How does your refresh rate time accounts for time slowing down for things moving fast (relative to you) regardless of spatial direction they are moving?
Spacetime simplifies many things for example in that framing nothing is ever at rest or nothing ever travels at different speed. The speed of everything is the same, it's just that things spatially at rest have all their speed in the direction of time. Accelerating something in spatial direction is rotating (mathematically) their motion away from time direction, into some spatial direction. This requires energy so the time direction is lowest energy but to rotate it away from it you need to put in energy. If you want to rotate it to 45 deg you need infinite energy.
Also consider the speed of light is also the speed of causality. If there was no such limit it means it would be possible for effects to precede causes which would lead to a very different kind of universe!
How could an effect precede a cause if there were no speed limit to causality?
No matter how fast an effect propogates, it is always after the cause (with an infinite speed, I guess effects happen instantaneously, but not before).
Of course, this doesn't fit with a universe described by general relativity, where time can be different for different observers. But you wouldn't have a universe described by general relativity without that constraint in the first place.
> How could an effect precede a cause if there were no speed limit to causality?
> No matter how fast an effect propogates, it is always after the cause (with an infinite speed, I guess effects happen instantaneously, but not before).
If everything happens instantaneously then there is no real cause and effect, and the universe would be over before it really got started.
old grannies driving at 30mph on the freeway, me at infinity.
on edit: not everything travels at the speed limit, if the speed limit right now is the speed of light - then why doesn't everything travel at the speed of light?
People say if the speed limit was infinite that everything would happen instantaneously - but they still need to explain why everything should go at the speed limit in this other universe, when not everything goes at the speed limit in ours.
Almost everything (electrical fields, atomic radius, even speed of sound in materials) seems to derive in some way from the speed of light and related effects.
perhaps this is an effect of having a speed limit in a universe, if a universe does not have any set speed limit (which is somewhat different than the phrasing speed limit is infinite) perhaps the discussed derivation of other speeds would not exist in the way it does in our universe.
There can be many types of effects in a hypothetical universe.
Imagine a universe like Conway's way of life, where only neighboring cells can be affected in one timestep. Now add to it a rule that all blocks have a color, and the color of all blocks are changed when one block changes color. Now you have a universe with both immediate and non-immediate effects.
But what is “One time step” in that universe? We have the idea of a light clock - light bouncing between two perfect mirrors in a vacuum - as an ultimate clock.
The distance between the mirrors is a number of meters. A meter is based on how far light travels in a second. How long it takes light to go between them is based on the speed of light. Speed, distance and time are connected.
If we untether the speed of light and it’s unlimited, then in some sense there is no way to say how long it takes light to bounce between the mirrors - it doesn’t take any time. And there is no way to say how far apart the mirrors are, if light passes between them instantly that implies there must be no gap to cross. If light crosses no distance in no time then it also bounces back covering no distance in no time, ahh does lots of bounces in no time. There goes the concept of a time step and any concept of “non immediate effects”.
If you try and add time as a separate thing, then you have some kind of Conway’s game simulation - but that gives you a way to track where light is (which simulation cell it’s in) and therefore a kind of distance (how far the mirrors are apart in simulation cells) and then you lock down how light moves in “simulation cells travelled per timestep” which brings you back to a fixed speed of light again.
what assumptions have to be true for such a universe to exist? did it just appear fully formed with N number of cells and defaulting to a color?
a hypothetical universe is mostly worth discussing seriously if there's a physics that is coherent, not just a mathematical landscape. At least it isn't that interesting in the discussion of universes, but might be in discussing mathematical ideas, but those do not necessarily mean there's a universe represented by it.
I'm having trouble with this assertion. Light travels slower in water than in air, by your assertion that light is the limit of causality; then surely we can create a paradox with ftl right in a pool.
Yes. You can pretty easily think of an experiment where a waterborne person throws a switch that changes some distant object, only to see that object change "before" they threw the switch because the experiment actually communicated the switch change via an airborne method unavailable to the waterborne observer.
I don’t think that actually works. In this case you’re talking about a round trip, with the switch’s outbound signal traveling fast (airborne/vacuum light speed) and the return signal of the object visually changing traveling slower (water light speed). The total round-trip where you see the effect of flipping the switch would take longer if either leg involved water, but it wouldn’t cause the perception of it to happen ahead of the act of flipping the switch.
Observer A and observer B are mermaids. A throws a switch that turns on a light on a light house. Relative to each observer, the can see the cause and effect. B invents a periscope that allows them to see faster than light. Now B will be able to see the light turn on before the switch is flipped.
Replace periscope with “wormhole” and you get a more traditional experiment. The question of can we use this to violate casualty is non-sensical, because we can’t violate casualty (even with faster than light travel). In the traditional experiment, if I see the light turn on, the cause has already happened; sending a message “back in time” won’t change that.
However, this is only because all frames of reference stay the same. If you could actually travel back in time, who knows what would happen. That’s largely why this whole conversation makes no sense. You can’t violate casualty with FTL, only with time machines and FTL isn’t a Time Machine.
It's just that light (if there is nothing in its way, so in a vacuum) will travel at the max speed of causality.
Causality violation can happen in general relativity when something moves faster than the max speed of causality (which is the same speed as light in a vacuum).
That doesn't mean that light (causality) couldn't be faster, right? You could increase the speed of light (causality) as much as you want and wouldn't run into any paradox.
With respect to what, though? One light-second would still be one light-second. The sizes of atoms and elementary particles probably also are a function of that. (We don’t know that, but it seems plausible.)
What does it mean to increase the speed of causality? This seems like asserting that we can add as many tick marks to the axis as we like, since the only universal unit of measurement is a velocity's percentage of C.
If we imagine something going faster than the speed of causality, we're simply misconcieving the properties of space.
An infinite speed implies instantaneous effect. So it wouldn't matter how you were moving. If two people launched something that travelled with infinite speed, one on the train travelling at 100mph, and one on the ground beside it, it would take zero time for both of them to reach their destination.
At least, that's what I surmise. I'm not a physicist.
Actually, it does. Because of relativity events that occur at the same time in one frame of reference do not occur at the same time in another. A delay of zero between two different points implies that there is a reference frame where the delay is negative.
I'm not sure that holds when you take the speed of light to be infinite. Depending on which end you look at it, you'll either be dividing by zero or having infinite energy, so I don't think relativity the way we understand it would still make sense in any way.
Relativity was derived as a direct consequence of imposing an invariant speed of causality to the Lorentz transformations, therefore it cannot tautologically be used as justification for an invariant speed of causality.
"Imposing an invariant speed of causality to the Lorentz transformations" does not sound quite right. I think it is more like assuming that the Lorentz transformations are the true symmetry of mechanics. If one wants to keep that causal, there cannot be information moving faster than the speed of light because there is a reference frame where said information would be moving backwards in time.
What even is the speed of causality? Is there any way to determine that causality has made it halfway from cause to effect?
Or is this just a metaphysical way of saying that no particle can move faster than the speed of light, assuming that causality is just an abstraction of moving particles around?
It kind of is that (a metaphysical restatement), but it's more precisely understood as a kind of half-statement of the theory.
That is, if you assume relativity, then for anything which moves faster than speed c, there exists some reference frame where it appears to move backwards in time. (This needs to be slightly qualified because it's kind of like when you're looking in a mirror and you intuitively don't think it does what it actually does -- flip front to back -- but you mentally rotate and then think that it flips left-to-right. So to be clear, if someone on a hyperluminal rocket cracks an egg into a pan, there exists someone else whose best understanding of this situation is a rocket that is traveling "backwards" engine-first, onboard of which an egg is flying up from the pan into an eggshell. But you would mentally reorient to say that the rocket is traveling "forwards" and that "forwards" direction is backwards in time.)
Now, this doesn't directly violate causality by itself, it depends on whether you can move faster than light according to an arbitrary observer. So if Carol goes faster than light according to Alice and then turns and goes faster than light according to Bob, and Bob is moving relative to Alice, only then can Carol potentially meet up with her "past self" according to Alice & Bob. The idea is that the first time she moves, Alice says she's moving very fast, but forward in time, and Bob says she's moving backward in time. Then the second time she moves, Bob says she's moving very fast, but forward in time, and Alice says she's moving backward in time. You combine these two to find that both agree that she has objectively moved backward in time.
The way this manifests in the mathematics is that in relativity, after something happens, light kind of "announces" that it happened to the rest of the world, via an expanding bubble of photons traveling away from the event at speed c. This expanding bubble is formally known as a "light cone". There is another light cone as well: before the event happens you can understand a contracting bubble of photons traveling towards the event. And basically these partition the world into five regions: The contracting bubble is the "objective past" of the event, that bubble itself is the "null past" of the event, the spacetime between the bubbles is the "general present" of the event, the expanding bubble is the "null future" of the event, and the points inside of the bubble are the "objective future" of the event. Moving faster than light, is moving from the objective future of an event, into its general present. This is "general" because different reference frames regard these points as either before or after the event in time. You need a second trajectory to then go from the general present of the event, to its objective past.
There's a lot of ways to implement that and most of them aren't a problem.
For example: If there isn't a speed of light, how fast does light go? If it's variable but not instant, then depending on the details causality violations could still be very rare or impossible. If it's instant, then how do we define instant for different observers? I feel like relativity-style calculations don't really work. If "instant" is agreed upon by all observers then we won't have causality issues.
“Instant” (i.e. infinite speed of light) also permits causality. That’s the historical Galilean model.
That is in fact the only other way to make a causal universe that satisfies a few common sense assumptions (“the laws of physics are the same in every location”, “the laws of physics are the same in every direction”, “the laws of physics are the same over time”).
“One more derivation of the Lorentz transformation” by Lévy-Leblond is a very accessible derivation of this if you’re interested in reading more. It was suggested that perhaps relativity should be taught this way in high school, instead of the historical approach of “c appears to be constant in experiments, so how do we work around that with math”.
> Couldn't you have the laws of physics change based on your speed but without changing based on location, direction, or over time?
No you can’t, that’s basically what e.g. the Levy-Leblonde reference proves :).
I encourage giving a read if you’re interested! The proof is just a few pages long, and doesn’t require more advanced mathematics than the average intro to special relativity.
If you’re willing to give up either causality itself, or the invariances of physical laws we discussed above, then of course many other alternatives open up.
> Also infinite speed of causality doesn't have to imply infinite speed of light, does it?
That is correct!
Without experimental data, we can just prove that there must be a “speed of causality” that is constant for every observer in a universe with the properties we discussed above.
That there exist “photons” in this universe that manage to travel at this speed is an experimental result. The exact value of that upper “speed limit” is also an experimental result.
> The principle of reality is first stated in general terms, leading to the idea of equivalent frames of reference connected through "inertial" transformations obeying a group law. [...] Only the Lorentz transformations and their degenerate Galilean limit obey these constraints.
> I will take as a starting point the statement of the principle of relativity in a very general form: there exists an infinite continuous class of reference frames in space-time which are physically equivalent. [...] no physical effects can distinguish between them.
Sounds like this entire paper is built on a foundation of assuming the laws of physics don't change based on speed. Am I misreading?
In that case, the paper proves that the Lorenz transforms are the only way to have both relativity and those rules, but they don't show that those rules by themselves imply relativity.
Could you even measure or experience variable speed causality? Or, it doesn’t matter what made up constant you assign the speed of causality. You’re just bits on a page and you only perceive anything as the clock cycles.
I've heard it claimed that we can only measure the round-trip speed of light, not the one-way speed of light, because the maths says that reality would look identical if it was 0.5c in the x+ direction and ∞ in the x- direction.
I find this hard to stomach, but I'm going to trust it also applies to e.g. magnetism being Lorenz transformed electric fields, because relativity violates "common sense" all over the place and reality doesn't care about my stomach.
I also have heard that, multiple times. I don't buy it. I think there are at least two experiments that could show the difference.
First, you could time the travel of light from one place to another. To do that, you need synchronized clocks. The easy way to do that is to start with clocks synchronized at a central point, then very slowly move them from the central point to the endpoints. Why very slowly? Because you have to worry about time dilation with the clocks. For small v, the difference in the rate of time is approximately v^2/2c^2 (to first order). The amount of time you have to maintain it is t = d/v. The corresponding difference in clock time still approaches zero as v approaches zero, so in principle, the clocks can be arbitrarily close to each other in time if you just move them slowly enough.
But what if c has different values in opposite directions? Well, then time dilates different amounts for the clocks going in opposite directions, but the amount of time dilation for each clock still approaches zero if the velocity is low enough.
Second: If you have a cyclotron or synchrotron, with charged particles moving in a circle in a magnetic field, and those charged particles are moving a significant fraction of the speed of light, if the speed of light is not uniform, their motion should deviate from a circle. Why? Because the force on them due to the magnetic field should be the same, but the acceleration should be different depending on what fraction of the speed of light they're moving. (Due to increased mass, if you think of it that way. If you don't, well, the equation doesn't change.)
I think that some experiments would fail to show a non-uniform speed of light, but I think experiments could be devised that would show it.
Unfortunately, if the one-way speed of light is anisotropic, the correct time dilation factor becomes 1/(γ(1−κv/c)), with the anisotropy parameter κ between -1 and +1.[17] This introduces a new linear term, meaning time dilation can no longer be ignored at small velocities, and slow clock-transport will fail to detect this anisotropy. Thus it is equivalent to Einstein synchronization.
> Your motion through the x dimension in space, for example, is completely independent of your motion through the other two (y and z) spatial dimensions.
If one considers motion at (or near) the speed of light, that speed would have to be shared among space dimensions, just as with the time dimension. So not that independent.
We constantly move at the speed of light through space-time.
If we start to move through space, we slow down through time.
If we go full speed through space, like a photon, we will not experience time at all. So from the perspective of a photon, everything happens at the same time, from the big bang to the heat death.
Think of it as a maximum vector length. As one component of the vector nears the maximum length, the other components most reduce until the vector is aligned with only one axis and at the maximum length - the other components must all equal zero.
That is - to my limited understanding - essentially why photons are “timeless”.
If I understand correctly, we experience time at nearly the speed of light. What I mean by that is that any particle’s 4 dimensional velocity vector has the magnitude of c which means that if it is mostly at rest in space then time has to be the major contributing factor but the magnitude of the vector. On the other hand something like a photon experiences to time at all as it moves through the 3 space dimensions at a total of c.
You have understood it about as well as the article did!
Now, there is a huge nuance here, which is that you are moving near the speed of light, to certain observers. This is like the whole "relativ-" prefix in "relativity", you are at rest in your rest frame, you are moving very fast in some other rest frames. The cosmic muon crashing into Earth, sees you as time-dilated! So with that nuance "we experience time at nearly the speed of light" just becomes kind of a tautology like "we experience time how we experience time."
But a better way to think about this is, you are about two meters high, you are about a meter wide, about a half-meter dorsoventrally... and about 30 000 000 m in the other direction, if we're looking at the human reaction time/blink-of-an-eye range of 0.1s (think about how 10fps video is at the cusp of being continuous and how 20Hz is where clicks stop sounding differentiated and instead start sounding like a bass note).
What this means is that if we look at you relativistically, you kind of look like a big "rope" with worldlines of other atoms coming in, braiding into your body, eventually leaving... but the strands of this rope are bundled into these cells that have worldlines over 99.9999% parallel. (Atoms within those cells move faster, but you're probably at least 99.999% parallel even if we make that statement?) And that astonishing parallelism is precisely why relativity is not very intuitively plausible to us.
> and about 30 000 000 m in the other direction, if we're looking at the human reaction time/blink-of-an-eye range of 0.1s
So: distance over time, but is the time dimension only measurable in distance over time? Is there a purely time unit, or does that not make sense when speaking of spacetime?
Yeah normal time units still exist in relativity, clocks gotta clock.
But ratber it's that there exists an operation which is almost entirely like rotation, but it rotates x, y, or z into w=ct, where w is measured in meters just like x,y,z are, but t is measured in time units, and c is the speed of light converting between them. Instead of a rotation's formula with sines and cosines like
x' = x cos θ + y sin θ
y' = y cos θ – x sin θ
(x')² + (y')² = x² + y²
relativity has a slightly different set of functions sinh and cosh that are very closely related to sin and cos. (Sine and cosine have Taylor series where the polynomials alternate, sin(x) = x – x³/6 + x^5/120 – ..., and sinh and cosh have the exact same Taylor series with all + signs rather than alternating + – + –.) The analogous expressions are then,
w' = w cosh φ — x sinh φ
x' = x cosh φ — w sinh φ
(w')² – (x')² = w² – x².
This transformation, in relativity, is just built into how any acceleration works. So whenever you accelerate, even in pre-relativistic physics, you expect to see the emergence of some Doppler shifts. In relativity these shifts are not quite as strong as expected from the classical theory, and as a result when you subtract off the Doppler shifts and try to say "what has happened" you get an answer that "the meaning of the present moment, which historically defined a 3D universe frozen at a point in time, identifies a different 3D slice of the 4D spacetime." And this is what "rotates", it's the rotation of the plane that you think is the "present moment".
The fact that you are discretely "you" about ten times per second, I am taking as a fact of biology. But if you try to convert that biology into physics, that's where you convert t into w to get that t=0.1s converts to w = 30,000 km.
It's better to think that our 4 velocity always has a magnitude of 1 and use c only as a scaling factor necessary because our weird choice to use different units for time and space.
Acceleration is a rotation in this weird 3-1 dimensions.
I think it better to think about 4 velocity as a unitless quantity. Because our intuitions about units and dimensions are formed by 3 dimensional space where every dimension can be swapped with any other and everything is still the same. 1 meter rotated is still 1 meter. Doesn't become 0.56m/s
If you use seconds and light-seconds as the units instead of meters, then the magnitude of the vector is just a constant 1.
Another way of putting that: This isn’t a vector at all, it’s just a direction. Treating it as a vector gives rise to silly statements like “one second per second”, which is yet another way to explain that it’s magnitude 1… because it’s a direction.
I think that’s GP’s point. If you take at face value that your speed through spacetime is constant and that the only thing that can vary is the magnitude distributed through (x, y, z, t), then the only important component of your spacetime velocity is its angle in 4D space (e.g., your “direction”).
But also our own personal velocity is stationary. We (AIAU, IANAP) always perceive our own velocity vector as (0, 0, 0, 1). When we undergo acceleration it only ever affects the directional components of every other part of the universe, not our own experiential frame.
A fidget spinner illustrates this for me--bear with me. When I spin it and it just stays at rest in my hand, it spins fast. But when I quickly move my hand carrying the spinner, you can see it slows down the spin rate, and then when I stop moving it, it speeds back up. While the mechanisms are entirely different (classical vs. relativistic) they both show motion can affect certain fundamental properties of a system, whether it be spin rate or the passage of time
You can't "experience" time. Experience is memory and memory is the only thing you can "experience". Whether that memory has anything to do with time as such is debatable. Personally I'd say no.
You're thinking of subjective experience, conscious perception of time. OP is referring more generally to the local speed of causality in a system at rest.
I've heard this described as "we all move at the speed of light." Also, since another way to describe alignment of two vectors is an angle, motion can be characterized by the angle it makes with the time axis.
I believe that’s an accurate model, with the caveat that it’s all relative. There’s no universal reference frame. So for the photon and his pal photons, they experience time while you (in your reference frame sitting still) are the one moving at the speed of light and not moving through time.
Edit: See below, the photon doesn’t have its own reference frame so they still don’t experience time.
Photons absolutely do not experience time. The spacetime interval of any photon is always zero, and the spacetime interval tells you how much time any particle experiences. Note that it’s invariant.
I still don't get it, photon comes into existence and then slams into a thing for us to notice the existence. Between the being born and slamming into something time passes, no?
Here’s something I’ve never understood; perhaps a more knowledgeable commenter can explain it to me.
If I get in a spaceship and accelerate up to about 0.9c, then cruise for a while, then flip around and come home at the same speed, I will have experienced much less time than the people on Earth. But from my frame of reference, they were the ones going really fast, and I was sitting still. If all motion is relative, what makes me the one to experience less time?
I only got my undergrad in physics, but I think there is something there to be mined between time as a dimension and the second law of thermodynamics. Why this one?
First, I will render a quote which never failed to amuse me: "The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations -- then so much the worse for Maxwell's equations. If it is found to be contradicted by observation -- well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it to collapse in deepest humiliation." (Eddington)
Why such honor? For one, in statistical physics, you can more or less derive the second law of thermodynamics, from scratch. No need for observation. It's just there the same way the quadratic equation is. Somewhere I have a cheap Dover reprint which contains a relatively easy to follow construction of the second law. It's the math. You can measure things badly, you can find one phenomenon creating the appearance of another, but you cannot fool The Math.
And so the statistical physics you can get from just math gives you this arrow of time, flying only one way, just as we see from spacetime.
To me, and again, I only got a few grad courses under my belt in it, this suggests not just a deep connection between entropy and spacetime, but the inevitability of it from the basic math (really, a talented high schooler could be coached through it) means that there is something about large (for n = ?) numbers of particles losing the reversibility which is so often present in particle interactions where n is smaller. What gives there? How do we go from this "trend" emerging to it being a property of spacetime even if no particles are sitting in said spacetime.
Not that I would have dared write the great Wheeler, but I have wondered if his "geon" concept would have fit in with this sort of thing. It seems so fundamental. One can imagine a universe with a different number of un-unified forces, or gravity dropping as the inverse-cube, or varying physical constants, but the math is still the same in these universes and it then suggests that there's no, uh, room for an option wherein the time facet of spacetime is anything but an arrow flying forever on towards entropy in its many masks.
A great task, or perhaps a very alluring windmill, for someone younger and brighter than I.
I'm in a similar boat, but I've always felt the opposite! I've always felt the second law is kind of a shoe-in and maybe even shouldn't be a law at all.
The first and third laws, "energy is never created or destroyed" and "for every action there's an equal and opposite reaction" are always true! To my knowledge, no process is ever allowed to break either law. (With exceptions for cosmological process like the expansion of the universe that we really don't purport to understand.)
The second, "entropy can only increase" isn't! That's right, I said it. The processes it describes (a cup unshuttering, or coffee unmixing, or particles all finding their way into the same side of a box) are totally legal process, albeit statistically unlikely. If you restrict your system to few enough particles (say, n=3), random processes that decrease entropy are not only possible, but something that happens with regularity!
Now, I make no claims to be right here. I suspect that Eddington fellow probably knows what he's talking about. But, this has been a longstanding thorn in my understanding of physics, so I'd be interested if anybody has any interesting insights!
> With exceptions for cosmological process like the expansion of the universe that we really don't purport to understand
That's not accurate, expansion of the universe (that the standard model of cosmology describes) does not violate conservation of energy. It makes it a little different from the classical view.
In classical mechanics, energy conservation is a well-defined concept in a static or non-expanding spacetime. However, in an expanding universe, especially one described by general relativity (like ours), the energy of the universe is not necessarily conserved in the traditional sense, because the global energy of the universe is difficult to define when spacetime itself is dynamic (expanding)
So GR does not require global conversation of energy in the same way classical (here classical means strictly newtonian mechanics) mechanics does. This dynamic nature of the spacetime allows for energy to appear to "change" due to the expansion. It is more complicated when you add things like dark energy to the equation.
One interesting aspect is the phenomenon of cosmological redshift. As the universe expands, light travelling through space is redshifted. This means that ita wavelength increases and its energy decreases. This "loss" of energy from light is not violating conservation of energy. It is rather consequence of the expansion itself.
Now lets back to dark energy which is driving the accelerated expansion of the universe, the energy associated with the vacuum of space remains constant per unit volume, but as space itself expands, the total energy associated with dark energy increases. This again does not violate the laws of physics because energy conservation is more complex in general relativity than in Newtonian mechanics. And of course the local energy conservation works in a well-defined way if you take a localized region of the spacetime.
From the Wikipedia page on the second law of thermodynamics:
>For example, the first law allows the process of a cup falling off a table and breaking on the floor, as well as allowing the reverse process of the cup fragments coming back together and 'jumping' back onto the table, while the second law allows the former and denies the latter. The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always tend toward a state of thermodynamic equilibrium where the entropy is highest at the given internal energy.[4] An increase in the combined entropy of system and surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time.[5][6]
Entropy is also defined as the number of different arrangements of particles in a system. We say that entropy is increasing in our universe. But we have also found that space is increasing. If space increases faster than particles move, entropy could even decrease
The older I am (and I am at my 50s) the more I have this intuition that entropy is a fundamental force driving not only physical phenomena but also social interactions, economy etc.
Formalising this intuition is another story though...
Tools from statistical physics have long been used in sociological and economical models.
It's no wonder, because statistical physics was devised as a tool for the study of complex systems.
For the same reason I don't deem entropy to be a fundamental property of physics, but one of complex systems. As far as I remember from university, the 2nd law of thermodynamics simply arises from the fact, that there are exponentially more unordered than ordered states.
Though information itself may be a fundamental physical property. The recent interest in Quantum computers shines new light on the connection between information and Quantum Mechanics. It remains to be seen, how that point of view is compatible with relativity.
I hope, that one day someone finds out, that the "time dimension" arises in the macroscopic limit from a graph of discrete causal events.
Not disputing anything you said but... The issue I see is that without notion of time it is difficult to talk about causality (I guess you could only talk about "entanglement"). It is actually difficult to talk about "events" at all - I guess you can only talk about "facts"?
We have the sun to provide us with low entropy energy and the atmosphere to dissipate high entropy energy, so stuff tbat happens on earth can be lowering in entropy possibly. Climate change excepted.
Could you pls. point to the said book or some other resource for me to learn about this? As such, I follow what you have said, but would love to see the math too. Thanks.
Ilya Prigogine wrote a lot about this, see eg Order Out of Chaos. He won the Nobel prize in chemistry for his work on nonequilibrium thermodynamics.
Boltzmann had originally tried to prove that the second law is a mechanical (statistical) fact and several others tried as well. But Poincaré showed that those systems which, regardless of their initial state, inevitably increase entropy later on inevitably reduce it (his recurrence theorem). There are also in fact reversible processes in nature, so it can't be that mechanics alone implies the procession of time. Something more involved is going on.
Carlo Rovelli has also written a lot about the "thermal time" concept in his books.
My takeaway from them is that you can't really get time out of mechanics by itself (statistical or otherwise). In the same way that you can't get baryon asymmetry. It is intrinsically a selection principle on initial conditions.
Even with this, would the Poincaré recurrence time not be (probabilistically) be very large for any complex system, and thereby practically imply the second law of thermodynamics?
I also just re-read about Maxwell's demon (https://en.wikipedia.org/wiki/Maxwell%27s_demon), but see that there are already various arguments against it even before arguments about the demon moving the system towards Poincaré recurrence.
Our universe is a 3D Manifold in a higher dimensional space.
All event horizons have a "surface normal" (orthogonality) direction at any point. For example a conventional Black Hole (2D one) has an event horizon that is a 2D surface. That is, for a flatland creature living on that EH it takes two coordinates to define a location, but these flatlanders would experience "time" as the "growth" of the EH (like when more mass falls into it, and the EH grows), and the direction is "outward" (perpendicular to EH surface)
Now here's the interesting part: Event Horizons come in all dimensions. Our "Universe" is a 3D EH, but of course at any point in space there's a unique "rate of time" and a common "direction" of time, which from a higher dimensional space perspective is simply the "orthogonal direction" to all our space directions. (Time orthogonal to Space [i.e. Minkowski]).
As matter falls into our "Universe", that moves time forward for us. But our universe itself consists of all the "points" (Quantum Decoherence Points) which are co-located on a 3D manifold embedded in a higher dimensional space.
This means the Big Bang has things exactly "inverted", and is wrong. Matter didn't "originate from inside". It's the opposite o that. Everything "fell in" from outside. The reason our universe is expanding and accelerating is because it's a black hole EH. Black Holes mainly just grow (excluding tunneling etc).
I agree. The similarity between black holes and our universe is striking. The fact that matter inside it can not be observed from outside opens possibilities for all kind of quantum states, which is maybe, just the configuration of a universe (for example that one we are living in).
There are many different "lines of reasoning" that lead to this conclusion as well. For example as an object approaches the speed of light, an observer will see it become smashed perfectly flat (length contraction) in the direction of it's travel, which is the logical equivalent of a "loss of one dimension".
In other words as something tries to "escape" our 3D manifold the effect that has is to remove one a spatial dimension. Also as something goes to nearer to speed of light, we know it also loses "time" dimension. No flow of time (from perspective of observer).
And all of these same "divide by zero" kind of impossibilities are precisely what's also happening on event horizons. In other words Special Relativity reinforces this theory. My claim is that even the Lorentz equations are showing us the way in which a dimension is lost. Lorentz is a "smooth" way of going from N dimensions to N minus 1 dimensions.
EDIT: So there must be a stronger relationship between Spinors and Lorentz than what's currently known! By having complex components, Spinors is the way to have "partial moves" in a direction, while still technically maintaining orthogonality to all other directions.
I think it's one of those things that borders on the unfalsifiable, similar to multiverse theory. I've had this concept for about a decade, but I did actually see a youtube video of a Cambridge (or some well known University for Physics) where a professor/researcher did present the idea, yes.
It won’t necessarily convey all the different views, but The Order of Time by Carlo Roveli is an absolutely beautiful walk through the various interpretations of time down to the quantum level. The nature of time is not fully understood and Roveli understandably (and openly) has and endorses his own view here, but he covers the ground upon which there’s consensus quite well.
My understanding from Einstein’s book Relativity is that the four dimensions of general relativistic spacetime do not correspond to any one of the time or space dimensions of special relativity or classical physics.
It’s a great read, and short too. He explains it much better than I could.
"This is the underlying reason why, when you move at speeds that approach the speed of light, you start to experience phenomena such as time dilation and length contraction:"
This is not even possible in pulp science fiction. In order to be able to move with the speed of light you need to transform yourself into a photon. Only a photon can move with the speed of light. Saying "close to the speed of light" changes nothing. You need to be light to move with the speed close to the speed of light. Macroscopic objects cannot move with speeds approaching light speed.
> This is not even possible in pulp science fiction
Incorrect - anything is possible in pulp scifi.
> In order to be able to move with the speed of light you need to transform yourself into a photon. Only a photon can move with the speed of light.
Incorrect - any massless particle will move at the same speed as light.
> Saying "close to the speed of light" changes nothing. You need to be light to move with the speed close to the speed of light.
Incorrect - it's perfectly feasible to accelerate particles to over 99% of the speed of light. e.g. the LHC can accelerate protons to 0.999999990 c. Also, it's not possible for massless particles including photons to move at anything other than the speed of light in a vacuum, so "close to the speed of light" is not possible unless the object has mass.
> Macroscopic objects cannot move with speeds approaching light speed.
Incorrect, though humans haven't been able to accelerate macroscopic (e.g. visible to human eye) objects to more than approx 0.064c (Parker Solar Probe), it's just a question of using enough power to accelerate the relevant object. There's no reason to think that a black hole accretion disk couldn't easily accelerate a lump of matter to more than 0.99c.
“Close to the speed of light” means, like, 99% of the speed of light. You can even see the speeds listed on the graphs, which are given as a fraction of c.
> Not just 99%, but 99.99999999% or however many you want.
Badly enough, even that's not true.
We have a frame of reference given by the cosmic microwave background. When you move faster and faster at some limiting speed will create pions that will slow down the particle creating an effective slower max speed.
Our current speed is 99.999999% the speed of light, according to some frame of reference, 10% according to another frame of reference and 0% according to another.
A lot of work is done by the words "get to" which is colloquial for "accelerate".
I guess you guys found a way to accelerate human body to the speed of light without disintegrating. Why don't you prove your technique first with G-forces?
1G of acceleration (which I'd hope you agree is survivable by humans) over an extended time period can easily reach relativistic speeds.
1 day .0028c
1 week .02c
1 month .086c
1 year .77c
2 years .97c
3 years .996c
4 years .9995c
5 years .9999c
The thing stopping us from doing this today is economics, not physics. Current rockets have about enough fuel for minutes of acceleration, and fuel requirements increase exponentially due to the tyranny of the rocket equation. If you skip the need for fuel (laser propulsion?) and find some way to decelerate (laser cooling propulsion???), then interstellar travel to pretty much anywhere becomes entirely reasonable within human lifespans.
I think you're handwaving away the other issues with physics that make near-lightspeed travel effectively impossible for humans. How exactly do you propose sustaining 1g acceleration for 5 years, for instance? You can't just "skip the need for fuel". Lasers aren't perfectly collimated and spread out over distance. Even an Epstein drive from The Expanse will eventually run out of fuel. The other big problem is: how exactly do you deal with collisions with space debris? Even at the speeds we currently travel, micrometeorites are a problem, but at 0.9999c, even stray hydrogen atoms (which deep space is full of) are going to destroy your ship.
Honestly, Star Trek way back in the 1960s was pretty brilliant at getting around many of these technical problems by inventing "warp drive".
Even if we somehow magically solved our economic problems overnight, that isn't going to make relativistic speeds feasible for humans anytime soon, if ever.
Nothing with mass can have the same speed as light, but you can trivially accelerate a human body - or something similar - to a speed which is arbitrarily close to it, without risking anything from the G-forces involved.
You just need to do it very slowly.
That is, in any case, neither here nor there, since this is a thought experiment used in a discussion about the effects of moving at a speed close to c - people in thought experiments are stronk.
My favourite explanation (which IIRC is in a book by Brian Greene) is that you can think that everything always moves at the speed of light in a 4D spacetime. That way, if you stand still, you're moving only along time, and as you tilt your velocity vector more and more toward the space dimensions you have to travel more slowly along the time dimension. At the limit you are moving at the speed of light along some space axis and technically your time is "frozen".
Some of the answers at https://physics.stackexchange.com/q/33840 explain why "everything always moves at the speed of light in a 4D spacetime" is a statement that, at best, has no content.
Or as I tell people, kidding on the square, we're trapped in a time machine hurtling us into the future at the rate of one minute every sixty seconds! It is important you say that last bit in a panicked, breathless voice.
My God, that means every three hundred sixty-five days or so, we'll have gone forward a year!
Hm. That’s a possibility. As I understand it though, an infinitely massive object would not move in space, and would experience time at the absolute rate of one second per second.
Although that sounds theoretically impossible, I would remind you that somehow the opposite seems to be possible (a particle with zero mass that moves through time at a rate of zero seconds per second), despite that not making a lot of sense to a layperson.
Footnote: Talking about time in seconds makes very little sense here because our notion of time is so heavily linked to how light moves through space, but hopefully my point is clear. Maybe someone has a better unit we could use to measure time independently of space?
Your point is clear. As far as can wrap my head around those theoretical concepts: An infinitely heavy object can’t move in space because there isn’t any space left to move. I would say that this object would have concentrated all mass in one point, no space left to
move. No observer left to measure. I would also say that there can’t be two or more infinite masses at the same time, or they would move (at the speed of c (?) But that would have additional implications on mass and time) to the point between them.
But back to observable reality: let’s say you fall into a dark place where the time stands still and that means you are not moving, from an outside observer you are still moving relative to the space outside your black hole. Let’s say the observer fall on his way to your black hole into another black hole and experience the same phenomenon like you, from a third observers perspective everyone is moving.
> In the presence of gravity spacetime is described by a curved 4-dimensional manifold for which the tangent space to any point is a 4-dimensional Minkowski space.
Perhaps? A good way to lose 99% of the readers before the end of the first sentence.
I'm a huge fan of providing laymen explanations. And at some point if you _actually_ want to understand you have to stop using those and pickup and understand the math.
Ok, but almost nobody is going to read an article that requires you to work through 21 lectures, 9 tutorials, and 3 assignments first. It'd be great if they did, and it'd be nice to give the link for interested people, but otherwise it is just making the subject inaccessible to almost everyone.
That's in the article on Minkowski space. It's actually a good summary, with a hyperlink to manifold.
Here's the introduction to the "spacetime" page:
> In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events occur.
Reminds me of Geoffrey Hinton who, when asked how to imagine a 14-dimensional space, said: “imagine a 3-dimensional space, and say ‘fourteen’ very loudly”
>>> After Hilbert was told that a student in his class had dropped mathematics in order to become a poet, he is reported to have said "Good--he did not have enough imagination to become a mathematician"
Its a bit more complex but that’s a basic summary from the guy who came up with the “space and time” thing. Read the “Transcendental Aesthetic” in the Critique of Pure Reason for more.
Of course the math check out, they are correct, but in my opinion, time is not a dimension, it's the 'refresh rate' of matter.
To me, there are only 3 dimensions, that of space.
That does not mean the relativity math is useless. On the contrary, what they describe is real and we can experimentally verify it.
But that does not mean we can 'move' into time, as we 'move' into space. That's why time is not a dimension.
How does your refresh rate time accounts for time slowing down for things moving fast (relative to you) regardless of spatial direction they are moving?
Spacetime simplifies many things for example in that framing nothing is ever at rest or nothing ever travels at different speed. The speed of everything is the same, it's just that things spatially at rest have all their speed in the direction of time. Accelerating something in spatial direction is rotating (mathematically) their motion away from time direction, into some spatial direction. This requires energy so the time direction is lowest energy but to rotate it away from it you need to put in energy. If you want to rotate it to 45 deg you need infinite energy.
Also consider the speed of light is also the speed of causality. If there was no such limit it means it would be possible for effects to precede causes which would lead to a very different kind of universe!
How could an effect precede a cause if there were no speed limit to causality?
No matter how fast an effect propogates, it is always after the cause (with an infinite speed, I guess effects happen instantaneously, but not before).
Of course, this doesn't fit with a universe described by general relativity, where time can be different for different observers. But you wouldn't have a universe described by general relativity without that constraint in the first place.
> How could an effect precede a cause if there were no speed limit to causality?
> No matter how fast an effect propogates, it is always after the cause (with an infinite speed, I guess effects happen instantaneously, but not before).
If everything happens instantaneously then there is no real cause and effect, and the universe would be over before it really got started.
No speed limit does not mean that everything goes infinitely fast.
Agreed, an infinite speed was just the most extreme edge case of having no limit.
If the speed limit is infinite, what else would you expect to happen?
old grannies driving at 30mph on the freeway, me at infinity.
on edit: not everything travels at the speed limit, if the speed limit right now is the speed of light - then why doesn't everything travel at the speed of light?
People say if the speed limit was infinite that everything would happen instantaneously - but they still need to explain why everything should go at the speed limit in this other universe, when not everything goes at the speed limit in ours.
Almost everything (electrical fields, atomic radius, even speed of sound in materials) seems to derive in some way from the speed of light and related effects.
perhaps this is an effect of having a speed limit in a universe, if a universe does not have any set speed limit (which is somewhat different than the phrasing speed limit is infinite) perhaps the discussed derivation of other speeds would not exist in the way it does in our universe.
Light traveling at infinite speeds, atoms and such not.
If effects were instantaneous then atoms would not exist.
There can be many types of effects in a hypothetical universe.
Imagine a universe like Conway's way of life, where only neighboring cells can be affected in one timestep. Now add to it a rule that all blocks have a color, and the color of all blocks are changed when one block changes color. Now you have a universe with both immediate and non-immediate effects.
But what is “One time step” in that universe? We have the idea of a light clock - light bouncing between two perfect mirrors in a vacuum - as an ultimate clock.
The distance between the mirrors is a number of meters. A meter is based on how far light travels in a second. How long it takes light to go between them is based on the speed of light. Speed, distance and time are connected.
If we untether the speed of light and it’s unlimited, then in some sense there is no way to say how long it takes light to bounce between the mirrors - it doesn’t take any time. And there is no way to say how far apart the mirrors are, if light passes between them instantly that implies there must be no gap to cross. If light crosses no distance in no time then it also bounces back covering no distance in no time, ahh does lots of bounces in no time. There goes the concept of a time step and any concept of “non immediate effects”.
If you try and add time as a separate thing, then you have some kind of Conway’s game simulation - but that gives you a way to track where light is (which simulation cell it’s in) and therefore a kind of distance (how far the mirrors are apart in simulation cells) and then you lock down how light moves in “simulation cells travelled per timestep” which brings you back to a fixed speed of light again.
what assumptions have to be true for such a universe to exist? did it just appear fully formed with N number of cells and defaulting to a color?
a hypothetical universe is mostly worth discussing seriously if there's a physics that is coherent, not just a mathematical landscape. At least it isn't that interesting in the discussion of universes, but might be in discussing mathematical ideas, but those do not necessarily mean there's a universe represented by it.
A ‘one level of cells in one timestep’ is a speed limit, and a very slow one actually.
I'm having trouble with this assertion. Light travels slower in water than in air, by your assertion that light is the limit of causality; then surely we can create a paradox with ftl right in a pool.
Causality does not depend on the speed of light. Rather, light travelling in a vacuum happens to travel at the maximum speed of causality.
If light is slower in other mediums, that has no effect on how quickly causation can happen.
Yes. You can pretty easily think of an experiment where a waterborne person throws a switch that changes some distant object, only to see that object change "before" they threw the switch because the experiment actually communicated the switch change via an airborne method unavailable to the waterborne observer.
I don’t think that actually works. In this case you’re talking about a round trip, with the switch’s outbound signal traveling fast (airborne/vacuum light speed) and the return signal of the object visually changing traveling slower (water light speed). The total round-trip where you see the effect of flipping the switch would take longer if either leg involved water, but it wouldn’t cause the perception of it to happen ahead of the act of flipping the switch.
Observer A and observer B are mermaids. A throws a switch that turns on a light on a light house. Relative to each observer, the can see the cause and effect. B invents a periscope that allows them to see faster than light. Now B will be able to see the light turn on before the switch is flipped.
Replace periscope with “wormhole” and you get a more traditional experiment. The question of can we use this to violate casualty is non-sensical, because we can’t violate casualty (even with faster than light travel). In the traditional experiment, if I see the light turn on, the cause has already happened; sending a message “back in time” won’t change that.
However, this is only because all frames of reference stay the same. If you could actually travel back in time, who knows what would happen. That’s largely why this whole conversation makes no sense. You can’t violate casualty with FTL, only with time machines and FTL isn’t a Time Machine.
In general relativity, FTL can be used as a time machine.
>Light travels slower in water than in air, by your assertion that light is the limit of causality
The limit of causality is the light speed limit in vacuum, not "whatever happens to be the max speed of light in some medium".
Light (as in visible light) is also irrelevant to this, it's just an example of something moving at that speed.
I fail to see how a vacuum permits violations of casualty. Care to explain?
The vacuum has nothing to do with causality.
It's just that light (if there is nothing in its way, so in a vacuum) will travel at the max speed of causality.
Causality violation can happen in general relativity when something moves faster than the max speed of causality (which is the same speed as light in a vacuum).
Here's a great video explaining how, due to relativity, FTL travel can cause grandfather paradoxes: https://youtu.be/an0M-wcHw5A?si=RYFGOmQOlaC2t0bM
Edit: in short, not all reference frames can agree on the order of events, and FTL events propogate "backwards" between some reference frames.
That doesn't mean that light (causality) couldn't be faster, right? You could increase the speed of light (causality) as much as you want and wouldn't run into any paradox.
With respect to what, though? One light-second would still be one light-second. The sizes of atoms and elementary particles probably also are a function of that. (We don’t know that, but it seems plausible.)
What does it mean to increase the speed of causality? This seems like asserting that we can add as many tick marks to the axis as we like, since the only universal unit of measurement is a velocity's percentage of C.
If we imagine something going faster than the speed of causality, we're simply misconcieving the properties of space.
Mainly in the sense that you can create an amp that goes to 11.
Right. The speed limit itself is arbitrary.
Nice video, thanks for posting.
How would you compare two infinities? E.g. speed of light inside a moving train vs speed of light outside of it.
An infinite speed implies instantaneous effect. So it wouldn't matter how you were moving. If two people launched something that travelled with infinite speed, one on the train travelling at 100mph, and one on the ground beside it, it would take zero time for both of them to reach their destination.
At least, that's what I surmise. I'm not a physicist.
The possibility of delays being zero does not imply that negative delays are possible.
Actually, it does. Because of relativity events that occur at the same time in one frame of reference do not occur at the same time in another. A delay of zero between two different points implies that there is a reference frame where the delay is negative.
I'm not sure that holds when you take the speed of light to be infinite. Depending on which end you look at it, you'll either be dividing by zero or having infinite energy, so I don't think relativity the way we understand it would still make sense in any way.
Well, it is quite well known what you get when taking the speed of light to infinity. It is classical mechanics.
Point being, in that case you don't have relativistic effects nor effects preceding causes and whatnot.
Relativity was derived as a direct consequence of imposing an invariant speed of causality to the Lorentz transformations, therefore it cannot tautologically be used as justification for an invariant speed of causality.
"Imposing an invariant speed of causality to the Lorentz transformations" does not sound quite right. I think it is more like assuming that the Lorentz transformations are the true symmetry of mechanics. If one wants to keep that causal, there cannot be information moving faster than the speed of light because there is a reference frame where said information would be moving backwards in time.
What even is the speed of causality? Is there any way to determine that causality has made it halfway from cause to effect?
Or is this just a metaphysical way of saying that no particle can move faster than the speed of light, assuming that causality is just an abstraction of moving particles around?
Network propagation delay ;-)
Imagine the world without a speed of causality, where everything was updated instantaneously. No CAP theorm, no Byzantine generals.
Being a programmer/information theorist would be so much easier lol
It kind of is that (a metaphysical restatement), but it's more precisely understood as a kind of half-statement of the theory.
That is, if you assume relativity, then for anything which moves faster than speed c, there exists some reference frame where it appears to move backwards in time. (This needs to be slightly qualified because it's kind of like when you're looking in a mirror and you intuitively don't think it does what it actually does -- flip front to back -- but you mentally rotate and then think that it flips left-to-right. So to be clear, if someone on a hyperluminal rocket cracks an egg into a pan, there exists someone else whose best understanding of this situation is a rocket that is traveling "backwards" engine-first, onboard of which an egg is flying up from the pan into an eggshell. But you would mentally reorient to say that the rocket is traveling "forwards" and that "forwards" direction is backwards in time.)
Now, this doesn't directly violate causality by itself, it depends on whether you can move faster than light according to an arbitrary observer. So if Carol goes faster than light according to Alice and then turns and goes faster than light according to Bob, and Bob is moving relative to Alice, only then can Carol potentially meet up with her "past self" according to Alice & Bob. The idea is that the first time she moves, Alice says she's moving very fast, but forward in time, and Bob says she's moving backward in time. Then the second time she moves, Bob says she's moving very fast, but forward in time, and Alice says she's moving backward in time. You combine these two to find that both agree that she has objectively moved backward in time.
The way this manifests in the mathematics is that in relativity, after something happens, light kind of "announces" that it happened to the rest of the world, via an expanding bubble of photons traveling away from the event at speed c. This expanding bubble is formally known as a "light cone". There is another light cone as well: before the event happens you can understand a contracting bubble of photons traveling towards the event. And basically these partition the world into five regions: The contracting bubble is the "objective past" of the event, that bubble itself is the "null past" of the event, the spacetime between the bubbles is the "general present" of the event, the expanding bubble is the "null future" of the event, and the points inside of the bubble are the "objective future" of the event. Moving faster than light, is moving from the objective future of an event, into its general present. This is "general" because different reference frames regard these points as either before or after the event in time. You need a second trajectory to then go from the general present of the event, to its objective past.
There's a lot of ways to implement that and most of them aren't a problem.
For example: If there isn't a speed of light, how fast does light go? If it's variable but not instant, then depending on the details causality violations could still be very rare or impossible. If it's instant, then how do we define instant for different observers? I feel like relativity-style calculations don't really work. If "instant" is agreed upon by all observers then we won't have causality issues.
“Instant” (i.e. infinite speed of light) also permits causality. That’s the historical Galilean model.
That is in fact the only other way to make a causal universe that satisfies a few common sense assumptions (“the laws of physics are the same in every location”, “the laws of physics are the same in every direction”, “the laws of physics are the same over time”).
“One more derivation of the Lorentz transformation” by Lévy-Leblond is a very accessible derivation of this if you’re interested in reading more. It was suggested that perhaps relativity should be taught this way in high school, instead of the historical approach of “c appears to be constant in experiments, so how do we work around that with math”.
Couldn't you have the laws of physics change based on your speed but without changing based on location, direction, or over time?
Also infinite speed of causality doesn't have to imply infinite speed of light, does it?
> Couldn't you have the laws of physics change based on your speed but without changing based on location, direction, or over time?
No you can’t, that’s basically what e.g. the Levy-Leblonde reference proves :).
I encourage giving a read if you’re interested! The proof is just a few pages long, and doesn’t require more advanced mathematics than the average intro to special relativity.
If you’re willing to give up either causality itself, or the invariances of physical laws we discussed above, then of course many other alternatives open up.
> Also infinite speed of causality doesn't have to imply infinite speed of light, does it?
That is correct!
Without experimental data, we can just prove that there must be a “speed of causality” that is constant for every observer in a universe with the properties we discussed above.
That there exist “photons” in this universe that manage to travel at this speed is an experimental result. The exact value of that upper “speed limit” is also an experimental result.
> The principle of reality is first stated in general terms, leading to the idea of equivalent frames of reference connected through "inertial" transformations obeying a group law. [...] Only the Lorentz transformations and their degenerate Galilean limit obey these constraints.
> I will take as a starting point the statement of the principle of relativity in a very general form: there exists an infinite continuous class of reference frames in space-time which are physically equivalent. [...] no physical effects can distinguish between them.
Sounds like this entire paper is built on a foundation of assuming the laws of physics don't change based on speed. Am I misreading?
In that case, the paper proves that the Lorenz transforms are the only way to have both relativity and those rules, but they don't show that those rules by themselves imply relativity.
Could you even measure or experience variable speed causality? Or, it doesn’t matter what made up constant you assign the speed of causality. You’re just bits on a page and you only perceive anything as the clock cycles.
I've heard it claimed that we can only measure the round-trip speed of light, not the one-way speed of light, because the maths says that reality would look identical if it was 0.5c in the x+ direction and ∞ in the x- direction.
I find this hard to stomach, but I'm going to trust it also applies to e.g. magnetism being Lorenz transformed electric fields, because relativity violates "common sense" all over the place and reality doesn't care about my stomach.
https://www.youtube.com/watch?app=desktop&v=pTn6Ewhb27k&them...
I also have heard that, multiple times. I don't buy it. I think there are at least two experiments that could show the difference.
First, you could time the travel of light from one place to another. To do that, you need synchronized clocks. The easy way to do that is to start with clocks synchronized at a central point, then very slowly move them from the central point to the endpoints. Why very slowly? Because you have to worry about time dilation with the clocks. For small v, the difference in the rate of time is approximately v^2/2c^2 (to first order). The amount of time you have to maintain it is t = d/v. The corresponding difference in clock time still approaches zero as v approaches zero, so in principle, the clocks can be arbitrarily close to each other in time if you just move them slowly enough.
But what if c has different values in opposite directions? Well, then time dilates different amounts for the clocks going in opposite directions, but the amount of time dilation for each clock still approaches zero if the velocity is low enough.
Second: If you have a cyclotron or synchrotron, with charged particles moving in a circle in a magnetic field, and those charged particles are moving a significant fraction of the speed of light, if the speed of light is not uniform, their motion should deviate from a circle. Why? Because the force on them due to the magnetic field should be the same, but the acceleration should be different depending on what fraction of the speed of light they're moving. (Due to increased mass, if you think of it that way. If you don't, well, the equation doesn't change.)
I think that some experiments would fail to show a non-uniform speed of light, but I think experiments could be devised that would show it.
Unfortunately, if the one-way speed of light is anisotropic, the correct time dilation factor becomes 1/(γ(1−κv/c)), with the anisotropy parameter κ between -1 and +1.[17] This introduces a new linear term, meaning time dilation can no longer be ignored at small velocities, and slow clock-transport will fail to detect this anisotropy. Thus it is equivalent to Einstein synchronization.
https://en.wikipedia.org/wiki/One-way_speed_of_light
A lot of scientists have thought about this. Step one is checking their work.
Ah, I see.
I see nothing there that would invalidate my synchrotron argument, though.
If you apply the more detailed equation I bet it says the mass doesn't change, so there is no change around the circle to measure.
I'm sure someone has thought of an experiment that simple. If you can't find anything close enough you can ask on one of the stack exchanges.
Wouldn’t it just happen instantly and settle on some fixed point?
Speed of light may be dependent on other constants and it will have then unpredictable effects
> Your motion through the x dimension in space, for example, is completely independent of your motion through the other two (y and z) spatial dimensions.
If one considers motion at (or near) the speed of light, that speed would have to be shared among space dimensions, just as with the time dimension. So not that independent.
i've never really 'properly' understood spacetime - can you expand on your comment?
why would going v fast in the x direction affect y and z?
We constantly move at the speed of light through space-time.
If we start to move through space, we slow down through time.
If we go full speed through space, like a photon, we will not experience time at all. So from the perspective of a photon, everything happens at the same time, from the big bang to the heat death.
If I am seen to go at [v_x, v_y, v_z] = [0.9, 0.9, 0.9]c, then I would be going at about 1.56c in the [1, 1, 1] direction, which is impossible.
Think of it as a maximum vector length. As one component of the vector nears the maximum length, the other components most reduce until the vector is aligned with only one axis and at the maximum length - the other components must all equal zero.
That is - to my limited understanding - essentially why photons are “timeless”.
If I understand correctly, we experience time at nearly the speed of light. What I mean by that is that any particle’s 4 dimensional velocity vector has the magnitude of c which means that if it is mostly at rest in space then time has to be the major contributing factor but the magnitude of the vector. On the other hand something like a photon experiences to time at all as it moves through the 3 space dimensions at a total of c.
You have understood it about as well as the article did!
Now, there is a huge nuance here, which is that you are moving near the speed of light, to certain observers. This is like the whole "relativ-" prefix in "relativity", you are at rest in your rest frame, you are moving very fast in some other rest frames. The cosmic muon crashing into Earth, sees you as time-dilated! So with that nuance "we experience time at nearly the speed of light" just becomes kind of a tautology like "we experience time how we experience time."
But a better way to think about this is, you are about two meters high, you are about a meter wide, about a half-meter dorsoventrally... and about 30 000 000 m in the other direction, if we're looking at the human reaction time/blink-of-an-eye range of 0.1s (think about how 10fps video is at the cusp of being continuous and how 20Hz is where clicks stop sounding differentiated and instead start sounding like a bass note).
What this means is that if we look at you relativistically, you kind of look like a big "rope" with worldlines of other atoms coming in, braiding into your body, eventually leaving... but the strands of this rope are bundled into these cells that have worldlines over 99.9999% parallel. (Atoms within those cells move faster, but you're probably at least 99.999% parallel even if we make that statement?) And that astonishing parallelism is precisely why relativity is not very intuitively plausible to us.
> and about 30 000 000 m in the other direction, if we're looking at the human reaction time/blink-of-an-eye range of 0.1s
So: distance over time, but is the time dimension only measurable in distance over time? Is there a purely time unit, or does that not make sense when speaking of spacetime?
Yeah normal time units still exist in relativity, clocks gotta clock.
But ratber it's that there exists an operation which is almost entirely like rotation, but it rotates x, y, or z into w=ct, where w is measured in meters just like x,y,z are, but t is measured in time units, and c is the speed of light converting between them. Instead of a rotation's formula with sines and cosines like
relativity has a slightly different set of functions sinh and cosh that are very closely related to sin and cos. (Sine and cosine have Taylor series where the polynomials alternate, sin(x) = x – x³/6 + x^5/120 – ..., and sinh and cosh have the exact same Taylor series with all + signs rather than alternating + – + –.) The analogous expressions are then, This transformation, in relativity, is just built into how any acceleration works. So whenever you accelerate, even in pre-relativistic physics, you expect to see the emergence of some Doppler shifts. In relativity these shifts are not quite as strong as expected from the classical theory, and as a result when you subtract off the Doppler shifts and try to say "what has happened" you get an answer that "the meaning of the present moment, which historically defined a 3D universe frozen at a point in time, identifies a different 3D slice of the 4D spacetime." And this is what "rotates", it's the rotation of the plane that you think is the "present moment".The fact that you are discretely "you" about ten times per second, I am taking as a fact of biology. But if you try to convert that biology into physics, that's where you convert t into w to get that t=0.1s converts to w = 30,000 km.
It's better to think that our 4 velocity always has a magnitude of 1 and use c only as a scaling factor necessary because our weird choice to use different units for time and space.
Acceleration is a rotation in this weird 3-1 dimensions.
I think it better to think about 4 velocity as a unitless quantity. Because our intuitions about units and dimensions are formed by 3 dimensional space where every dimension can be swapped with any other and everything is still the same. 1 meter rotated is still 1 meter. Doesn't become 0.56m/s
If you use seconds and light-seconds as the units instead of meters, then the magnitude of the vector is just a constant 1.
Another way of putting that: This isn’t a vector at all, it’s just a direction. Treating it as a vector gives rise to silly statements like “one second per second”, which is yet another way to explain that it’s magnitude 1… because it’s a direction.
Not really because a light second is meters.
I mean like yes you can measure time and space with the same units in the way you suggest but then the concept of velocity changes as well.
I think that’s GP’s point. If you take at face value that your speed through spacetime is constant and that the only thing that can vary is the magnitude distributed through (x, y, z, t), then the only important component of your spacetime velocity is its angle in 4D space (e.g., your “direction”).
But also our own personal velocity is stationary. We (AIAU, IANAP) always perceive our own velocity vector as (0, 0, 0, 1). When we undergo acceleration it only ever affects the directional components of every other part of the universe, not our own experiential frame.
A fidget spinner illustrates this for me--bear with me. When I spin it and it just stays at rest in my hand, it spins fast. But when I quickly move my hand carrying the spinner, you can see it slows down the spin rate, and then when I stop moving it, it speeds back up. While the mechanisms are entirely different (classical vs. relativistic) they both show motion can affect certain fundamental properties of a system, whether it be spin rate or the passage of time
You can't "experience" time. Experience is memory and memory is the only thing you can "experience". Whether that memory has anything to do with time as such is debatable. Personally I'd say no.
You're thinking of subjective experience, conscious perception of time. OP is referring more generally to the local speed of causality in a system at rest.
I've heard this described as "we all move at the speed of light." Also, since another way to describe alignment of two vectors is an angle, motion can be characterized by the angle it makes with the time axis.
https://www.youtube.com/watch?v=au0QJYISe4c
I believe that’s an accurate model, with the caveat that it’s all relative. There’s no universal reference frame. So for the photon and his pal photons, they experience time while you (in your reference frame sitting still) are the one moving at the speed of light and not moving through time.
Edit: See below, the photon doesn’t have its own reference frame so they still don’t experience time.
Photons absolutely do not experience time. The spacetime interval of any photon is always zero, and the spacetime interval tells you how much time any particle experiences. Note that it’s invariant.
Yes you’re right.. the photon has no reference frame of its own then.
So then that would just apply to massive objects with their own reference frames.
I still don't get it, photon comes into existence and then slams into a thing for us to notice the existence. Between the being born and slamming into something time passes, no?
For everything around it .. But not for the photon?
how do you know?
Here’s something I’ve never understood; perhaps a more knowledgeable commenter can explain it to me.
If I get in a spaceship and accelerate up to about 0.9c, then cruise for a while, then flip around and come home at the same speed, I will have experienced much less time than the people on Earth. But from my frame of reference, they were the ones going really fast, and I was sitting still. If all motion is relative, what makes me the one to experience less time?
This is a well known paradox: https://en.wikipedia.org/wiki/Twin_paradox
TL;DR: The two scenarios are not symmetric, the person in the spaceship undergoes acceleration whereas the observer staying behind does not.
I only got my undergrad in physics, but I think there is something there to be mined between time as a dimension and the second law of thermodynamics. Why this one?
First, I will render a quote which never failed to amuse me: "The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations -- then so much the worse for Maxwell's equations. If it is found to be contradicted by observation -- well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it to collapse in deepest humiliation." (Eddington)
Why such honor? For one, in statistical physics, you can more or less derive the second law of thermodynamics, from scratch. No need for observation. It's just there the same way the quadratic equation is. Somewhere I have a cheap Dover reprint which contains a relatively easy to follow construction of the second law. It's the math. You can measure things badly, you can find one phenomenon creating the appearance of another, but you cannot fool The Math.
And so the statistical physics you can get from just math gives you this arrow of time, flying only one way, just as we see from spacetime.
To me, and again, I only got a few grad courses under my belt in it, this suggests not just a deep connection between entropy and spacetime, but the inevitability of it from the basic math (really, a talented high schooler could be coached through it) means that there is something about large (for n = ?) numbers of particles losing the reversibility which is so often present in particle interactions where n is smaller. What gives there? How do we go from this "trend" emerging to it being a property of spacetime even if no particles are sitting in said spacetime.
Not that I would have dared write the great Wheeler, but I have wondered if his "geon" concept would have fit in with this sort of thing. It seems so fundamental. One can imagine a universe with a different number of un-unified forces, or gravity dropping as the inverse-cube, or varying physical constants, but the math is still the same in these universes and it then suggests that there's no, uh, room for an option wherein the time facet of spacetime is anything but an arrow flying forever on towards entropy in its many masks.
A great task, or perhaps a very alluring windmill, for someone younger and brighter than I.
I'm in a similar boat, but I've always felt the opposite! I've always felt the second law is kind of a shoe-in and maybe even shouldn't be a law at all.
The first and third laws, "energy is never created or destroyed" and "for every action there's an equal and opposite reaction" are always true! To my knowledge, no process is ever allowed to break either law. (With exceptions for cosmological process like the expansion of the universe that we really don't purport to understand.)
The second, "entropy can only increase" isn't! That's right, I said it. The processes it describes (a cup unshuttering, or coffee unmixing, or particles all finding their way into the same side of a box) are totally legal process, albeit statistically unlikely. If you restrict your system to few enough particles (say, n=3), random processes that decrease entropy are not only possible, but something that happens with regularity!
Now, I make no claims to be right here. I suspect that Eddington fellow probably knows what he's talking about. But, this has been a longstanding thorn in my understanding of physics, so I'd be interested if anybody has any interesting insights!
> With exceptions for cosmological process like the expansion of the universe that we really don't purport to understand
That's not accurate, expansion of the universe (that the standard model of cosmology describes) does not violate conservation of energy. It makes it a little different from the classical view.
In classical mechanics, energy conservation is a well-defined concept in a static or non-expanding spacetime. However, in an expanding universe, especially one described by general relativity (like ours), the energy of the universe is not necessarily conserved in the traditional sense, because the global energy of the universe is difficult to define when spacetime itself is dynamic (expanding)
So GR does not require global conversation of energy in the same way classical (here classical means strictly newtonian mechanics) mechanics does. This dynamic nature of the spacetime allows for energy to appear to "change" due to the expansion. It is more complicated when you add things like dark energy to the equation.
One interesting aspect is the phenomenon of cosmological redshift. As the universe expands, light travelling through space is redshifted. This means that ita wavelength increases and its energy decreases. This "loss" of energy from light is not violating conservation of energy. It is rather consequence of the expansion itself.
Now lets back to dark energy which is driving the accelerated expansion of the universe, the energy associated with the vacuum of space remains constant per unit volume, but as space itself expands, the total energy associated with dark energy increases. This again does not violate the laws of physics because energy conservation is more complex in general relativity than in Newtonian mechanics. And of course the local energy conservation works in a well-defined way if you take a localized region of the spacetime.
From the Wikipedia page on the second law of thermodynamics:
>For example, the first law allows the process of a cup falling off a table and breaking on the floor, as well as allowing the reverse process of the cup fragments coming back together and 'jumping' back onto the table, while the second law allows the former and denies the latter. The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always tend toward a state of thermodynamic equilibrium where the entropy is highest at the given internal energy.[4] An increase in the combined entropy of system and surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time.[5][6]
Entropy is also defined as the number of different arrangements of particles in a system. We say that entropy is increasing in our universe. But we have also found that space is increasing. If space increases faster than particles move, entropy could even decrease
The older I am (and I am at my 50s) the more I have this intuition that entropy is a fundamental force driving not only physical phenomena but also social interactions, economy etc.
Formalising this intuition is another story though...
Tools from statistical physics have long been used in sociological and economical models.
It's no wonder, because statistical physics was devised as a tool for the study of complex systems.
For the same reason I don't deem entropy to be a fundamental property of physics, but one of complex systems. As far as I remember from university, the 2nd law of thermodynamics simply arises from the fact, that there are exponentially more unordered than ordered states.
Though information itself may be a fundamental physical property. The recent interest in Quantum computers shines new light on the connection between information and Quantum Mechanics. It remains to be seen, how that point of view is compatible with relativity.
I hope, that one day someone finds out, that the "time dimension" arises in the macroscopic limit from a graph of discrete causal events.
Not disputing anything you said but... The issue I see is that without notion of time it is difficult to talk about causality (I guess you could only talk about "entanglement"). It is actually difficult to talk about "events" at all - I guess you can only talk about "facts"?
We have the sun to provide us with low entropy energy and the atmosphere to dissipate high entropy energy, so stuff tbat happens on earth can be lowering in entropy possibly. Climate change excepted.
Could you pls. point to the said book or some other resource for me to learn about this? As such, I follow what you have said, but would love to see the math too. Thanks.
Ilya Prigogine wrote a lot about this, see eg Order Out of Chaos. He won the Nobel prize in chemistry for his work on nonequilibrium thermodynamics.
Boltzmann had originally tried to prove that the second law is a mechanical (statistical) fact and several others tried as well. But Poincaré showed that those systems which, regardless of their initial state, inevitably increase entropy later on inevitably reduce it (his recurrence theorem). There are also in fact reversible processes in nature, so it can't be that mechanics alone implies the procession of time. Something more involved is going on.
Carlo Rovelli has also written a lot about the "thermal time" concept in his books.
My takeaway from them is that you can't really get time out of mechanics by itself (statistical or otherwise). In the same way that you can't get baryon asymmetry. It is intrinsically a selection principle on initial conditions.
Thanks a lot for a detailed and simple answer! I have many keywords now to read more on.
I just read about Poincaré's recurrence theorem here: https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theor...
Even with this, would the Poincaré recurrence time not be (probabilistically) be very large for any complex system, and thereby practically imply the second law of thermodynamics?
I also just re-read about Maxwell's demon (https://en.wikipedia.org/wiki/Maxwell%27s_demon), but see that there are already various arguments against it even before arguments about the demon moving the system towards Poincaré recurrence.
Thanks.
One Speculative Theory of Spacetime:
Our universe is a 3D Manifold in a higher dimensional space.
All event horizons have a "surface normal" (orthogonality) direction at any point. For example a conventional Black Hole (2D one) has an event horizon that is a 2D surface. That is, for a flatland creature living on that EH it takes two coordinates to define a location, but these flatlanders would experience "time" as the "growth" of the EH (like when more mass falls into it, and the EH grows), and the direction is "outward" (perpendicular to EH surface)
Now here's the interesting part: Event Horizons come in all dimensions. Our "Universe" is a 3D EH, but of course at any point in space there's a unique "rate of time" and a common "direction" of time, which from a higher dimensional space perspective is simply the "orthogonal direction" to all our space directions. (Time orthogonal to Space [i.e. Minkowski]).
As matter falls into our "Universe", that moves time forward for us. But our universe itself consists of all the "points" (Quantum Decoherence Points) which are co-located on a 3D manifold embedded in a higher dimensional space.
This means the Big Bang has things exactly "inverted", and is wrong. Matter didn't "originate from inside". It's the opposite o that. Everything "fell in" from outside. The reason our universe is expanding and accelerating is because it's a black hole EH. Black Holes mainly just grow (excluding tunneling etc).
I agree. The similarity between black holes and our universe is striking. The fact that matter inside it can not be observed from outside opens possibilities for all kind of quantum states, which is maybe, just the configuration of a universe (for example that one we are living in).
There are many different "lines of reasoning" that lead to this conclusion as well. For example as an object approaches the speed of light, an observer will see it become smashed perfectly flat (length contraction) in the direction of it's travel, which is the logical equivalent of a "loss of one dimension".
In other words as something tries to "escape" our 3D manifold the effect that has is to remove one a spatial dimension. Also as something goes to nearer to speed of light, we know it also loses "time" dimension. No flow of time (from perspective of observer).
And all of these same "divide by zero" kind of impossibilities are precisely what's also happening on event horizons. In other words Special Relativity reinforces this theory. My claim is that even the Lorentz equations are showing us the way in which a dimension is lost. Lorentz is a "smooth" way of going from N dimensions to N minus 1 dimensions.
EDIT: So there must be a stronger relationship between Spinors and Lorentz than what's currently known! By having complex components, Spinors is the way to have "partial moves" in a direction, while still technically maintaining orthogonality to all other directions.
Has this been investigated in detail by physicists? Does it hold up in theory?
I think it's one of those things that borders on the unfalsifiable, similar to multiverse theory. I've had this concept for about a decade, but I did actually see a youtube video of a Cambridge (or some well known University for Physics) where a professor/researcher did present the idea, yes.
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I see a variety of discussions of time with different views. Is there a good summary or journal review article?
This is the sort of question I think is useful to explore with ChatGPT et al, and of course you can ask for links.
In the meantime, Stanford and IEP are always good for this sort of thing (including as a background for conversing with the former):
https://plato.stanford.edu/entries/time/
https://iep.utm.edu/time/
It won’t necessarily convey all the different views, but The Order of Time by Carlo Roveli is an absolutely beautiful walk through the various interpretations of time down to the quantum level. The nature of time is not fully understood and Roveli understandably (and openly) has and endorses his own view here, but he covers the ground upon which there’s consensus quite well.
You’re just going to get philosophizing with scientific language.
Beyond the mathematical model used for a particular physics question, there just isn’t much consensus.
Correct, it's a mathematical dimension.
The ontological dissonance in that title is spectacularly simulacrum level 4.
My understanding from Einstein’s book Relativity is that the four dimensions of general relativistic spacetime do not correspond to any one of the time or space dimensions of special relativity or classical physics.
It’s a great read, and short too. He explains it much better than I could.
Do you mean "Relativity: the special and general theory"?
Yes
"This is the underlying reason why, when you move at speeds that approach the speed of light, you start to experience phenomena such as time dilation and length contraction:"
This is not even possible in pulp science fiction. In order to be able to move with the speed of light you need to transform yourself into a photon. Only a photon can move with the speed of light. Saying "close to the speed of light" changes nothing. You need to be light to move with the speed close to the speed of light. Macroscopic objects cannot move with speeds approaching light speed.
> This is not even possible in pulp science fiction
Incorrect - anything is possible in pulp scifi.
> In order to be able to move with the speed of light you need to transform yourself into a photon. Only a photon can move with the speed of light.
Incorrect - any massless particle will move at the same speed as light.
> Saying "close to the speed of light" changes nothing. You need to be light to move with the speed close to the speed of light.
Incorrect - it's perfectly feasible to accelerate particles to over 99% of the speed of light. e.g. the LHC can accelerate protons to 0.999999990 c. Also, it's not possible for massless particles including photons to move at anything other than the speed of light in a vacuum, so "close to the speed of light" is not possible unless the object has mass.
> Macroscopic objects cannot move with speeds approaching light speed.
Incorrect, though humans haven't been able to accelerate macroscopic (e.g. visible to human eye) objects to more than approx 0.064c (Parker Solar Probe), it's just a question of using enough power to accelerate the relevant object. There's no reason to think that a black hole accretion disk couldn't easily accelerate a lump of matter to more than 0.99c.
You might want to look up the word “approach” in a dictionary.
> Only a photon can move with the speed of light.
Any massless particle must move at the speed of light. Gluons, the carrier of the strong force, are another example.
"Any massless particle must move at the speed of light"
Does not change my argument. Human body is not a massless particle.
And it can't move at the speed of light. It can approach the speed of light which isn't the same thing as moving at it.
No, but it does betray your lack of formal exposure to the topic.
Read the formula: https://en.wikipedia.org/wiki/Lorentz_factor
Which means you can approach the speed of light, but never travel at this speed in space.
> Saying "close to the speed of light" changes nothing.
https://en.wikipedia.org/wiki/Oh-My-God_particle
“Close to the speed of light” means, like, 99% of the speed of light. You can even see the speeds listed on the graphs, which are given as a fraction of c.
"'Close to the speed of light' means, like, 99% of the speed of light"
So, you are saying that it is possible to accelerate human body to 99% of speed of light without transforming the body into a massless particle?
Yes.
Gven the average mass of a human body at 66kg: (((1/sqrt(1-((0.99c)^2/c^2)))--1) 66kg * c^2) = 50,000PJ
which is the amount of electrical energy the entire US produces in 0.287h???
I’d need about 40 minutes.
Yes.
It will never be possible to get to 100%, but I principle anything below that is possible. Not just 99%, but 99.99999999% or however many you want.
Of course, it's not actually feasible, you would need galaxies worth of energy to do so.
But for something like 10% or even 50% of the speed of light, it's not even that implausible.
> Not just 99%, but 99.99999999% or however many you want.
Badly enough, even that's not true.
We have a frame of reference given by the cosmic microwave background. When you move faster and faster at some limiting speed will create pions that will slow down the particle creating an effective slower max speed.
https://bigthink.com/starts-with-a-bang/speed-limit-below-sp...
What is our current speed?
Our current speed is 99.999999% the speed of light, according to some frame of reference, 10% according to another frame of reference and 0% according to another.
A lot of work is done by the words "get to" which is colloquial for "accelerate".
I guess you guys found a way to accelerate human body to the speed of light without disintegrating. Why don't you prove your technique first with G-forces?
Why don't you? Here's a calculator:
https://gregsspacecalculations.blogspot.com/p/blog-page.html
1G of acceleration (which I'd hope you agree is survivable by humans) over an extended time period can easily reach relativistic speeds.
The thing stopping us from doing this today is economics, not physics. Current rockets have about enough fuel for minutes of acceleration, and fuel requirements increase exponentially due to the tyranny of the rocket equation. If you skip the need for fuel (laser propulsion?) and find some way to decelerate (laser cooling propulsion???), then interstellar travel to pretty much anywhere becomes entirely reasonable within human lifespans.https://en.wikipedia.org/wiki/File:Roundtriptimes.png
I think you're handwaving away the other issues with physics that make near-lightspeed travel effectively impossible for humans. How exactly do you propose sustaining 1g acceleration for 5 years, for instance? You can't just "skip the need for fuel". Lasers aren't perfectly collimated and spread out over distance. Even an Epstein drive from The Expanse will eventually run out of fuel. The other big problem is: how exactly do you deal with collisions with space debris? Even at the speeds we currently travel, micrometeorites are a problem, but at 0.9999c, even stray hydrogen atoms (which deep space is full of) are going to destroy your ship.
Honestly, Star Trek way back in the 1960s was pretty brilliant at getting around many of these technical problems by inventing "warp drive".
Even if we somehow magically solved our economic problems overnight, that isn't going to make relativistic speeds feasible for humans anytime soon, if ever.
> accelerate human body to the speed of light
Nothing with mass can have the same speed as light, but you can trivially accelerate a human body - or something similar - to a speed which is arbitrarily close to it, without risking anything from the G-forces involved.
You just need to do it very slowly.
That is, in any case, neither here nor there, since this is a thought experiment used in a discussion about the effects of moving at a speed close to c - people in thought experiments are stronk.
I would really appreciate if people writing these types of articles first give rigorous and unique definitions of space and time.
My favourite explanation (which IIRC is in a book by Brian Greene) is that you can think that everything always moves at the speed of light in a 4D spacetime. That way, if you stand still, you're moving only along time, and as you tilt your velocity vector more and more toward the space dimensions you have to travel more slowly along the time dimension. At the limit you are moving at the speed of light along some space axis and technically your time is "frozen".
Some of the answers at https://physics.stackexchange.com/q/33840 explain why "everything always moves at the speed of light in a 4D spacetime" is a statement that, at best, has no content.
But then it gets weird and the time axis changes scale relative to other elements in space.
For an observer, maybe
There is no absolute frame.
Or as I tell people, kidding on the square, we're trapped in a time machine hurtling us into the future at the rate of one minute every sixty seconds! It is important you say that last bit in a panicked, breathless voice.
My God, that means every three hundred sixty-five days or so, we'll have gone forward a year!
Thee is no „Stillstand“, you can’t stand still relative to anything in the universe.
Hm. That’s a possibility. As I understand it though, an infinitely massive object would not move in space, and would experience time at the absolute rate of one second per second.
Although that sounds theoretically impossible, I would remind you that somehow the opposite seems to be possible (a particle with zero mass that moves through time at a rate of zero seconds per second), despite that not making a lot of sense to a layperson.
Footnote: Talking about time in seconds makes very little sense here because our notion of time is so heavily linked to how light moves through space, but hopefully my point is clear. Maybe someone has a better unit we could use to measure time independently of space?
Your point is clear. As far as can wrap my head around those theoretical concepts: An infinitely heavy object can’t move in space because there isn’t any space left to move. I would say that this object would have concentrated all mass in one point, no space left to move. No observer left to measure. I would also say that there can’t be two or more infinite masses at the same time, or they would move (at the speed of c (?) But that would have additional implications on mass and time) to the point between them.
But back to observable reality: let’s say you fall into a dark place where the time stands still and that means you are not moving, from an outside observer you are still moving relative to the space outside your black hole. Let’s say the observer fall on his way to your black hole into another black hole and experience the same phenomenon like you, from a third observers perspective everyone is moving.
Something like (from Wikipedia):
> In the presence of gravity spacetime is described by a curved 4-dimensional manifold for which the tangent space to any point is a 4-dimensional Minkowski space.
Perhaps? A good way to lose 99% of the readers before the end of the first sentence.
I'm a huge fan of providing laymen explanations. And at some point if you _actually_ want to understand you have to stop using those and pickup and understand the math.
http://therisingsea.org/post/mast30026/
Has a good introduction to space, and the notion of a manifold, and what a Minkowski space is.
Ok, but almost nobody is going to read an article that requires you to work through 21 lectures, 9 tutorials, and 3 assignments first. It'd be great if they did, and it'd be nice to give the link for interested people, but otherwise it is just making the subject inaccessible to almost everyone.
That's in the article on Minkowski space. It's actually a good summary, with a hyperlink to manifold.
Here's the introduction to the "spacetime" page:
> In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events occur.
Just represent it in a 4x4 multidimensional array that corresponds to the metric tensor.
Yes, that will really pull in the laymen...
Reminds me of the mathematician who was asked how he mentally visualizes a 4 dimensional space.
"I simply imagine an n-dimensional space, and then set n to 4"
Reminds me of Geoffrey Hinton who, when asked how to imagine a 14-dimensional space, said: “imagine a 3-dimensional space, and say ‘fourteen’ very loudly”
This is great, can't believe I haven't heard it before.
>>> After Hilbert was told that a student in his class had dropped mathematics in order to become a poet, he is reported to have said "Good--he did not have enough imagination to become a mathematician"
https://scienceworld.wolfram.com/biography/Hilbert.html
Time: a separation between individual events that can be crossed by cause and effect.
Space: a separation between individual events that cannot be crossed by cause and effect.
"Individual event" is meant in the familiar sense, like a "bang" from a gun, or your birthday party.
That's a solid burn, suggesting that nobody else came to their party
As per Kant:
Time: inner sense, intuition of continuity, unity
Space: outer sense, intuition of objects
Its a bit more complex but that’s a basic summary from the guy who came up with the “space and time” thing. Read the “Transcendental Aesthetic” in the Critique of Pure Reason for more.