Are virtual particles real or just math filler

In summary, virtual particles are just a convenient visual aid used in the math of Quantum Field Theory. There is no known physical test that could further answer the question of whether they are "real" or not.
  • #71
Thinking again about the math of virtual particles. They are supposed to come in pairs, but together they don't result in anything permanent. What kind of math would do that? What kind of math leads to complete annihilation or cancellation for two particles that both start at the same point at the same time and both end at the same different point at the same time? Presumably they are described by some sort of amplitude with a magnitude and phase. So I don't think you'd multiply the two amplitudes because even if you got the phases to cancel, you can't get the magnitude to equal zero. So I think we're talking about adding the amplitudes in superposition to try to get cancellation. But even here you can't have one being the complex conjugate of the other because that does not guarantee that the two vectors/amplitudes are 180° out of phase in order to cancel. Is there some way to make sure the two amplitudes are 180° out of phase even though they start at the same place at the same time and end at a different place at the same time?
 
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  • #72
friend said:
Thinking again about the math of virtual particles. They are supposed to come in pairs, but together they don't result in anything permanent. What kind of math would do that? What kind of math leads to complete annihilation or cancellation for two particles that both start at the same point at the same time and both end at the same different point at the same time?

Obviously math you do not understand.

Its simply terms in what's called a Dyson series:
https://en.wikipedia.org/wiki/Dyson_series

Your continual harping on about it will not change anything and simply leads to posts that repeat the same thing over and over.

Thanks
Bill
 
  • #73
Is there a paper explaining Hawking Radiation without succumbing to virtual particles similar to Jaffe's paper on the Casimir Effect? Unfortunately, Gravitation by MTW (the only GR textbook I have) doesn't cover hawking radiation and a cursory glance at google all mention pair-creation.

Or, if there is a specifcally good textbook treatment of it, I'd appreciate it.
 
  • #74
DelcrossA said:
Is there a paper explaining Hawking Radiation without succumbing to virtual particles similar to Jaffe's paper on the Casimir Effect?

Yes. Hawking's original paper.
 
  • #75
Vanadium 50 said:
Yes. Hawking's original paper.

Available from project Euclid:
 
  • #76
friend said:
Thinking again about the math of virtual particles. They are supposed to come in pairs, but together they don't result in anything permanent. What kind of math would do that? What kind of math leads to complete annihilation or cancellation for two particles that both start at the same point at the same time and both end at the same different point at the same time? ...

The transition amplitude for a particle to go from |x> to |x'> is
[tex] < x'|U(t)|x > \,\,\, = \,\,\,{\left( {\frac{m}{{2\pi \hbar it}}} \right)^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}}{e^{im{{(x' - x)}^2}/2\hbar t}}.[/tex]
I take this as true even for a virtual particle. The antiparticle is said to travel backwards in time between the same two points. So its transition amplitude would be
[tex] < x|U(t)|x' > \,\,\, = \,\,\,{\left( {\frac{{ - m}}{{2\pi \hbar it}}} \right)^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}}{e^{ - im{{(x - x')}^2}/2\hbar t}}[/tex]
by simply replacing t with -t. (Or take the complex conjugate). Yes, you can argue that these transitions are not measurable at these specific points since the |x> basis is a continuous spectrum. Granted! But bear with me because I'm trying to prove just that. I'm just considering the transition from some generic point to another generic point for a virtual particle pair that is said to go from some point to another.

The minus sign comes out of the square-root as the complex number i. So, we get
[tex] < x|U(t)|x' > \,\,\, = \,\,\,i{\left( {\frac{m}{{2\pi \hbar it}}} \right)^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}}{e^{ - im{{(x - x')}^2}/2\hbar t}}[/tex]
This is not a transition from one point by a particle and then back again by the antiparticle. The two transitions happen at the same time. And a real particle might interact with one or the other, and we can't say which. So we can consider these two virtual particles to be in superposition with each other. And then the expectation value for measuring these particles would be
[tex]| < x'|U(t)|x > {|^2}\,\, + \,\,\,| < x|U(t)|x' > {|^2}[/tex]
As seen from the above, the only difference between these terms is the complex number i in the antiparticle. After squaring it the only difference would be a minus sign, and the sum would be zero. This is what we are told, that they exist as wave functions but have zero expectation value of ever being measured. So you could fill space with as many virtual particle pairs as you like, even infinitely many, and it would not be noticeable by any observer.

Did I get my math right?
 
Last edited:
  • #77
friend said:
I take this as true even for a virtual particle.

Since virtual particles are not real why you assume that beats me.

Yes some your math is correct but you are atrociously mixing concepts.

friend said:
This is not a transition from one point by a particle and then back again by the antiparticle. The two transitions happen at the same time. And a real particle might interact with one or the other, and we can't say which. So we can consider these two virtual particles to be in superposition with each other. And then the expectation value for measuring these particles would be

That's utter nonsense.

You need to study an actual textbook.

Thanks
Bill
 
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  • #78
bhobba said:
Since virtual particles are not real why you assume that beats me.
If virtual particles exist at all, then they have a wave function that guides the way they transition from place to place.

I've heard professors say that space itself is made of virtual particles. And I've come to understand this in my own way. So if a particle propagates it must be through this sea of virtual particles (=space). If virtual particles have the same kind of transition amplitudes as those found in the propagator, then this provides a method of propagation through that sea. The propagation proceeds as follows: There already exists virtual particle pairs everywhere, including near a real particle. If a virtual particle-antiparticle pair appears near a real particle, then the real particle can annihilate with the antiparticle of the virtual pair. This leaves real the virtual particle that did not annihilate with its original partner. Thus the real particle use the transition amplitude of the virtual particle to jump from one position to the next. And now that the "real-ness" has been handed off to the virtual particle that did not annihilate, it is now subject to another jump by annihilating with yet another virtual pair, and so on through the path normally described with the path integral. If there is no expectation whatsoever of ever observing a virtual particle pair, then this is as good an interpretation of what's going on in the path integral as any other. If we accepted virtual particles to begin with, then maybe that would have led to the path integral formulation much sooner. Who knows what other properties can be described with them.

bhobba said:
That's utter nonsense.
This is a pretty safe comment. No speculation there. And you're not even saying I'm wrong.

bhobba said:
You need to study an actual textbook.
That's always a good idea. All in all, you've not said anything, though a bit snarky on your part.

I've looked, and I've not seen any books that go into a lot of detail about the math of virtual particles. It's disturbing that just about every professor in the classroom as well as the popular stage uses virtual particles to describe what's going on. But non of them go into depth into the math. Maybe that's what you're frustrated with.
 
  • #79
friend said:
If virtual particles exist at all, then they have a wave function that guides the way they transition from place to place.

Why are you starting with a falsehood? And that is not what a wave-function is.

friend said:
I've looked, and I've not seen any books that go into a lot of detail about the math of virtual particles. .

This does:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

friend said:
IIt's disturbing that just about every professor in the classroom

A number of professors post here and they don't.

This is my last post to you in this thread. Go away and study a textbook.

Thanks
Bill
 
  • #80
bhobba said:
Go away and study a textbook.
Honestly, I doubt I'm going to find what I'm looking for in a textbook, though it may help. I'm looking into foundational issues, why QM is the way it is? What logic justifies QM to begin with. However, most textbooks give a record of the history of its development. And the math they use seems to be used only because it works. But in my opinion, that does not explain why it is the way it is. It only describes that it is that way and what the implication of that are to application.
 
  • #82
friend said:
And I've come to understand this in my own way.
This is generally a bad thing to do without any guidance. You will come out on the other side with several misunderstandings, such as the ones you have displayed in this thread and in the rest of the quoted paragraph.

friend said:
I've looked, and I've not seen any books that go into a lot of detail about the math of virtual particles.
Then you have not looked very well. Essentially any introductory text on quantum field theory will cover this and the mathematics is rather straight forward given the required previous knowledge.

friend said:
It's disturbing that just about every professor in the classroom as well as the popular stage uses virtual particles to describe what's going on. But non of them go into depth into the math.
This is also wrong. You will see professionals use this kind of language in popular science and perhaps in courses which do not go very deep into the underlying quantum field theory aspects. Through popular science and survey courses you will learn about science, you will not learn science.

friend said:
And the math they use seems to be used only because it works.
This is the only reason to use anything in an empirical science. People who know QFT know what they are talking about when they mention virtual particles and they know how they enter into the mathematics. Just because you cannot figure it out on your own does not mean it is not already known.

With that said, I believe it is time to close this thread. The original question has been answered several times over.
 
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<h2>1. Are virtual particles real or just math filler?</h2><p>This is a commonly asked question in the field of quantum mechanics. The answer is that virtual particles are a mathematical concept used to explain certain phenomena, but they do not have a physical existence in the same way that particles we observe do. They are a useful tool for understanding the behavior of particles at a subatomic level.</p><h2>2. How do virtual particles differ from real particles?</h2><p>Virtual particles are different from real particles in several ways. Real particles have mass, spin, and can be directly observed and measured. Virtual particles, on the other hand, do not have mass or spin, and cannot be directly observed. They only exist as mathematical constructs to help explain certain phenomena.</p><h2>3. Can virtual particles be detected?</h2><p>No, virtual particles cannot be directly detected. This is because they do not exist in the same way that real particles do. They are a mathematical concept used to explain certain behaviors of particles at a quantum level. However, their effects can be indirectly observed through experiments and calculations.</p><h2>4. Do virtual particles violate the laws of physics?</h2><p>No, virtual particles do not violate the laws of physics. They are a part of the mathematical framework of quantum mechanics, which is a well-established and highly successful theory. While their behavior may seem strange and counterintuitive, they are consistent with the laws of physics and have been confirmed through various experiments.</p><h2>5. How do virtual particles contribute to the vacuum energy of space?</h2><p>Virtual particles are constantly popping in and out of existence in the vacuum of space. This contributes to the vacuum energy, also known as the zero-point energy. However, the total energy of the vacuum is still considered to be zero because the positive and negative energy contributions from virtual particles cancel each other out. This is known as the vacuum energy catastrophe problem.</p>

1. Are virtual particles real or just math filler?

This is a commonly asked question in the field of quantum mechanics. The answer is that virtual particles are a mathematical concept used to explain certain phenomena, but they do not have a physical existence in the same way that particles we observe do. They are a useful tool for understanding the behavior of particles at a subatomic level.

2. How do virtual particles differ from real particles?

Virtual particles are different from real particles in several ways. Real particles have mass, spin, and can be directly observed and measured. Virtual particles, on the other hand, do not have mass or spin, and cannot be directly observed. They only exist as mathematical constructs to help explain certain phenomena.

3. Can virtual particles be detected?

No, virtual particles cannot be directly detected. This is because they do not exist in the same way that real particles do. They are a mathematical concept used to explain certain behaviors of particles at a quantum level. However, their effects can be indirectly observed through experiments and calculations.

4. Do virtual particles violate the laws of physics?

No, virtual particles do not violate the laws of physics. They are a part of the mathematical framework of quantum mechanics, which is a well-established and highly successful theory. While their behavior may seem strange and counterintuitive, they are consistent with the laws of physics and have been confirmed through various experiments.

5. How do virtual particles contribute to the vacuum energy of space?

Virtual particles are constantly popping in and out of existence in the vacuum of space. This contributes to the vacuum energy, also known as the zero-point energy. However, the total energy of the vacuum is still considered to be zero because the positive and negative energy contributions from virtual particles cancel each other out. This is known as the vacuum energy catastrophe problem.

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