Time is a dimension, but not like space
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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.
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...
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.
https://en.wikipedia.org/wiki/One-way_speed_of_light
A lot of scientists have thought about this. Step one is checking their work.
I see nothing there that would invalidate my synchrotron argument, though.
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.
Before I looked at stack exchange, I thought of another, much simpler experiment. Generate plane wave radio waves of a frequency such that the nominal wavelength would be meters or tens of meters. (By "nominal wavelength", I mean the wavelength l=c/f, the wavelength as if the speed of light were the same both directions.) Run those plane waves into a reflector a couple of nominal wavelengths away. Measure the RF energy at various points along the path to the reflector. Does it look like a standing wave of the expected wavelength, or not?
I actually saw that idea on the discussion I found on stack exchange. The only reply I saw was "well, the relationship between wavelength and frequency might not hold if the speed of light is asymmetrical", which seemed very weak to me. What, we have waves propagating with velocity v, but wavelength l =/= v/f? How can you do that without destroying the continuity of the wave? How much of physics is that going to destroy? And, how many "well, maybe..." items are you willing to stack up to make it impossible to detect your first "well, maybe"?
I didn't leave a question on stack exchange. The discussion was nine years old.
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”.
Also infinite speed of causality doesn't have to imply infinite speed of light, does it?
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.
> 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.
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.
At least, that's what I surmise. I'm not a physicist.
Edit: in short, not all reference frames can agree on the order of events, and FTL events propogate "backwards" between some reference frames.
If we imagine something going faster than the speed of causality, we're simply misconcieving the properties of space.
> 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.
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.
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.
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.
many people believed in, and advocated for, string theory. Don't make it real.
I don't believe I asserted that pop-science is true just because it's popular. Quite the opposite, in fact.
See also [https://en.m.wikipedia.org/wiki/Electromagnetic_four-potenti...]
Notably, light is a form of electromagnetism, so this shouldn’t be as surprising as it is. c is an explicit part of many formulas, interestingly. And electromagnetism was the first thing tackled in special relativity.
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.
In this universe, fundamental forces like electromagnetism directly contain things like c, so if c is infinite, everything is going to work very differently.
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.
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).
The only theoretical case I’m aware of are closed timelike curves (CTC) which are paths in spacetime that loop back on themselves, allowing an object to return to its own past. A famous example is the Gödel metric, a solution to Einstein’a field equations.
It should be noted, however, that these solutions are generally regarded as unphysical because they require conditions that don’t seem to exist in our universe (such as a globally rotating universe).
You wrote: "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."
I answered that the "speed of casuality" is not "how fast light travels in a given medium": it's the maxiumum speed of light, which is the speed of light in a vacuum.
So that the light travels slower in a pool doesn't mean we can violate casuality - the overall casuality "speed limit" remains regardless (it's a maximum limit in the universe, not a regional one).
Btw, light doesn't really slow down in a medium like water. Photons always travel at the speed of light. The aggregate light appears to slow down in the water, as invidividual photons are converted to energy when interacting with the water particles and then the energy is emitted again as new photons.
The photons while they exist (i.e. before and after the conversion to/from energy) always run at the speed of light, even inside a medium like water or whatever else. Some of them will be converted to heat though, warming up the water - but in that case they're not light anymore.
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.
If light happens to move slower than c under some conditions, that is irrelevant. It isn't the speed of light we care about, it is c.
Essentially, when we say FTL, it means "faster than c", not "faster than light".
Light actually has nothing to do with it; it just happens to travel at the max speed allowed by the universe when there's nothing that impedes it's motion (i.e. in a vacuum).
So the acronym should really be "FTLIAV"!
In quantum entanglement, two particles can be entangled in such a way that measuring one particle instantly determines the state of the other, even if they are light-years apart. This "instantaneous" connection seems faster than light, but it cannot be used to transmit usable information in a meaningful way.
The phenomenon does not violate relativity because no classical information can travel between the particles faster than light. Entanglement is a correlation, not a means of communication and hence NOT a means of causation.
If light is slower in other mediums, that has no effect on how quickly causation can happen.
Edit: wrong one https://youtu.be/yP1kKN3ghOU?si=hsBj0RpzOb3JZWdS the one above is the "why."
That or you misunderstood the physicist. You need to watch both videos to understand what's happening here.
The speed of light is not "slower in water". Light propagates more slowly through water. The subtle difference is not just pedantic semantics. It's the key to understanding how we don't have a paradox on our hands.
I can't think of anything purely in the physical plane, though there's this:
https://en.m.wikipedia.org/wiki/Retrocausality
But if one includes metaphysics, one example (there are others) is an individual's anticipation of another individual doing something in the future could cause them to act in the present.
This is quite the stretch on its own, but if you include this (which exists, as much as people don't like to admit it depending on the context):
https://en.m.wikipedia.org/wiki/Consensus_reality
...it is possible, in that it comes down to the question of is it true that the effect proceeded the cause, and if enough people believe something is true, it is true. And if you disagree, observe human behavior for a while and see for yourself - people will tell you it is true with absolute sincerity, and they often will act in the physical plane based upon that "truth". Wars are started over "not true" "truths", perhaps even all of them.
And if that's not enough, another route is perhaps people really can see the future. People with absolute sincerity tell me they can constantly. Perhaps they are hallucinating (they swear to me they are not), but perhaps they are not, maybe it is yet another thing that science has yet to discover, or cannot discover due to non-determinism, non-falsifiability, consensus reality (a theory cannot be(!) true unless there is consensus agreement that it is true), etc.
Please don't shoot the messenger.
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?
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
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.
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.
Formalising this intuition is another story though...
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.
>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]
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!
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.
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.
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.
Edit: See below, the photon doesn’t have its own reference frame so they still don’t experience time.
So then that would just apply to massive objects with their own reference frames.
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 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.
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.
Moving your point of view from one inertial frame of reference to another is easy enough, but there should be some overarching mathematical construct that can model all the inertial frames and their relationships at once. Phenomenons such as energy, mass and acceleration should be easier to understand within it.
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.
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?
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
w' = w cosh φ — x sinh φ
x' = x cosh φ — w sinh φ
(w')² – (x')² = w² – x².
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.
Acceleration is a rotation in this weird 3+it 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 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.
why would going v fast in the x direction affect y and z?
That is - to my limited understanding - essentially why photons are “timeless”.
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.
Also, AFAICT, nobody has yet actually worked out spacetime with masses properly, right? Where masses influence and are influenced by space, each other and time, all at the same "time", in general?
Edit: Looks like people are working on it? (for mergers of binary stars) https://arxiv.org/abs/2405.06035
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?
TL;DR: The two scenarios are not symmetric, the person in the spaceship undergoes acceleration whereas the observer staying behind does not.
It’s a great read, and short too. He explains it much better than I could.
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).
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.
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.
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.
Exactly. Time is just a very useful fudge to describe change. If nothing changes, there's been no time. If something changes, there has been time.
A dimension is just a useful number that you can operate on. You can have a physics where the fourth dimension is how blue something is, and the fifth dimension is how good Mary thinks it tastes.
In the meantime, Stanford and IEP are always good for this sort of thing (including as a background for conversing with the former):
Beyond the mathematical model used for a particular physics question, there just isn’t much consensus.
> 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 simply imagine an n-dimensional space, and then set n to 4"
http://therisingsea.org/post/mast30026/
Has a good introduction to space, and the notion of a manifold, and what a Minkowski space is.
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.
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.
My God, that means every three hundred sixty-five days or so, we'll have gone forward a year!
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?
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.
> I would also say that there can’t be two or more infinite masses at the same time
...for the same reason that there can both be infinitely many fractional parts between 1 and 2 and at the same time, infinitely many between 2 and 3.
You raise the question on 'observable' reality, which is interesting. I would say that the example is a bit flawed (you can't 'observe' things that happen inside an event horizon'). Indeed, from an outside observer's perspective, what actually happens is that you arrive at the event horizon and 'freeze' in time and movement. Eventually, you red shift into invisibility.
I previously considered this to be a strange artifact of light, but perhaps the correct understanding is that you actually start moving at '1 second per second' through time, and stop moving through space completely?
It feels like this is the sort of thing people much cleverer than me would already be able to answer, so perhaps I'm way out of my depth here :)
Mathematically true but wouldn’t a infinite mass have infinite gravity? That means every other mass (infinite or not) would fall into that mass at the speed of light - even if they are far far away. If they are in the same space of course.
An infinite mass would mean that there is no „flat space“ left and everything is on the slippery slope to the center of that infinite mass.
That’s what I mean with my badly worded „ 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.“
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.
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.
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?
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.
A lot of work is done by the words "get to" which is colloquial for "accelerate".
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...
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???
> 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.
Does not change my argument. Human body is not a massless particle.
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.
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.
1 day .0028c
1 week .02c
1 month .086c
1 year .77c
2 years .97c
3 years .996c
4 years .9995c
5 years .9999c
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.
We really can skip the need for fuel, for example. Sails (with or without lasers) are a technology we have proven in the field. Lasers do lose collimation over distance, but you can reach relativistic speeds before then (I'd argue that .02c from 1wk of 1G is relativistic). That won't get you to the center of the galaxy (or solve the deceleration issue), but there are proposals being reviewed today to use lasers to send probes for a flyby of Proxima Centauri.
https://www.nasa.gov/general/swarming-proxima-centauri/
https://en.wikipedia.org/wiki/Breakthrough_Starshot
But we don't need science fiction tech for this to work, we just need impractical amounts of fuel. Starship only has enough fuel to last 10m? Just send 50k starships and you can burn for a year. Tyranny of the rocket equation requires additional fuel to push all that fuel? Just send another billion Starships or whatever. Going too fast and now the interstellar medium hits like high-energy cosmic rays? Just send more shielding and fuel. This assumes we can build and fuel billions of Starships, which is certainly infeasible, but I'm calling this an economics issue as we have these technologies today.
If we want to get really sci-fi, I'd point you towards stellar engines. The thought process here is that the Earth already provides radiation shielding, and the Sun already burns fuel to provide massive amounts of energy, so we might as well just make use of what we got! Add mirrors to concentrate the Sun's light in one direction, and our entire solar system becomes an interstellar spaceship. It might take millions or even billions of years, but the Sun has enough fuel to accelerate the whole system to about .27c.
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.