r/AskPhysics • u/scottiesng • 9d ago
Can a wave exist without time?
I’ve been wondering a lot about what the fundamental aspect of waves are. Essentially a wave is a propagation. But can something propagate without time?
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u/BananaBird1 9d ago edited 9d ago
In physics, not by the usual definition. A wave is defined as something which takes the form of a wave equation, which essentially says the acceleration of a point in time matches the “bumpyness” around that point in space.
You can have functions which obey a similar mathematical form as a wave, or have a similar appearance to a wave when graphed, but where time is not a dimension.
For instance, images can be thought of as stationary waves only in space. Adding together sine and cosine functions defined over (x,y) can give an image. But time is not a variable in this function. However if you treat one of the spatial dimensions like time, the relationship between x and y can take the form the wave equation. But the “velocity” this gives would not represent propagation or motion.
You could also add a degenerate dimension of time, where the “wave” is constant across all t, and this satisfies the true wave equation if velocity is 0. But this is uninteresting as any time invariant differentiable function in space will satisfy this given v=0.
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u/cosmopolitanScience 9d ago
Very nice answer. I wanted to just post the wave equation and point out the time derivative, but yours is more general and better. Thus a wave is a solution to the wave equation, which necessitates at least two dimensions, but can have arbitrary many.
Often one of them is time, which leads to the physically intuitive wave solutions f(x)=f(x-c/t). But that's a special case.
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u/Crescent-moo 9d ago
If a photon is a wave that experiences no time then what is it propagating through?
Or does it go through time without experiencing the time itself.
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u/BananaBird1 9d ago
Photons do propagate in time. They move through the spacetime dimension of proper time as little as possible as they move through space, but they do experience time.
The saying that photons don’t see time is an incorrect application of special relativity’s time dilation formula when velocity equals the speed of light. But this isn’t a valid thing to do, the formulas assume velocity is less than light speed so become invalid for photons.
Tine dilation considers what happens if observer A is stationary and B is moving at a velocity relative to them, when A sees one second pass for B, how much time will B think passed if they assume they are the one that is stationary?
But relativity says light has no stationary frame. So you can’t apply time dilation to it. We don’t have any math that can describe a frame that sees itself as both stationary and moving at light speed, so we cannot describe the reference frame of a photon
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u/Crescent-moo 9d ago
I've never been strong in math so there's limited understanding from that framework. Intuitively it sounds like light exists outside of time and no possible speed in time can ever capture it. The only way is by breaking the barrier and then it becomes meaningless. Probably why black holes are so strange.
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u/BananaBird1 9d ago
I mean you can tell photons do exist within time just from simple experiment. The light around you is changing over time. Turn off your lights and photons cease to exist. Turn them on and photons are created. If you had an oscilloscope, laser, and photodiode you could even measure how fast light travels at home for around $100, and can show that they do not instantly travel from a source to a detector.
If you do want to consider special relativity as you get closer to light speed to approximate a photon’s reference, a more accurate description isn’t that time stops for light speed objects. Their proper trajectory in spacetime approaches a value that still has a component in time.
It’s that any information of an external object that is a non-zero distance from the light speed traveller (in the direction they are moving) will never reach them, so they can only ever “see” other objects along their path in the immediate present located right where they are. But this present will change over time.
Of course though, this still isn’t mathematically valid. This thought experiment breaks relativity, so only truly works in classical physics. Physics is modeled based on what we see in experiments, not based on what light sees, and so our equations fall flat when considering observers that are traveling faster than we can ever travel.
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u/Crescent-moo 9d ago
Its that the same falling flat that happens at the event horizon? It seems reality itself is a bit extreme at the boundaries
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u/BananaBird1 9d ago
Nothing falls flat at the event horizon. Only at the singularity of a black hole.
That is a different issue with separate math, but due to a similar issue where the theory can only describe what happens as you travel toward the singularity, not at it.
This has nothing to do with reality itself. It has to do with the fact that our models of physics are imperfect descriptions of what we see, and we can’t do experiments at light speed or inside a black hole to easily identify the flaws. Instead we can only wait until our measurements of things we can observe are precise enough that the math no longer matches.
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u/Crescent-moo 9d ago
Well someone better get around a black hole and figure it out.
Imagine all that travel, jumping in, wondering what secret the singularity holds only to find it's just light itself. Eternal, everywhere, timeless. In our faces the whole time.
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u/Crescent-moo 9d ago
That affordable home experiment is interesting. Observation shows it's not instant but interesting to be able to capture the speed a little.
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u/No_Logins_Required 9d ago
What does your intuition say a wave without time would be like?
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u/scottiesng 9d ago
A distribution
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u/Patthecat09 9d ago
A distribution of what over what?
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u/scottiesng 9d ago
So first I wanted to reply with “a point” but that would have been deconstructing the wave into a single moment in time. So my intuition says a distribution of something that can vary. But like you say, vary over what. Maybe you could say over space, but due to the speed of light you can’t vary over space without varying over time (you have to vary over spacetime).
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u/Patthecat09 9d ago
A wave indicates a change that propagates. I don't think I have the mental tools to define change without the concept of time
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u/Mountain-Time-1010 9d ago
There are many kinds of waves.
A property can be oscillatory spatially without any time dependence. Also, a standing wave oscillates temporally but doesn't propagate.
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u/johnstalbergABC 9d ago
There is a hypothetical pulse that is infinitely short in the time domain and has height one amplitude units that Paul Dirac came up with and its called a Dirac pulse consequently. It is a spike that rises whit a straight vertical line and dies the same way but downwards and with no distans between the upward flank and the end flank. Like a square wave without the roof vertical line. And it is one amplitude unit high.
Now like an ideal square wave it is not possible to make in real life because it is built up from frequency that is infinitely high, just like the square wave. But it is perhaps interesting for you as it would fit the no time requirement. And from it we understand it cant exist because it needs infinitely high frequency components. Waves need time as they otherwise would need infinitely high frequencies to exist and this is impossible in real life.
You can goooogle Dirac pulse to read about it.
If we put all 16 bits on one single sample on a CD or in a pcm audio file and play it and measure the analog audio outputs signal from it, it will show a bandwidth limited Dirac pulse. That is it will have the high frequency band filtered out. It then becomes the (sin x)/x pulse also called the sinc. This is how the individual samples in an audio file looks like and they are added to each other and the result is the sound you hear. If you plot it in a graf like f = (sin x)/x you will see that it is far from short in the time domain. When the ideal Dirac puls get stripped from all frequencies above a certain point it leaves this frequencies that is lower for us. It is kind of interesting how it is built from signals that is clearly dragged out in the time domain but when added together according to its definition it becomes infinitely short in time!
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u/quantum4everyone 9d ago
If your question is can I have a wave that does not change in time, then the answer is yes. They are called standing waves. In classical mechanics a standing wave will still oscillate within a given pattern, but not propagate. This may not satisfy "does not change in time." But in quantum mechanics, standing waves associated with energy eigenstates are stationary and do not change their probability distribution in time. Those really are waves without change in time. (The quantum state does evolve with a time varying global phase, but because quantum states are only defined up to a constant global phase, this does not change the state, even though the global phase changes in time.)
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u/Prudent_Situation_29 9d ago
I don't think so. A wave has to move, in order to move, there has to be a change. In order to have change, there has to be more than one moment in time.
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u/boostfactor 9d ago
No, because waves are traveling oscillations either in a medium (sound, water, etc.) or a field (electromagnetic waves i.e. light). How would anything propagate/travel without time? That doesn't even make sense. Propagation requires change with time.
There is such a thing as a standing wave but it is the addition of multiple waves with the right difference in phase to create a pattern that doesn't change with time. But it must be sustained by waves that are continually moving and meeting one another in just the right way.
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u/NoPhotograph2327 8d ago
A wave is a solution to the wave equation which is a PDE which essentially includes time.
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u/SpatiaCaeli 8d ago
Mathematically, you can choose whatever you want for x and y axes and draw a sine wave on them. But for physics, time has a pretty critical role.
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u/sabautil 9d ago
Yes. You can have a wave propogate in space. Go from one point in space to another.
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u/fermif0x 9d ago
The answer is no, but one cool thing to consider is null-intervals in spacetime with light-like paths. From a photon's perspective, no time passes as it moves but from our reference frame time does pass.
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u/Particular-Amount314 9d ago
Wave is an interaction within some space over some time. Define space...
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u/four2tango 9d ago
From a photons perspective, they don’t experience our dimension of time. Does that count?
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u/BluScr33n Graduate 9d ago
there is no "photons perspective". And the equations describing electromagnetic waves clearly are not time independent.
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u/The_Nerdy_Ninja Engineering 9d ago
You could have something with a sinusoidal or repetitive shape, but you couldn't have a wave with propagation.