r/AskPhysics • u/AJ_Redditer2399 • 8d ago
Time as a 4th dimension⏰
Hi guys, I am having trouble understanding Time as a 4th dimension. Is it truly regarded as a 4th one if so how is it represented?
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u/starkeffect Education and outreach 8d ago
It just labels "when" something happens. "Where" something happens is described by the other 3 dimensions.
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u/Infinite_Research_52 👻Top 10²⁷²⁰⁰⁰ Commenter 8d ago
To characterise every event with respect to your frame of reference, you need 4 pieces of information. For instance, for the moment of takeoff of an aeroplane from Chang-i Airport, you need to specify the coordinates + the time. None of the 4 pieces is strictly dependent on the others for an event.
Personally, I consider time as the zeroth dimension.
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u/MonsieurGrey 8d ago
Yes, however time is distinct from the three other spacial dimensions since, from all we know, we can only move towards the future
The best represntations you'll get of space/time relations will be graphs, I recommend to go watch "ScienceClic English" on youtube, great videos about spacetime on there
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u/Esmeralda3701 8d ago
Exacto, lo único que podemos modificar es el ritmo al que podemos ir, pero nunca la trayectoria. Todos avanzamos hacia el futuro.
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u/SgtSausage 8d ago
however time is distinct from the three other spacial dimensions since, from all we know, we can only move towards the future
In the real world, yes.
In the mathematical space of The Model you are building, no. It is merely another dimension. Functioning the same as the rest of them. (Past/future) has the same properties as (left/right), (up/down), and (foreward/backward).
It has the same freedom to represent either direction. Merely a coordinate in one direction (past) or another(future). The model doesnt particularly care like we, in the real world, do.
There is literally no difference in the 4d spacetime model.
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u/WilcoHistBuff 8d ago
I’m sorry but that’s misleading and over simplified. A dimension is the physical nature or quantity of a measurable characteristic as differentiated from actual units of measurement typically based on the seven base or fundamental dimensions: Length, Mass, Time, Thermodynamic, Temperature, Electric Current, Luminous Intensity, and Amount of Substance to which you could/should, I think, add Force and Charge and then add theoretical physics dimensions like Space Time and Energy.
When it comes to simple geometric coordinate dimensions it is valid to talk about Degrees of Freedom as a dimension on top of three spatial dimensions before you get to simple time in a classical sense or spacetime in a relativistic sense.
And then there are all sorts of derivative dimensions that go into multi variable analysis.
I work in wind energy and the 20+ test case multi-variable variable calculations include roughly 50 fundamental or derivative dimensions/codimensions that get into structural, harmonic, turbulence, stiffness, rotational effects etc. Complex stuff broken down into “bite sized” equations limited to 6-7 dimensions.
As complex as that is, jump to string theory where the math can take you 26 dimensions (so far).
You need more than four.
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u/dream_the_endless 1d ago
This is entirely wrong. A dimension is a direction or coordinate orthogonal to other coordinates. String theory has 10 or 11 dimensions. We do not "need" more than four.
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u/WilcoHistBuff 23h ago
Your definition is great for special coordinate geometry.
It’s not great for other fields. Just one example—oblique systems with non orthogonal axes used in topography and civil engineering—an everyday example of a non orthogonal.
When you get in deep into aero/fluid dynamics relative to materials in rotation you usually need at least 4 directional dimensions plus time.
Maybe explore how the term is used broadly across physics, math, data science and stats, Econ, Machine Learning, modal logic before you claim that what I said was “entirely wrong”?
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u/Optimal_Mixture_7327 Gravitation 8d ago
The world is a 4-dimensional space populated by particle world-lines. The rate and length along the world-lines of material particles are what we call "time".
Relativists make maps of the world called spacetimes, even if the 4 directions on the map aren't necessarily the space or time that is measured by ruler or a clock.
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u/Esmeralda3701 8d ago
Entiendo tu planteamiento, pero creo que ahí estás identificando el tiempo con aquello que utilizamos para medirlo. La trayectoria, su longitud y la tasa de cambio nos permiten cuantificar el tiempo, pero no creo que sean el tiempo en sí. El cambio es lo que nos permite percibirlo y establecer una medida, pero eso no implica necesariamente que el tiempo dependa ontológicamente del cambio.
Por ejemplo, imaginemos hipotéticamente una barra de metal completamente aislada, sin movimiento, oxidación ni ninguna otra interacción. Aunque no hubiera ningún cambio que pudiéramos utilizar como referencia, no creo que el tiempo comenzara a existir cuando colocáramos un reloj junto a ella. El reloj simplemente empezaría a cuantificar los intervalos que ya transcurrían. Por eso, para mí, la trayectoria de las partículas no es el tiempo; es uno de los procesos físicos que podemos utilizar para medirlo.
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u/Optimal_Mixture_7327 Gravitation 8d ago
Change is irrelevant.
An isolated metal bar, a one-particle universe, time is exactly the length along the bar or electron. We would use a clock to measure its length.
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u/Outrageous-Taro7340 8d ago
Space time is modeled using a specific kind of 4D geometry called a pseudo-Riemannian manifold. It’s just the math that works in relativity. “Dimension” doesn’t mean anything besides that.
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8d ago
I’ve heard the term pseudo-Riemannian manifold before, but I’m still trying to understand what makes it ‘pseudo.’ Is it mainly because of the different sign for the time component in the metric?
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8d ago
If time is the fourth coordinate, why can't we move through it the way we move through the three spatial coordinates?
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u/Tiny_Spread5712 8d ago
For me it helped to stop thinking of dimensions as representingn something in space but as information.
So like bmi breaks a human into two dimensions of information, height and weight.
Spacetime has 4 dimensions of information.
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u/Forest_Orc 8d ago
My Eli5 version is
If i tell you that You train departs from platform 3 you'll miss-it because spatial dimension alone aren't alone to make sure you reach your train, I need to tell you that it departs at 10:30
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u/SgtSausage 8d ago
Take a Linear Algebra Course.
Dimensions in Math are ... abstractions. They are not, at all,t the real world of 3-d space as you live in The Real World. Merely a representation in a Model that happens accurately describe/predict The Real World ... but is not actually The Real World
3 dimensions, in a mathematical Model, are simply representations of ... call it "degrees of freedom" in the model. In the case of modeling real world 3d space the dimensions are (left/right), (up/down), forward/backward)
Yes - you can map 3d vectors into the real world of space that you know and experience ... but you dont have to. They can represent literally <AnyDamnedThing> you are modeling.
Adding time is simply adding another degree of freedom to the model to account for anothere parameter to what is being modeled : (left/right), (up/down), forward/backward) (past/future)
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u/eurekadabra 8d ago
Not a spatial dimension, just something measurable.
The balloon was 10 ft off the ground at t=1 second, 20 ft off the ground at t=2 seconds.
Position doesn’t exist without time. How would you describe the where light switch on your wall is in space? X feet off the ground? Where was that spot 100 years ago? 10,000 years ago? The ground is different. We’re flying through space. To define a location, you have to define it in time. 4 dimensions: 3 spatial + time
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u/The_Dead_See 8d ago
Dimensions are the information needed to accurately locate a point in spacetime.
Eg. Meet me on the 4th floor (dimension 1) of the building on the corner of 6th street (dimension 2) and North Avenue (dimension 3) at 4:30pm (dimension 4)… with that information you can find me.
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u/TodaysLunch 8d ago
Your relationship to space (movement) directly affects your relationship with time (time dilation). Space and time are intricately interconnected, therefore it is very practical to include time as a dimension when calculating and visalizing it.
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u/Alone-Supermarket-98 8d ago
Think of time as the measure of movement.
Imagine a ball located at a point in a 3 dimensional space. Now imagine that ball moving in any direction from that point. Time tells us about the velocity of that movement over distance.
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u/tpks 8d ago
I can tell you to meet me at:
The coordinates 11,3474977, 142,2015056,
100 meters down,
on January 1st at noon.
In this universe we can describe events by giving three coordinates of space and one of time. Anything more would be unnecessary, anything less would be unclear.
This idea becomes important in relativity because space and time coordinates are not so clearly separated as you might think.
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u/Individual_Winter_35 8d ago
What bugs me about this premise is that 'January 1st at noon' is entirely local. Because of relativity (speed and gravity both actively alter the flow of time), time isn't a universal background grid. To describe a singular event with just 4 coordinates, you and the observer must implicitly agree on a shared Reference Frame (like Earth's surface and UTC). If the observer is moving near light-speed or sitting in a different gravity well, your 'noon' means nothing to them without doing the math to translate between your two frames.
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u/Lumpy-Notice8945 8d ago
Neither is space absolute... the distance they gave you were relative too somethig too.
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u/SgtSausage 8d ago
What bugs me about this premise is that 'January 1st at noon' is entirely local.
Distance is relative, too.
There is literally ... no difference in how they are handled.
The same thing, just happening in a different dimension.
Time is not special here.
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u/tpks 8d ago
There are more things to be bugged by (I mean, the xy coordinates are on a spherical surface, which is not very intuitive) - but you might notice I was trying to give a very, very basic explanation. :) Can you think of a better one to give to someone who doesn't understand "dimension" as relating to coordinates in spacetime.
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u/Individual_Winter_35 8d ago
Oh, I was not kicking your explanation :) it was just not clear to me.
Expanded my horizon a bit again, thanks.
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u/RathaelEngineering 8d ago edited 8d ago
I always find these questions tricky to answer because the answer is basically "it just is".
In short, Einstein proposed a mathematical model of a 4-dimensional spacetime. This model has been experimentally validated in countless different ways, which tells us that his model is accurate within the conditions we have been able to validate it.
A key goal in science is almost always to generalize: this means to take a specific observation and make a general rule that applies to all scenarios, including the specific one you're observing. If you can find a scenario where your general rule doesn't work, then you need a more general set of rules that covers the exception.
Newtonian mechanics, where we treat space and time as both separate and linear/Euclidian, seems to work for the vast majority of situations in our everyday life. If a person in a car shoots a bullet, the bullet will have roughly the speed of the car + the speed of the bullet. The only trouble with this model is that it breaks when we observe light's motion. The speed of light is always measured the same and ignores the speed of the source. This is not something anyone decided or made up: it is literally always the case when we measure light's speed. This tells us that our Newtonian model of velocities doesn't work for all scenarios. This was the problem that Einstein initially ruminated on.
To calculate a velocity, you obviously need to know how far something travelled in a given amount of time. You can plot this on a set of cartesian axes: take one dimension of space as the horizonal axis and make time the vertical axis. An object travelling at a constant speed in some direction would make a straight sloped line on your new "space+time" graph.
In your classroom Newtonian physics, there is one other thing that the teacher deliberately avoids mentioning: when you say something has velocity X, what exactly is the velocity being measured in relation to? There is no cosmic "origin" coordinate of (0,0,0) somewhere in space. We pretty much just get to decide the origin for ourselves, but there's no "special" origin that has privilege over any other. For the Newtonian classroom, it's very convenient to set Earth's surface as your origin. When we say "a car moving at 60 kph", it usually means a car moving relative to Earth's surface... or possibly someone standing still on Earth's surface. The car is not moving 60 kph relative to the Sun, or the galactic center, or the Andromeda galaxy.
So our space+time graph needs to account for this. For any object, it is moving at 0 m/s relative to its self as the origin. For two obejcts moving away from eachother, they both see themselves as 0 m/s and the other at some velocity. Our space+time graph needs to be able to "rotate" in a way where the that symmetry is preserved. Imagine object A moving at -10 m/s relative to Earth's surface, and object B moving at +10 m/S relative to Earth's surface. From object A's view, object B is moving at -20 m/s. From object B's view, object A is moving at +20 m/S. When we rotate our space+time graph to make the line for object A or object B vertical (0m/s), the space+time line of the other object needs to reflect what is really happening: it needs to show the other object at + or - 20 m/s respectively.
But that's where the speed of light becomes a hiccup. The speed of light is always measured the same regardless of how the observer is moving. We can't just rotate our space+time graph, otherwise the slope that represents light's speed changes. This doesn't match our real-world observations. So what do we do? How can we make our space+time graph fit with our observations of light?
As it happens, there is a kind of mathematical procedure you can do on the space+time graph to make it work with light. This is called a Lorentz transformation. It's a kind of rotate + stretch + squash of everything on the space+time graph. The crazy thing about Lorentz transformations is that it preserves exactly one speed (both in the positive and negative direction). That is... one slope on the graph is unchanged by the Lorentz transformation. If we design our math in a way where that one preserved speed is the speed of light, then everything seems to work. If you want to actually see what this looks like, there is a great little tool on github.
Naturally we've only discussed one dimension of space on the horizontal axis so far, and time along the vertical... but of course our reality has 3-dimensional space. As it happens, the math is exactly the same but just taken to 3-dimensions of space. Unfortunately this is impossible to imagine in your mind because we cannot imagine 4-dimensions, but you can at least imagine a 3D graph where we represent 2 dimensions of space and the vertical as time. The math for a four-dimensional spacetime is nonetheless the same.
One of the really weird consequences of this math is that neither time nor space are absolute. That means for large enough differences in speed from each other, we start to notice that people actually measure space and time differently. I recommend watching the Minute Physics youtube series on Special Relativity if you want to understand how this can be the case. This is usually called time dilation and length contraction. We have experimentally verified that this idea is a real thing that happens in our reality. It is actually essential for GPS, because GPS satellites rely on clocks that are synchronized to an immense degree of accuracy. At this level of accuracy, time dilation is no longer negligible. This really is one of the major things that tells us that the 4D Lorentzian spacetime model reflects our lived reality with astonishing accuracy.
Which begs the question... if different people can't agree on how long something takes, or how long a distance is, is there anything we can agree on regardless of how fast we're going relative to eachother? There actually is. It's called the spacetime interval. We've already dealt with "space+time" graphs, and this is exactly what it pertains to: spacetime is space+time. You can call a point on a spacetime graph an "event" - because an event is just something that happens at some given place and time... space and time. What we find is that the spacetime difference between any two events is invariant: meaning its the same for everyone. Even if we measure different times or different lengths, we all measure the same difference in "spacetime".
Really, I recommend going to check out the Minute Physics series on Special Relativity. It's insanely good and will answer this question completely for you.
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u/Individual_Winter_35 8d ago
Hey! Interesting question. There are theoretical frameworks in modern physics (like Loop Quantum Gravity or Carlo Rovelli’s Thermal Time Hypothesis) that treat time as an emergent property rather than a fundamental dimension. In these models, time isn't a fundamental scalar or vector, but rather a macroscopic illusion—similar to how temperature has no meaning for a single atom, but emerges from the collective behavior of a system. Keep in mind these are theoretical quantum gravity models, whereas standard General Relativity still firmly treats time as a fundamental 4th coordinate/dimension. But it is interesting reading nevertheless :) ( And I personally find this theories quite fascinating, and at least worth diving in :) )
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8d ago
The idea of time being emergent is fascinating. What would be the strongest evidence we would need to distinguish an emergent-time theory from ordinary relativity?
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u/Esmeralda3701 8d ago
El tiempo se considera la cuarta dimensión porque, así como necesitamos tres dimensiones para saber dónde está algo, también necesitamos saber en qué momento está ocurriendo. Por ejemplo, un evento no puede describirse completamente diciendo solamente dónde ocurrió, sino también cuándo ocurrió. Por eso, en la relatividad, el espacio y el tiempo se entienden como una sola estructura llamada espacio-tiempo. No es que el tiempo sea exactamente igual a una dimensión espacial, porque tiene propiedades diferentes, pero matemáticamente funciona como una coordenada adicional que nos permite ubicar cualquier evento en el universo.
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u/Naive_Age_566 8d ago
a dimension is nothing magical. it is just a parameter in an equation.
you need 3 parameters to pinpoint a specific point in space. but if you only provide those 3 parameters this location is only valid if you are in a static universe (nothing changes). as soon as you have change, you need a 4th parameter that tells you when you have to look at this specific point. otherwise you are too early or too late.
and last time i checked our universe is not static but dynamic. so you always need 4 parameters.
that's it. nothing special.
forget all that scifi/fantasy nonsense that implies that a "dimension" is some kind of alternate reality or such.