This discussion reminds me of time reversed waves, which are very real and have practical applications.

In general, the waves from a splash of water propagate out from the focal point. But the wave can also move in reverse, formed at the edge and moving back towards the focal point, and create a splash out of nothing at the convergence point from the wave energy.


http://en.wikipedia.org/wiki/Time_reversal_signal_processing

"Time Reversal Signal Processing is a technique for focusing waves. A Time Reversal Mirror (TRM) is a device that can focus waves using the time reversal method. TRMs are also known as time reversal mirror arrays, as they are usually arrays of transducers, but they do not have to be arrays.


http://www.usna.edu/Users/math/rmm/Papers/fink2.pdf

Article: Time Reversed Acoustics, Scientific American, November 1999

 

Not necessarily. Have you ever wondered by the NASA guy says, "T minus 1 hour"? It's because the reference for the measurement, T, is at a point in the future, namely main engine ignition.
A reference time in the future is often used when planning or preparing for some event.
Even in a physical measurement, we may take measurements prior to the start of the event we are measuring -- for instance, at t=0s we discharge a powerful lamp and record the response of various detectors. We would often be taking measurements before this to establish a baseline and those measurements are occuring at negative time relative to the reference.
Why?

Well, I am afraid we are confusing discrete time values T with time PERIODS (difference t=T2-T1). And - I think - only these differences matter.
Coming back again to the original question (negative frequencies) we are counting events in a certain time PERIOD. And, of course, the difference between T2=-10 sec and T1=-15 sec is t=+5sec.
I think, in the above examples the reference point is arbitrarily shifted - however, the running time goes into one direction only and each measurement period, therefore, must be positive. And each counting of events within this period also is positive.

 

I thing the point about "reference point" is an important one.
On my oscilloscope I can dial a negative time and be able to examine events that happen prior to the reference point.
In Ham radio we tune in to SSB (single side band) RF transmissions. We can select the positive frequencies, upper side band, or negative frequencies, lower side band.

* Oscilloscope: For my opinion, this is nothing else than an artificial shift of the reference point.
Does this "dial procedure" really proof that there are negative time periods?
* Ham radio: Do you claim that the lower side band is at a negative frequency?

 

The more philosophical among us may enjoy this interview with Keith Devlin.

The point is that mathematics is a lens into the human mind. We choose things like always-positive time and energy (we demand that heat flows, not cold) to make the physics and math look more sensible to our human brains. These conventions don't constrain the real world, they just help us see the elegance of it.

 

wayneh - yes, I agree. Thanks for providing the link.
The definition/assumption (?) that the time does flow into one direction only (and a certain time period, therefore, must always be positive) helps to "make the physics and math look more sensible to our human brains".

 

So we fall into the trap that it is real only if our humans brains can make sense of it.

 

* Oscilloscope: For my opinion, this is nothing else than an artificial shift of the reference point.
Does this "dial procedure" really proof that there are negative time periods?
* Ham radio: Do you claim that the lower side band is at a negative frequency?

Consider a baseband frequency that is then frequency shift keyed using IQ modulation. For example, I have a center frequency of 1MHz and I want to shift the signal up 10kHz for a 1 and down 10kHz for a 0. Using IQ modulation, my baseband signal (i.e., where 0Hz is DC) is then simply either a sinusoid at +10kHz or at -10kHz. Further, if I modulate two signals (say the stereo channel components) and park one at +10kHz and the other at -10kHz in the baseband signal then when I IQ modulate them onto the carrier using I will have different upper and lower sidelobes in the signal about the carrier.

 

...
If two equal sized gears are meshed and one is turning at 4rpm then how is that any more or less real than the other gear that is turning at -4rpm?

They are both turning at a real (positive) 4 RPM, just in different directions.

... Obviously many things are defined as negative and positive. For example, how about an electron charge and a positron (or proton) charge. What other words could you use besides positive and negative for the charge of those?

OK, that's a better example, but is it really proof that negative magnitude exists? Equate that to a diaphragm with water pressure, you can call one side + and one side -, but what you REALLY have are two positive pressures >=0, and you just call the smaller pressure "negative" in comparison to the larger.

Maybe "complimentary" is a better term? It means "in the other direction" and does not necessarily imply "less than zero".

Similar to other arguments, ie; "T minus 5 minutes". It's not negative, it is a real value along a positive scale, and only negative in reference to a larger real value.

So we fall into the trap that it is real only if our humans brains can make sense of it.

Excellent point! Which is why we have so many "negative" values that humans like and accept, it's a nicety for our brains and our math nerds even though there's not a lot of evidence for REAL negative things.

 

So we fall into the trap that it is real only if our humans brains can make sense of it.

Common, haven't you guys seen the movie? In FREQUENCY. That is what the whole thing is about, negative frequency.

http://www.imdb.com/title/tt0186151/

Cheers
gT

 

Well my bank account is negative right now. Gee, I wish it weren't so real.

 

I assure that everyone has negative time, life can't completely smooth all the time.

 

..........................

Originally Posted by Crutschow
... Obviously many things are defined as negative and positive. For example, how about an electron charge and a positron (or proton) charge. What other words could you use besides positive and negative for the charge of those?

OK, that's a better example, but is it really proof that negative magnitude exists? Equate that to a diaphragm with water pressure, you can call one side + and one side -, but what you REALLY have are two positive pressures >=0, and you just call the smaller pressure "negative" in comparison to the larger.

Maybe "complimentary" is a better term? It means "in the other direction" and does not necessarily imply "less than zero".

.........................................

The positive charge of a proton and the negative charge of an electon are definitely two distinct charges. But I would say that is not related to the concept of "less than zero magnitude" which is not the usual definition of negative. So I think we are splitting hairs about what is really a mathematical function that is useful in the description of many and varied concepts, whether physical realizable or not.

So I see no reason to mess with the mathematical definition of negative as it's meaning is normally well understood by most and is unambiguous.

 

As has been pointed out a few times already, ALL mathematical concepts are abstract and they only have meaning in the real world to the degree that we attach that meaning.

The_RB is insisting on a single, inflexible meaning for a negative value and that being in the sense of an arithmetic number line in which any value that is to the left of another number is "less than" that number. So -1000 is "less than" +5.

But notice what has been done here. All we have is one particular situation in which we have assigned the interpretation of positive and negative values in relation to the abstract concept of one number being "less than" another number. It's a perfectly fine and useful interpretation and is applicable to many real world instances. But there are many other real world instances in which it isn't very useful and for which a different interpretation is more appropriate.

But what The_RB seems to be saying is, "Nope. Sorry. I'm only comfortable with the first interpretation of negative numbers I was ever taught and therefore anything that doesn't match that can't be "real". Period."

 

Do we have any negative frequency?
...........
...so is it just a theortical concept only?

At this point of the discussion (which now has revealed some philosophical aspects about time and negative values in general) I like to come back to the original question.

Revathy Nair - therefore, I like to ask you:
Have you derived a satisfying answer from all the various contributions?
Could you develop an opinion to the question if negative frequencies do exist in the real world, rather than being a "theoretical concept" only?
I think it is very important for young engineers to know and to understand the difference between
(a) real physical quantities which can be verified by measurements and
(b) some other parameters/variables which have been introduced because it makes sense to use them and/or because they are a powerful tool to analyze electronic circuits, although they have no physical relevance.

 

And to also reflect on the related question: If positive values seem to have physical relevance but negative values don't (and if negative values can be treated the same as positive values when "doing the math"), then is it a matter of positive values having physical meaning and negative values only being a useful mathematical construct, or does the notion that positive values might not have the "physical meaning" that we automatically assumed they did bear some closer scrutiny? Perhaps they are also really just a useful mathematical construct and don't have any more "physical relevance" than the negative values did -- that the "physical relevance" we automatically ascribed to them is, at best, indirect.

 

Do complex numbers exist?
Is the square root of negative one simply a theoretical construct and not real?
Are there more than four dimensions?

We have fallen into the trap that if we cannot wrap our brains around it, it cannot be real.

 

Do complex numbers exist?
Is the square root of negative one simply a theoretical construct and not real?
..................

It's unfortunate the "i" part of a complex number is called imaginary. It implies that is something less real about it as compared to the "real" part when, in reality, they are both equally real in the mathematical world (and that is what we are talking about anytime we discuss numbers). Complex numbers allow us to solve problems in the real world that could not otherwise be readily solved.

 

Well my bank account is negative right now. Gee, I wish it weren't so real.

Sure, if you think the negative dollars are "real", go and withdraw them from your bank account, and post a photo.

 

Negative dollars are real - eventually. Ask the bank if they are counting them as real dollars owed to them. I think I know the answer.

I see most of the discussion basically as a philosophical difference of opinion. No where has any facts been presented to change my mind.

Any dimension is measured by magnitude and direction. Just because we are not used to seeing all dimensions with both attributes, does not make them any less real. Just like we are not used to perceiving more than four dimensions, does not mean that there does not exist more.

 

No where has any facts been presented to change my mind.

Change from what? This is your first post on this thread, unless I just can't find another. Apologies if that's the case.

The dark energy hypothesis is a good example of how new observations can shake our brains. We would normally think of pressures being only positive. "Vacuum", we think, is merely the absence of pressure. But dark energy is thought to be a source of negative pressure driving expansion of the universe. In other words, a truly negative pressure. At least "negative" compared to our prior understanding.