Do one-dimensional signals truly exist?

  • Thread starter giann_tee
  • Start date
  • Tags
    Signals
In summary, the conversation discusses the interactions in nature, using radio waves as an example. The radio signal is described as one-dimensional, but it is not perfect and can be affected by obstacles and direction. The concept of one-dimensional signals is further explored and related to Feynman's "QED" and the idea of interactions between particles. The conversation also touches on the concept of virtual particles and the role of particle pathways in interactions. Finally, the idea of objects announcing their presence in all directions is mentioned.
  • #1
giann_tee
133
1
I would like to know more about the interactions in nature. Here's an example based on the observation of how radio waves efficiently transmit music from the radio stations.

You can carry the radio with you around the city, and the signal never disappears. It seems as though the position and the orientation of the radio in space do not represent any particular filter for the incoming signals. Of course, some glitches are possible when you are driving in a bus. I conclude that the radio signal is "one-dimensional", because it does not possesses any directionality or "shape". It is just a series of oscillations in space that are affecting the receiving antenna wherever it is located.

The radio is not that perfect, however. You could find a special kind of directional antenna and point out the direction of the radio station emitter. You could find the obstacles that the radio waves cannot pass. Most of the time, none of this seems to represent a problem. Most of the time the radio signals seem to have a single dimension.

Mobile/cell phones operate at higher frequencies and their signals possesses much smaller "shape"; their wavelength is measured in centimeters. Their signal reception is more sensitive to direction and the obstacles make the signals bounce around. Also, there are many more antennas for mobile operators all around the neighborhood.

It seems that the classical radio creates the best illusion of having a one-dimensional signal. What does it mean to be one-dimensional?

Imagine a computer screen. It has many individual pixels in different colors. The light coming from each pixel to the eyes is keeping its direction in some relevant way, so that we can distinguish the individual pixels.

A grid of radio antennas cannot accomplish the same thing as pixels can. They are all fuzzy in the "eye" of a common radio receiver. It can only choose a single frequency and listen to whichever antenna or antennas are broadcasting at that frequency.

My question is the following. Are there any true one-dimensional signals in the nature?
 
Physics news on Phys.org
  • #2
I conclude that the radio signal is "one-dimensional", because it does not possesses any directionality or "shape". It is just a series of oscillations in space that are affecting the receiving antenna wherever it is located.
Electromagnetic waves (including your radio waves and mobile phone transmissions) have a direction. In a town, you usually get a lot of reflections - it does not matter where exactly you are and which orientation your radio antenna has, there is some signal from somewhere.

What does it mean to be one-dimensional?
I do not understand your description of your definition of one-dimensional signals.

A grid of radio antennas can be sensitive to the direction of the signal.
 
  • #3
I graduated physics 5 years ago, but only this summer I managed to read Feynman's "QED", popular book from the 1980s. I think that the book is remarkable - it gives meaning to all that I learned. It is as if I never really studied QM, because I did not hear about its foundation slowly and simply.

Feynman mentions little arrow, but he does not use the word "vector", and associates the propagation of a photon with the arrow. He conveniently uses the idea of a clock (the timing of the emission) that enables one to compute what will happen to the photon depending from the time (phase) of its arrival. He claims that the square of arrow length represents certain probability.

He introduces Feynman diagrams as simple diagrams that analyze simple, everyday events such as reflection of light from a mirror. In order to analyze events in full, events that are not entirely simple, we need to calculate all possible ways in which a Feynman diagram associated with an event can be drawn. A more complete calculation approaches the numbers that the experiments are giving us, he says. It is a more accurate calculation.

Some diagrams are mysterious, because they introduce at least theoretically, virtual particles, antiparticles, and even a special view on antiparticles as particles that are going backwards in time. Indeed, who would say that the virtual photons are not real, physical entities, given that there is something in nature that enters the final calculation, regardless of how you want to call it.

I liked the topic so much, that my heart made a promise to think about all these mysteries of nature once again.

I noticed that all the interactions suggested in this book and in other textbooks, seem to include two particle interactions with the binary outcome. I must warn you that I did not learn much about these things. I found the terminology without any mainstream literature. Usually, a particle can hit another particle, or not hit it at all. (Newton noted that the simultaneous collision of three particles does not exist, because it is unlikely.)

Particle pathways play the key role in the shape of the events, so all these interactions remind me of small "wires", given that one path is one such "wire" or a "string". The interactions on a fundamental level are always directional; they are never one-dimensional. A thump of a large loudspeaker is perhaps one-dimensional to a small particle standing right in front of it, but what the particle receives is after all, a series of collisions if in a gas, or deformations if in fluids and solids that effectively push and pull the particle once away and towards the speaker.

Two atoms are also directional emitters and receivers. One atom could do something and the particles that it emits would hit perhaps another atom or two, but the exchange would stop there. Atom would not announce its presence in any other way, not by emitting a single photon in certain direction.

On the other hand, complex, macroscopic events seem to offer more "light". Objects do announce their presence in all directions - perhaps by means of a local field that surrounds them. A huge number of particles are responsible for what we call an electrostatic field.

If an atom is to do the same and "exist" in some way for its neighbors, it needs to exchange a lot of particles. If an atom would emit just a single photon from time to time, that would require energy and would not form the kind of interaction that would tell its neighbors that it is one element in a row of many, in a solid crystal lattice. There are many small-scale events happening in and around atom than just a single photon emission. Rushing electrons are a reminder that there is more activity there going on in any given atom.

The orbital motion of electrons is coordinated by the exchange of particles that establish the electric field between the electrons and the protons in the atomic nucleus. This continuous exchange gives me the impression of a feedback system, where communication is quite lively, especially since we divided our scale of observation into the smallest, fine-grained time and space.

Obviously, it's a bit too much to calculate and say how an atom works. The particle's directionality or dimensionality and motion seems to defy further reduction. The continuous exchange, which I called the "feedback" underlies the basic structures of matter. At this point the dimensionality might change, because an electron can "tune-in" to the proton's presence and continue in any direction along its circular path.

This is just a view that I think could be really beneficial for further study. There is no end to this story in sight, so it is also about story telling, expansion of thoughts into the incalculable?
 
  • #4
One dimensional signals?

Are you talking about polarisation or perhaps longitudinal waves?
 
  • #5
mfb said:
Electromagnetic waves (including your radio waves and mobile phone transmissions) have a direction. In a town, you usually get a lot of reflections - it does not matter where exactly you are and which orientation your radio antenna has, there is some signal from somewhere.


I do not understand your description of your definition of one-dimensional signals.

A grid of radio antennas can be sensitive to the direction of the signal.

I also heard long time ago, about radio wave reflections. Within certain limits, it appears as though the ether is saturated with the radio stations battling for their share of the (market). A grid of emitters close to each other do not mean a thing to any ordinary radio receiver, I was about to say. They are not like pixels for a number of reasons. All this creates an illusion I'd say, worthy of question. The radio receiver is insensitive locally to the orientation and small-scale changes in position. Could this be the last case in the whole of nature on all scales and in all experiments in which the frequency, i.e. tuning to the frequency represents the only parameter you can set and find the source of emission?
 
  • #6
Studiot said:
One dimensional signals?

Are you talking about polarisation or perhaps longitudinal waves?

Longitudinal waves could be the right thing to imagine. Also, the frequency, as a single parameter required to set in order to catch the signal.
 
  • #7
What do you mean by "One Dimensional"?
The degree to which diffraction effects can be observed merely depends upon the wavelength involved but all the same basic rules apply for all EM waves.
 
  • #8
giann_tee said:
The radio receiver is insensitive locally to the orientation and small-scale changes in position.
This is just a technical issue - a radio receiver does not need this sensitivity to play music. You can build better receivers.
 
  • #9
giann_tee said:
I also heard long time ago, about radio wave reflections. Within certain limits, it appears as though the ether is saturated with the radio stations battling for their share of the (market). A grid of emitters close to each other do not mean a thing to any ordinary radio receiver, I was about to say. They are not like pixels for a number of reasons. All this creates an illusion I'd say, worthy of question. The radio receiver is insensitive locally to the orientation and small-scale changes in position. Could this be the last case in the whole of nature on all scales and in all experiments in which the frequency, i.e. tuning to the frequency represents the only parameter you can set and find the source of emission?

This is getting a bit 'new age'. Where are you trying to take this? What did your Physics course tell you about EM waves and time varying signals? From what you are writing here, you seem to want to change all that.
An array of light sensors will measure the varying illuminatiion over an image, formed by a lens. Light is a short wavelength so you can obtain a high resolution (diffraction limits apply). Those same diffraction rules tell you that, because of the much longer wavelengths involved (tens of millions of times longer) the spatial resolution that you can obtain with a set of radio frequency sensors is a lot less. Nothing magical - just a difference in geometry and scale.

I am sure you learned that EM waves are Transverse. Do you really want to ignore this and suggest that they are Longitudinal?
Look up some of the basic ways that radio and TV signals are used to carry information. There is loads of accessible stuff available via google about all this. Radio antenna are also described on many web pages, to various technical levels.

I think you will get further from reading than writing at this stage. Concentrate on the classical stuff about waves before you launch out on QM.
 
  • #10
sophiecentaur said:
What do you mean by "One Dimensional"?
The degree to which diffraction effects can be observed merely depends upon the wavelength involved but all the same basic rules apply for all EM waves.

This is good thinking, because you are talking about patterns. Wavelength is equivalent to frequency and that is just one parameter to tune. The wavelength or frequency range represents the window of opportunity to see the patterns.
 
  • #11
mfb said:
This is just a technical issue - a radio receiver does not need this sensitivity to play music. You can build better receivers.

I think that this is how government promised to find us back in the 1990s, to find that we possesses a TV set with an antenna, while we are refusing to pay the subscription. They had some kind of directional hand-held antenna to scan the neighborhood. I waited my whole life to find out how that works and in the end, I think that they just did the poll by phone and made some statistics from there.

BTW, aren't we more interested in omnidirectional antennas that do not depend on many emitters in the neighborhood, unlike the directional receiving antennas? The quality consideration could be reversed.
 
  • #12
sophiecentaur said:
This is getting a bit 'new age'. Where are you trying to take this? What did your Physics course tell you about EM waves and time varying signals? From what you are writing here, you seem to want to change all that.
An array of light sensors will measure the varying illuminatiion over an image, formed by a lens. Light is a short wavelength so you can obtain a high resolution (diffraction limits apply). Those same diffraction rules tell you that, because of the much longer wavelengths involved (tens of millions of times longer) the spatial resolution that you can obtain with a set of radio frequency sensors is a lot less. Nothing magical - just a difference in geometry and scale.

I am sure you learned that EM waves are Transverse. Do you really want to ignore this and suggest that they are Longitudinal?
Look up some of the basic ways that radio and TV signals are used to carry information. There is loads of accessible stuff available via google about all this. Radio antenna are also described on many web pages, to various technical levels.

I think you will get further from reading than writing at this stage. Concentrate on the classical stuff about waves before you launch out on QM.

Yes, this is slightly newer than Tesla who allegedly discovered the radio. You want to say that the gigantic wavelength causes the loss of spatial resolution. Perhaps this gives us the approximately one-dimensional signal, which really draws my attention to the question itself - is it really possible that in nature there isn't any one-dimensional signal anywhere?

If you can have an array of atoms, where each atom can be traced by specific frequency, then the matter and the universe contain much more information than it meets the eye. Perhaps this is in collision with some fundamental law that states that all atoms are indistinguishable. I am not sure what law that would be, but it is good to walk through this :-)
 
  • #13
giann_tee said:
I think that this is how government promised to find us back in the 1990s, to find that we possesses a TV set with an antenna, while we are refusing to pay the subscription. They had some kind of directional hand-held antenna to scan the neighborhood. I waited my whole life to find out how that works and in the end, I think that they just did the poll by phone and made some statistics from there.

BTW, aren't we more interested in omnidirectional antennas that do not depend on many emitters in the neighborhood, unlike the directional receiving antennas? The quality consideration could be reversed.
Are you referring to transmitting antennae here? I can't think of a single UHF broadcast transmitting antenna design that is omnidirectional. Any 'Main Station' will consist of a stack of dipoles at the very least, to direct the main beam downwards into the service area. UHF power is too hard to come by just to spray it up into the sky.

The TV detector vans used an interferometer and looked at the local oscillator radiation from standard receivers. Nothing at all to do with what you are on about. In fact - what are you on about? Could we just deal with one thing at a time, please?
 
  • #14
sophiecentaur said:
Are you referring to transmitting antennae here? I can't think of a single UHF broadcast transmitting antenna design that is omnidirectional. Any 'Main Station' will consist of a stack of dipoles at the very least, to direct the main beam downwards into the service area. UHF power is too hard to come by just to spray it up into the sky.

The TV detector vans used an interferometer and looked at the local oscillator radiation from standard receivers. Nothing at all to do with what you are on about. In fact - what are you on about? Could we just deal with one thing at a time, please?

OMG, please don't remind the government... Just kidding. Yes, please just one topic :-)
 
  • #15
giann_tee said:
Yes, this is slightly newer than Tesla who allegedly discovered the radio. You want to say that the gigantic wavelength causes the loss of spatial resolution. Perhaps this gives us the approximately one-dimensional signal, which really draws my attention to the question itself - is it really possible that in nature there isn't any one-dimensional signal anywhere?

If you can have an array of atoms, where each atom can be traced by specific frequency, then the matter and the universe contain much more information than it meets the eye. Perhaps this is in collision with some fundamental law that states that all atoms are indistinguishable. I am not sure what law that would be, but it is good to walk through this :-)

You still haven't explained what you mean by one of these
This is just nonsense. In any case, I always bail out when someone mentions Tesla. It usually spells trouble.
 
  • #16
sophiecentaur said:
Are you referring to transmitting antennae here? I can't think of a single UHF broadcast transmitting antenna design that is omnidirectional. Any 'Main Station' will consist of a stack of dipoles at the very least, to direct the main beam downwards into the service area. UHF power is too hard to come by just to spray it up into the sky.

The TV detector vans used an interferometer and looked at the local oscillator radiation from standard receivers. Nothing at all to do with what you are on about. In fact - what are you on about? Could we just deal with one thing at a time, please?

sophiecentaur said:
You still haven't explained what you mean by one of these
This is just nonsense. In any case, I always bail out when someone mentions Tesla. It usually spells trouble.

Well, you tuned your antennas and you know how it goes with the topic of Tesla... but, if you care to notice, after a few pages of my writing, this is really not about Tesla at all.

This is about math and geometry. For example, you can have a point-like source that oscillates, or the whole space can oscillate. If an excitable atom does not know about the direction of the photon that excites one of its electrons, you can have the same effect, almost. If you did have the full effect, the atoms could share the common information source and sync to it. This is reminiscent of laser pumping. If the atoms do not know about the direction of the pumping, within some limits, it is as if there is a one-dimensional source of pumping from the perspective of atoms. Its also about the degrees of freedom, symmetries... the basic aspects of existence. I need to go now, but I can share some more thoughts tomorrow...

Thanks for looking into this everybody!
 
  • #17
I think you are deeply misunderstanding how a radio works. The radio signal drops the farther you go from the radio tower. It's certainly not 1-dimensional. If you go too far away, all you will hear is static. In 3D, signals drop off as 1/r^2 (the inverse square law). Radio might drop off a little less quickly because it bounces off the ionosphere, so it's probably drops off somewhere between 1/r and 1/r^2, so it's probably effectively fractal dimension. In 1-D, the signal doesn't drop off with distance unless it is absorbed.
 
  • #18
giann_tee said:
.... The radio receiver is insensitive locally to the orientation and small-scale changes in position. ...

Only because of 2 things...

1) as some one else mentioned ... the signal is being bounced/reflected in every direction ... and
2) when relatively close to the transmitter, the signal strength is so strong

both of these combine to mainly nullify the effects of the receiver antenna orientation

its only when you start getting some distance from the transmitter that the effects become noticable and that the orientation of the antenna in the receiver becomes important

Dave
 
  • #19
giann_tee said:
...Wavelength is equivalent to frequency and that is just one parameter to tune. ...

no its not ! wavelength is inversely proportional to frequency
... As the frequency increases the wavelength decreases

As sophicentaur said ... you need to do some serious reading up and relearning about
E-M generation, propagation and reception

cheers
Dave
 
  • #20
It's reasonable to say wavelength is equivalent to frequency, since they both contain the same information for light.
 
  • #21
sure there's a 1-D signal. its called a "wire".
 
  • #22
Khashishi said:
I think you are deeply misunderstanding how a radio works. The radio signal drops the farther you go from the radio tower. It's certainly not 1-dimensional. If you go too far away, all you will hear is static. In 3D, signals drop off as 1/r^2 (the inverse square law). Radio might drop off a little less quickly because it bounces off the ionosphere, so it's probably drops off somewhere between 1/r and 1/r^2, so it's probably effectively fractal dimension. In 1-D, the signal doesn't drop off with distance unless it is absorbed.

Very interesting. Although it seems that the receiving antenna does not react to orientation and short changes of distance, larger changes of distance indicate that the emitter is a physical object of certain size and "luminosity" - like a star, but in radio wave frequency range.

The simulation of reflections and the modification of the inverse-square law is a must. Its simply beautiful to consider what would happen with real signals in space (atmosphere). I need to think about how this is done.

Now I realized that a single atomic interaction with a single photon has a binary outcome AND it reminds me more of a 1-D signal, but its just a tiny moment in time. Its just that one "ray" and nothing more.
 
  • #23
davenn said:
Only because of 2 things...

1) as some one else mentioned ... the signal is being bounced/reflected in every direction ... and
2) when relatively close to the transmitter, the signal strength is so strong

both of these combine to mainly nullify the effects of the receiver antenna orientation

its only when you start getting some distance from the transmitter that the effects become noticable and that the orientation of the antenna in the receiver becomes important

Dave


This is something new. You say that the orientation of a lousy iron antenna does not matter within some limits, precisely because of the reflections?
 
  • #24
davenn said:
no its not ! wavelength is inversely proportional to frequency
... As the frequency increases the wavelength decreases

As sophicentaur said ... you need to do some serious reading up and relearning about
E-M generation, propagation and reception

cheers
Dave

Yes yes, I know about the frequency. What would you suggest about the EM wave reception, what's the punchline? I am thinking about some electrons in the metal being displaced in different directions as various EM waves pass through the metal. The motion of electrons along a wire as an induced alternating current is then amplified if necessary. When does the selection according to frequency occur?
 
  • #25
giann_tee said:
Yes yes, I know about the frequency. What would you suggest about the EM wave reception, what's the punchline? I am thinking about some electrons in the metal being displaced in different directions as various EM waves pass through the metal. The motion of electrons along a wire as an induced alternating current is then amplified if necessary. When does the selection according to frequency occur?

Did you think of googling 'simple radio receivers' or something like it?
You appear to want to be told everything about everything at once yet I wonder just how much reading around you are doing? This scattergun approach puts you in danger of learning nothing of significance.
 
  • #26
chill_factor said:
sure there's a 1-D signal. its called a "wire".

Yes! It reminds me of a network, internet. I have a friend who wrote about the Universal Field, an exploration in philosophy. She talked to the physicists and interviewed them. I had to restrain myself from being overly informative. The universality is accomplished by lifting different notions of field to the mental plane and encompassing them there. So, if we continue to behave like gentlemen, we may say that the universal field is in our minds and accept that it is okay as such.

The wire is interesting again, because the electrons are slowly traveling through the wire. But, they can be pushed out the other end very quickly. The field is transported, communicated to the other end.

For a single signal the shape of the wire does not matter. It leaves the illusion of perfect transport. A high-frequency signal would react to the shape of the wire due to self-induction.
 
  • #27
sophiecentaur said:
Did you think of googling 'simple radio receivers' or something like it?
You appear to want to be told everything about everything at once yet I wonder just how much reading around you are doing? This scattergun approach puts you in danger of learning nothing of significance.

You are correct, there is a danger. I have an organizational problem and I think that I googled and read everything before, so I should probably change the routine this time.
 
  • #28
giann_tee said:
Yes! It reminds me of a network, internet. I have a friend who wrote about the Universal Field, an exploration in philosophy. She talked to the physicists and interviewed them. I had to restrain myself from being overly informative. The universality is accomplished by lifting different notions of field to the mental plane and encompassing them there. So, if we continue to behave like gentlemen, we may say that the universal field is in our minds and accept that it is okay as such.

The wire is interesting again, because the electrons are slowly traveling through the wire. But, they can be pushed out the other end very quickly. The field is transported, communicated to the other end.

For a single signal the shape of the wire does not matter. It leaves the illusion of perfect transport. A high-frequency signal would react to the shape of the wire due to self-induction.

Nonsense. This speculation and wandering rambling interspersed with technical terms seems to be not appropriate here. This is a forum for science learning. Furthermore, since you claim to already "I googled and read everything before" in your most recent post, why bother pretending to be inquisitive?
 
  • #29
Bobbywhy said:
Nonsense. This speculation and wandering rambling interspersed with technical terms seems to be not appropriate here. This is a forum for science learning. Furthermore, since you claim to already "I googled and read everything before" in your most recent post, why bother pretending to be inquisitive?


I doubt that anything is appropriate for this forum, including conversation. As you can see, we have some answers in between. Maybe you can fill in where my PhD was incomplete, please?
 
  • #30
giann_tee said:
I doubt that anything is appropriate for this forum, including conversation. As you can see, we have some answers in between. Maybe you can fill in where my PhD was incomplete, please?

Your "organizational problem" seems to be much more severe than you realize. Everyone in this thread is frustrated by your inability to address one topic at a time and the rambling nature of your responses including some discussions that do not seem to be grounded in science but just a rambling collection of technical terms that don't hang together.

I realize this sounds harsh, and I do not wish to be rude, but you don't seem to "get" why it is that folks here are having difficulty with your "discussions"/"conversations"

See if you can pick a single topic and address it based on known science and perhaps we can go from there.
 
  • #31
giann_tee said:
I doubt that anything is appropriate for this forum, including conversation. As you can see, we have some answers in between. Maybe you can fill in where my PhD was incomplete, please?

Best not go there, I think. I could be an eminent Surgeon but what I might write about Keynsian Economics could be total rubbish. What one writes here is one's only relevant qualification and, on this topic, your output is very fanciful and certainly not Physics as we know it.
 
  • #32
sophiecentaur said:
Best not go there, I think. I could be an eminent Surgeon but what I might write about Keynsian Economics could be total rubbish. What one writes here is one's only relevant qualification and, on this topic, your output is very fanciful and certainly not Physics as we know it.

I think that it is a generous to be rich in contents, animate people and create something lasting. This is the kind of moderation I would do on my thread. There are many intuitive aspects of the topic, equivalences between abstract ideas, some of which possesses material links that can be qualified with further knowledge. Posts often tend to become one-liners. No problem there, but this constant forum-wide bickering about doing homework should stop, unless you want your purpose in life to be AUTOMATION in place of intelligent response.
 
  • #33
giann_tee said:
I think that it is a generous to be rich in contents, animate people and create something lasting. This is the kind of moderation I would do on my thread. There are many intuitive aspects of the topic, equivalences between abstract ideas, some of which possesses material links that can be qualified with further knowledge. Posts often tend to become one-liners. No problem there, but this constant forum-wide bickering about doing homework should stop, unless you want your purpose in life to be AUTOMATION in place of intelligent response.
I'm afraid that goes with the territory. If you want to have an informed opinion about a topic in Physics and to be sure you are understood then you need the knowledge and to use the accepted vocabulary. PF is pretty happy with the way it is, thank you. There are many other, less rigorous platforms where you can voice your opinions. I don't think you are likely to make this forum change to fit what you seem to require.
 
  • #34
This thread has changed directions so many times, even a GPS can't bring it back. It is done.

Zz.
 

1. What is a one-dimensional signal?

A one-dimensional signal is a type of signal that is represented by a single variable, typically time. It can be thought of as a sequence of values that are dependent on a single independent variable.

2. How is a one-dimensional signal different from a two-dimensional signal?

A one-dimensional signal only has one independent variable, while a two-dimensional signal has two independent variables. This means that a one-dimensional signal can only be represented on a one-dimensional graph, while a two-dimensional signal can be represented on a two-dimensional graph.

3. Can a one-dimensional signal exist in the physical world?

Yes, one-dimensional signals can exist in the physical world. They can represent various phenomena such as sound waves, electrical signals, and even the movement of objects along a single axis.

4. Are one-dimensional signals limited in their complexity compared to higher-dimensional signals?

No, one-dimensional signals can be just as complex as higher-dimensional signals. The complexity of a signal depends on the number of variables and the range of values that it can take, rather than the dimensionality.

5. What are some applications of one-dimensional signals?

One-dimensional signals have a wide range of applications, including audio and speech processing, signal filtering and analysis, and time series analysis in fields such as finance and economics. They are also used in various engineering and scientific disciplines for data representation and analysis.

Similar threads

  • Other Physics Topics
2
Replies
39
Views
3K
  • Other Physics Topics
Replies
5
Views
2K
Replies
14
Views
2K
  • Biology and Medical
Replies
7
Views
987
  • Astronomy and Astrophysics
Replies
14
Views
2K
  • Astronomy and Astrophysics
Replies
27
Views
3K
Replies
14
Views
2K
  • Electrical Engineering
Replies
1
Views
1K
Replies
68
Views
3K
  • Electrical Engineering
Replies
28
Views
3K
Back
Top