Time isn’t simply just another dimension
bigthink.com
bigthink.com
Not the clearest way to think about this. The speed of light isn't the speed limit, it's the only speed. If you're not moving in space, you're moving through time at c.
So for the above example, something moving in the x-direction at c, can't also be moving in the y or z components--spacial directions are also not independent with each other.
x, y, and z are just shorthand for orthonormal basis vectors. What you’ve described isn’t “traveling in all three dimensions” simultaneously, it’s traveling along on of the dimensions with a different basis.
Undoubtedly there must be something I’m missing here—I’ve taken physics courses but clearly I’m no expert. :)
That is, any vector is going to be inherently one dimensional, regardless of its coordinates. Dimension is a property of a set of vectors, dependent upon how many are linearly independent of the rest of the vectors in the set. What I described doesn’t imply that there are infinite dimensions.
The vector [0,0,1] is traveling through three dimensions just the same as [1,1,1].
If you set your velocity to [1,1,1,x], then x (your speed in time) MUST be sqrt(c^2-3). And still, once you've done that, you cannot "scale your velocity", because you cannot change your speed. We can only change direction.
> I can imagine a vector, [1,1,1] in cartesian space. Scale that vector by c and you are now going light speed in all three spatial dimensions.
But my point was if look at the magnitude or such a vector it would be >c and therefore exceed the speed limit of c.
It is fitting that we use a similar quantum phenomenon, oscillations of the Cesium atom to measure time.
You can ask for your overall speed in all spatial dimensions with dX/dt where dZ^2 = dy^2 + dx^2 + dz^2.
By analogy, you could say that your speed through all of spacetime is dS/dt, where dS = dx^2 + dy^2 + dz^2 - dt^2. You could then say that your speed through time us dT/dt, where dT=1-dS. Although this quanity is really measuring the difference between proper time and coordinate time, which is just time dilation. An equivalent derivation works for length contraction as well.
Importantly, all of these qualities are dependent on your choice of reference frames. Only dS and dT are frame independent, so (in some sense) they are the only true quantities. Both of them also rely on merging time and space to a single quantity.
Of course all of what I wrote applies to special relativity (flat spacetime). Once you get to curved spacetime, your metric gets more complicated, but the general ideas still apply.
Really, I don't see how you can make sense of general relativity as anything other than a 4 dimensional geometry with a really weird metric.
Do you mean cosmic inflation? If that happened at all, it must have been before the formation of the cosmic microwave background. The (standard) concordance cosmology provides a calculation for the PVF photon visibility function (PVF) -- when the surface of last scattering became transparent to photons. From detailed observation of the CMB (by the Wilkinson Microwave Anisotropy Probe among many others), we have data strongly supporting that the PVF's interval from opacity to transparency is about 110 000 years, opaque at the early time of about 370 000 years after the electroweak epoch. (The splitting of electroweak into electromagnetism and the weak force gave rise to electrons and other leptons, photons, and neutrinos, and their respective antiparticles; consequently there is also a Cosmic Neutrino Background). Prior to the start of the PVF, matter in the universe was too hot to form electrically neutral structures like atoms, and prior to the end of the PVF these structures would be broken apart by electromagnetic interactions.
Or do you mean the metric expansion of space? That's an ongoing observable, unlike cosmic inflation, which ended hundreds of millions of years before the formation of the first galaxy clusters, while the metric expansion continues to cause all galaxy clusters to drift apart from one another.
"Cosmic inflation" doesn't do anything to the motion of an object today; it switched off more than thirteen billion years ago.
How about expansion, then?
The universe at scales where galaxy clusters are like fine grains of dust or microscopic elements of a fluid is well represented by a set of equations -- the Friedmann equations -- that describe an expanding spacetime (the Robertson-Walker metric (R-W), if we subtract out all the galaxy clusters leaving only vacuum behind). However, the R-W metric is not a good description for galaxy clusters themselves, nor individual galaxies, nor individual stars, etc. Those are best described by a collapsing spacetime, with a metric like Lemaître-Tolman-Bondi (LTB), adapted for hierarchy and non-spherically symmetrical lumpiness of the collapsing matter. (You are on a lump right now! There is obviously a lot of dense mass in one direction, below you, but not so much above you). We can combine R-W and LTB into a "swiss-cheese" model, where the name is evocative of holes (the LTB collapsing spacetimes) embedded in the otherwise smooth, homogeneous, isotropic Friedmann-[Lemaître]-Robertson-Walker spacetime).
Our galaxy is in a "hole", and so there is no metric expansion within our galaxy.
(Or alternatively, and commonly put forward in popsci descriptions of dark energy, the expansion is so small within our solar system that we can ignore it. We have checked for local expansion experimentally, because if we could measure local expansion we might choose to explore otherwise-superfluous theoretical ideas. All measurements so far are consistent with no expansion in our solar system.)
Is it impossible to not move in space, as you say? I don't know. One can prove whether one is in gravitational free-fall, using highly sensitive accelerometers. One can then set down coordinates that freely-fall with you and your always-reading-no-acceleration accelerometers. In those coordinates, one could say that the rest of the universe is in motion about the coordinate origin, which is you. However, one would tend to reject the notion for reasons similar to the rejection of geocentrism.
It is however impossible to hold still in our spacetime. Our universe has a strong time-oriented causality and for good reason (including the behaviour of subatomic particles in countless laboratory experiments and astrophysical observations) we represent it as Lorentzian spacetime with certain constraints and energy conditions, and while that remains the best most fundamental representation of our universe it is safe to say that everything physical must be in constant motion through spacetime. So our freely-falling self-centred astronaut is only always at the 3-dimensional spatial origin of a set of 4-dimensional coordinates, one dimension of which is timelike. Indeed we can even say that minimizing the movement against spacelike axes, one must maximize the movement against the corresponding timelike axis. We are of course free to set down any set of coordinates we want -- doing so does not change the physical arrangements of matter, only how one represents those arrangements.
Your post did remind me of Cunningham‘s law though (it states "the best way to get the right answer on the internet is not to ask a question; it's to post the wrong answer.")
Maybe my mind was more thinking about absolute movement (which doesn’t exist insomuch as there is a missing universal reference frame) and quantum ground states still having movement…
I.e. if thermodynamics prevents the universe from having regions that reach zero Kelvin, maybe that’s analogous to how exactly 0 movement in space is impossible.
Cosmic inflation == turned off much sooner than 10^-30 seconds after it started. (That's a million million million million millionth of a second. A verrry short time.)
Metric expansion == demonstrably ongoing, and accelerating, until at least a couple of million years ago (and in no more than a couple million years future astrophysicists will be able to demonstrate that it was still ongoing as I typed this).
The strength of the metric expansion is increasing slowly for billions of years. The strength of cosmic inflation has been practically (or even exactly) zero since before there were even electrons and photons.
The metric expansion in the past few million years has much less than 10^-25 of the strength of cosmic inflation.
Finally, most physically-motivated variations on the simplest model of cosmic inflation gives the inflationary mechanism features that the expansion mechanism lacks, and cannot be hidden by equating expansion with super-weak inflation.
"Expansion" and "inflation" are not synonymous.
If you're genuinely interested, Alan Guth's 1998 book (while not representing the state of the art in physical cosmology) is probably more readable than what you'll get on hackernews. Guth is one of the originators of cosmic inflation, and his lively book explains how and why he got there. It also has useful appendices discussing aspects of relativity related to what you've written above. ISBN 9780201328400. It is a good "pop sci" book written by an actual scientist working and teaching in the field at the time. Konstantinos Dimopoulos's 2019 (1st ed.) introductory textbook is another good option; it is likely to become a standard textbook for second-entry undergraduates and advanced undergraduates. ISBN 9780367611040. Dimopoulos is a reader in particle cosmology at Lancaster University, in England. Most other (recent) textbooks at the top of my head are less focused on the issues you have "Cunninghammed" in this thread, or are clearly intended for graduate students.
I don't understand your third and fourth paragraphs, sorry.
Light is easy for us to observe so we mix the speed at which we perceive it to travel to the speed of causality.
Seen through that perspective, if you are at a fix point in space, you could apply the same logic for the time dimension and because it's the same point in time you literally can claim that you travel through time at the fasted speed causality allow it. (normally it would be infinite speed, but because our world is discrete, albeit at a very small scale, the speed of causality is also limited but very large - ie C)
"bigthink", "just have a think", "undecided [whatever]" (indicating that they are thinking about something and providing evidence in their videos)...
I'm sure there are more. in my limited experience, people who tell me that others are wrong, and that only they are thinking about something are about to lie to me and attempt to trick me into doing something that benefits them, and often damages me in some way.
I think it may be that I grew into the internet as it matured, and I've seen many bad actors try new things over the years to swindle gullible internet users.
I don't know. I just know that I do not trust anyone who centers their brand identity around the claim that they are thinking or that they are carefully weighing both sides of an issue before making a decision. People who say that aim to manipulate you, in my experience.
Then you get political parties or movements that claim that they are "true and real" or "genuine".
Just like "The People's Front of Judea" :)
Time present and time past
Are both perhaps present in time future,
And time future contained in time past.
If all time is eternally present
All time is unredeemable.
What might have been is an abstraction
Remaining a perpetual possibility
Only in a world of speculation.
What might have been and what has been
Point to one end, which is always present.
Footfalls echo in the memory
Down the passage which we did not take
Towards the door we never opened
Into the rose-garden
T.S. Eliot - Burnt Norton