings these two big ideas into one unified notion of four-dimensional spacetime. Learn why I don’t like talking about length contraction and time dilation!
The Biggest Ideas in the Universe | 6. Spacetime
And here’s the Q&A video:
The Biggest Ideas in the Universe | Q&A 6 - Spacetime
I love that spacetime gets its own category. So many authors cover space and time and leave the most fascinating aspects of their synthesis to the reader.
Was there a cat meowing in the background?
Question:
How does Minkowski spacetime arise from the theory of special relativity? Why is it that measuring “distance” with t^2 – x^2 makes spacetime describe the universe?
Does dark energy and space expansion affect light cones?
Question:
In Lorentz invariant, we have the square root of 1-v^2/c^2. If there is a particle traveling faster than the speed of light, we will get a negative number in the square root. Does that mean special relativity does not work for particles traveling faster than the speed of light?
Question:
can I determine how fast I’m traveling in space? Is there an absolute speed in regard to space and thus a speed of 0? Or is this all just relative to other objects in the universe?
Question:
Will the ”flattening” of the light cones in the figure at about 39 min, with time in min and space in m, essentially reproduce the Newtonian notion given at about 33 min?
Dr. Carroll – Thank you for doing these! One question – I remember reading somewhere that photons have momentum. How, if momentum is defined as mass x velocity and a photon has no mass?
I have 2 questions.1. I find it interesting that in special relativity and in Lagrangian analysis, the minus sign seems to be all important. That is in SR, what is conserved and integrated is motion through space minus motion through time, and in Quantum field theory what is integrated is the difference between kinetic and potential energies (rather than the normal sum of energies in traditional QM. Is this just a coincidence or is there something related?
2.4. I think I learned that for an observer outside a black hole when observing someone/thing at the event horizon, that external observer will say that time seems to move infinitely slowly for the thing at the horizon. That is from the point of view of external observer, the object never actually enters, but will hover. So my question is how did the black hole actually form from the point of view of external observer?
Thank you again for these lectures. Regarding the speed of light, we have all been taught (as you have indicated as well) that if an observer stands on the ground and watches a train passing by at a speed of 100m/s, and someone on the train walks at 200m/s in the direction the train is moving, the observer will see the person move at 100 + 200 = 300m/s. However if the man on the train moves at the speed of light (hypothetically, call him photon-man), the observer will see the man move at the speed 300,000,000 m/s, not 300,000,100m/s.
My question is – where does this transition happen between classical speeds and relativistic speeds? For instance, assume the train moves at 0.5c, and the man moves in the same direction at 0.6c, what does the observer see? It cannot be 1.1c – that violates our laws. But it also does not seem reasonable that it is 0.6c, because if it is, then where does this transition to the sum of the individual speeds?
Could you please show how the Lorentz Transformation relates to your way of presenting spacetime?
In Genereral Relativity – due to position in a gravity potential, or in Special Relativity due to relative speeds (in actual physical reality a combination of both) – when we consider that in each different ‘local’ a clock ‘is’ ticking differently to the clock in our own local (that we then make our velocity measurements relative to, ie: v=d/t , AND we consider that in each local a person will always measure the speed of light as 299 792 458 metres per *second* –
Q: – Can we logically state/measure the speed of light as travelling at a constant speed (as held relative to the length of seconds of our clock) ‘across’ all locals if the seconds at differing locals are of variable lengths?
(v=d/t where holding d constant to variable length seconds encountered across a constant distance renders c variable… ie: d is constant but t & therefore c is variable
As opposed to t=d/v where holding v (ie: c) constant to variable length (contracted/curved) distances renders time variable… ie: c is constant, but d & t are variable.)
New subscriber here. Sean, these Big Idea videos are excellent. You’re doing a great job presenting complicated subject matter in a way non-professional physicists can get their heads around.
This most recent video and talk about a block universe got me thinking about time more deeply. In a Newtonian/Euclidian block universe, time is just an index on spatial configurations. It’s not quite a unique ID, since in theory two configurations of the universe at different times could be identical (excepting scale due to constant inflation). So what does the “time” of an event really tell us? Just which spatial configuration it is part of.
We are trained to think that two spatial configurations can’t exist simultaneously, but is that really true? No it isn’t, not if many worlds if the true nature of reality. In which case, the time index only tells us something about a collection of realized quantum states of the universe that exist “simultaneously”. But if more than one configuration can exist simultaneously, why do we need a time index at all? Isn’t it possible that every configuration of the Universe that we associate with the past and future are in fact all existing simultaneously in a timeless reality? We wouldn’t have any way of distinguishing that situation from the one we imagine, in which there are these slices or foliations of this so-called space-time block or manifold that we call “instants”.
That raises the further question of what exactly “space” is, but that’s getting too far out there.
Anyway I’m no expert and I’ve heard that Einstein felt the general coordinate covariance of his spacetime theories were especially important somehow, which suggests to me that time is more than just an index on foliations and I’m missing some deeper meaning.
Now that you’ve introduced Minkowski spacetime, could you help me understand deSitter and anti-deSitter space as well, in the Q&A video?
You used the term “spacelike” while showing a point outside of the two lightcones. I’ve also heard the term “timelike” – in Q & A can you clarify what is meant by the two terms?
To what degree is the spacetime Minkowski interpretation of relativity “correct” versus just being a useful way to do math problems? Are there other valid interpretations including Einstein’s original interpretation?
Can there be more than one time dimension or would it ever make sense to talk about something like this? If not, why is there just one?
Is the invariance of light cones enough to guarantee causation is the same to everyone? That is, cause precedes effect in the same order for all observers?
Awesome video! I have a question to ask. I have read in textbooks that when it comes to quantum mechanics time is treated as background independent. I remember reading that the Schrodinger equation treats time as absolute. Doesn’t this conflict with general relativity’s treatment of time as dynamical. Also what about quantum entanglement? Doesn’t the fact that you can get information about one particle the moment that it is entangled with another particle which is far away seems to imply a contradiction with general relativity? If quantum entanglement is interpreted as facilitating faster than light communication then wouldn’t that seem to imply that there is some notion of absolute time on the quantum level? Or am I misunderstanding something?
Just want to say thank you so much for putting these videos together. I don’t understand it all, but I love it, and it’s stimulating my brain at a rather boring time. You’re my favorite scientist!
I would like to ask 3 questions that came up.
1. If we make the past light cone extend infinitely, then infinitely in the past it will eventually enclose infinite space (or all of space). That would imply that all of the universe would be infinitely within my past reach or in other words compressed into a infinitely small point. Is it just a coincidence that the Big Bang emerges just from this simple idea, if these assumptions are even correct?
2. Suppose we make a light cone. We then move somewhere into the future and from that point draw a new light cone. Now the past of the new light cone can reach into spacetime areas which are forbidden by the previous light cone, future or past. So if I state all of my past with the new light cone it violates the paths that were allowed by the previous light cone. We could just take the cross sections of the new and previous light cones and call that the only allowed areas (the new future will always be ok but the new past is where this problem appears) but that implys always having the knowledge of a previous light cone, which I assume we don’t have or do we?
3. We defined 4-velocity V^mu as having 4 conponents: one for time V^t and 3 regular space components. Similarly 4-momentum P^mu with P^0 for the time component, which = E. And P^x, P^y, P^z, which pake regular momentum p. If we take only the time components then P^0 = E = m*V^t. This would seem very similar to E = m*c^2 if we assume V^t = c^2. This is probably nonsense anyway but if there is some reason behind these assumptions, why would the time component of velocity lead to c^2 and not c? Am I combining incomparable things?
I enjoyed this video. I love thinking about spacetime. :o)
(Q1) Are you interested in sharing your video notes as downloadable PDF slides?
(Q2) In the twin “paradox,” if the second twin zig-zag accelerates, can that equal out to the first twin? Not just one small triangle as you drew but many small triangles added together? The smaller the triangles, the more of them needed? Little wiggles, so many imperceptible little wiggles.
=> To me, it seems defining c as max speed is Newtonian. c has one less component than everything else. In this way, c is the floor, not the ceiling. You hit the gas peddle hard enough, and you end up slamming on the breaks; Ouroboros. Regardless, flipping a thought into its negative (e.g. photography) is a useful tool, even if absurd on its face.
(Q3) I’ve spent a lot of time trying to unify data/code (halted, non-halting) to figure out how to write programming language as a queryable tree. Anyway, why is Pi/4 (45 degrees, sqrt(2)-driven) used for spacetime when Natural orthogonality seems to be Pi/2? Pi/2 has one less component, not Pi/4. Brunelleschi’s perspective doesn’t look at the sides of things (observer) but head-on (experiencer). Is there a unification of Brunelleschi and Minkowski somewhere?
=> For d^2 = x^2 + y^2, the (d-y)/x vanishing point “Infinite-tiles-finite” scale symmetry of x-by-2y tiles x-by-(d+y) can nest scale symmetries within each other unless it’s the Golden Ratio spiral. For instance, Silver’s, e.g. A4 paper’s, (sqrt(2) – 1) Infinite-within-finite scale can use the [ Infinite (4/4)-by-(6/4) tiles that are (5/4-3/4)/(4/4) = 1/2 scaled within a finite (4/4)-by-(5/4+3/4) boundary ] as its x-by-2y base instead of 1-by-2. Gold can’t nest (unless y=0) because d+y > x. Compare the Hilbert space limit.
=> Moreover, this vanishing point (d-y)/x scale symmetry works for all parallelograms, not just rectangles, but non-rectangles have a mirroring effect component that rectangles don’t have.
=> Reiterated, it seems Pi/2, “orthogonality/crosshairs,” has one less component, just like c, so why is Pi/4 used to depict c, not Pi/2? Maybe Pi/2 is used and I’m more ignorant than I realize! :o)
Thank you!
You said “There’s no such thing as at the same time”, which seems unambiguous but I’ve just been watching Brian Greene’s latest Daily Equation video, where he tells us that entangled particles influence each other instantaneously no matter how far apart they are. How can both statements be true?
I have just caught up with your casual conversation on the biggest Ideas of the Universe (Iam completely hooked), so sorry if my question is not as relevant for space time, but more towards time. My question concerns the time travelling twins stationary and rocket woman. When they meet at the fixed location in the future rocket woman’s clock would have ticked over less time than stationary, as rocket woman travelled a longer distance over time. However would this still be true, if stationary twin had been a harmonic oscillating twin. Zigzagging her way up around this stationary position towards their future meeting point? Thank you so much for your ‘conversation’ (to me it’s a brilliant lecture), Lex
The perpendicular coordinates (t’, x’) that appear to have an angle in “Reference Frames” section threw me even deeper in the abyss of a rabbit hole. I need to dig into another one of these many non-intuitive topics. Way to get hooked!
“Reference Frames” (55:00) section introduced a coordinate that is “very very analogous to rotating coordinate in good old Euclidean geometry”. Usually, the coordinates remain perpendicular to each other. However, the yellow coordinates (t’, x’) do not appear to be perpendicular. But in fact, as Dr. Carroll proceeded to say, they are perpendicular in Minskowskian sense! I don’t see the connection from the minus sign in Minskowskian geometry.